CONTRAST SENSITIZATION: FUNCTION, THEORY, AND …

CONTRAST SENSITIZATION: FUNCTION, THEORY, AND

MECHANISM OF A NOVEL RETINAL COMPUTATION

A DISSERTATION

SUBMITTED TO THE PROGRAM IN NEUROSCIENCE

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

David B. Kastner

June 2013

http://creativecommons.org/licenses/by-nc/3.0/us/

This dissertation is online at: http://purl.stanford.edu/pt514dd8480

© 2013 by David Barak Kastner. All Rights Reserved.

Re-distributed by Stanford University under license with the author.

This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.

ii



http://purl.stanford.edu/pt514dd8480

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Stephen Baccus, Primary Adviser


Denis Baylor


Richard Tsien


Brian Wandell

Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.

iii

iv

Abstract

Adaptation provides a ubiquitous strategy for neural circuits to encode their inputs

using their limited dynamic range within the variety of sensory environments that

they encounter. However, because of the inherent timescale necessary to optimize the

response properties of a cell to its environment, any form of adaptive plasticity can

cause a neuron to fail to encode the stimulus when the environment changes. Many

ganglion cells, the output neurons of the retina, adapt so as to lower their sensitivity

in an environment of high contrast, but if the contrast subsequently decreases the cell

will fall below threshold and fail to signal. I have found a distinct form of plasticity

within the retina that acts in coordination with the process of adaptation. Cells using

this new form of plasticity elevate their sensitivity after a transition to low contrast.

This process, called sensitization, occurs in retinas from multiple species. Multielec-

trode recordings from sensitizing and adapting cells indicate that both populations

encode the same visual signals. The complementary action of the two populations

helps the retina encode its input over a broader range of signals and environmen-

tal changes, with one population continuing to respond when the other fails. The

threshold placement of these two cell types further enhances their coordination be-

cause sensitizing cells maintain lower thresholds, while adapting cells maintain higher

thresholds. Using a theoretical model, I was able to show that this behavior maxi-

mized the amount of information that the two populations can provide about their

input. I have further studied the spatiotemporal region that controlled the sensitivity

of a cell–the adaptive field. Just as retinal circuitry uses excitation and inhibition

to form biphasic center-surround receptive fields, the retina can also use adaptation

and sensitization to form biphasic adaptive fields in both the spatial and temporal

v

domains. Since visual statistics are correlated across time and space, center-surround

biphasic receptive fields more e�ciently encode the input by subtracting a prediction

of the stimulus so as to just encode the deviation from that prediction. Biphasic adap-

tive fields appear to perform an opposite function, transmitting a prediction of the

stimulus at the transition of a stimulus environment to weaker signals. This assists in

the encoding of an uncertain environment by storing features of a predictable input.

A model indicates that sensitization within the adaptive field can be produced by

adapting inhibition, a form of plasticity whose function was previously unknown. Us-

ing pharmacology, I confirmed this prediction, showing that GABAergic inhibition is

necessary for sensitization. Using simultaneous intracellular recording from inhibitory

amacrine cells and multielectrode recording from ganglion cells, I show that trans-

mission from a single amacrine cell is su�cient to cause sensitization. Using a novel

approach to analyze a circuit, I quantitatively describe the changes in amacrine cell

transmission that underlie sensitization thus elucidating how the retina performs this

sophisticated computation.

vi

Acknowledgements

I have had the good fortune to work with many wonderful people during my graduate

studies. First and foremost among them is my advisor Stephen Baccus. Steve has

been a spectacular mentor. No issue was too small for him to provide suggestions

and advice. Whatever rigor and quality my work has is largely due to my interaction

with Steve. The members of the Baccus lab have provided me with wonderful col-

leagues over the years. I would like to specifically acknowledge Pablo Jadzinsky for

his companionship and advice, and Mike Menz for his unceasing helpfulness.

I would like to thank all of the members of my committee: Denis Baylor, Brian

Wandell, and Richard Tsien. Each of them was always willing to take time out of

their busy schedules to discuss my work. I benefitted greatly from the interaction.

The Stanford neuroscience community has provided a very rich environment for my

development. I would like to thank John Huguenard for running a wonderful graduate

program. I would like to thank Tom Clandinin for his teaching me to competently

present science. I would like to thank Greg Barsh, Seung Kim, PJ Utz, and the

Stanford MSTP for providing a fantastic educational environment. I would also like

to thank Jay McClelland for establishing and running the Center for Mind Brain and

Computation. The MBC has not only provided me with funding, but it has created a

vibrant interdisciplinary community in which I have been glad to participate. Daniel

Fisher and Tatyana Sharpee co-mentored me during di↵erent points of my MBC

training. I gained broadening insight from both of them on di↵erent aspects of my

work. Andrew Huberman, Saskia de Vries, Georgia Panagiotakos, and Andrew Olson

were very considerate and helpful with technical assistance.

Many people have allowed me to focus on science without having to worry too

vii

much about ancillary things. Ross Colvin, Katie Johnson, Lorie Langdon, Moira

Louca, and Laura Hope have all been incredibly helpful. I would not have been able

to accomplish all that I have without their assistance.

Many people contributed to my being able to come to Stanford. First and fore-

most I have to thank my parents, Beverly and Michael Kastner. They provided me

with every opportunity I needed to succeed, I could not have asked for better par-

ents. I would like to thank my brother, Eitan Kastner, for always being available for

useful and interesting conversations. I must thank my sisters, Jennifer Newman and

Ayelet Hoenig, who always respected and supported my pursuits. I am thrilled to

acknowledge and thank my grandmother, Francis Kastner. I greatly appreciated her

unceasing and, often times, unwarranted support.

I have had many excellent teachers, formal and informal, over the years. Joan

Haahr, Bruce Hrnjez, Carl Feit, Jeremy Wieder, among others at Yeshiva University,

provided me with excellent intellectual training. I would particularly like to acknowl-

edge Joshua Gottlieb, who introducing me to the “ineluctable modality of the visible.”

I would like to acknowledge Aaron Cypess, who introduced me to the possibility of

an MD-PhD, and helped and encouraged me along the way, and Daniel Feldman,

who, for most of my youth, provided me with an excellent role model. I would like

to acknowledge Murray Goldberg, who gave me my first labaroty exposure, making

me realize how much I enjoyed science. And I would like to thank Deborah Fass and

Thomas Sakmar, in whose labs I first experienced the fertile and fun world of scientific

research.

While at Stanford, I have had the good fortune of being a part of a wonderful

community outside of acadmia. I would like to thank Larry and Marlene Marton, Ari

Tuchman, Maya Bernstein and Noam Silverman, Jeremy and Sara Goldhaber-Fiebert,

David Singer, Emily Schoenfeld and Binyamin Blum, Avital Livny, and Amos Bitzan

and Marina Zilbergerts. They have all opened their houses to me for wonderful meals,

great conversations, and, far more importantly, valued companionship.

viii

Contents

Abstract v

Acknowledgements vii

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Summary of thesis work . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Coordinated dynamic encoding 5

2.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3.1 Adaptation and Sensitization in retinal ganglion cells . . . . . 7

2.3.2 Adapting and sensitizing populations encode the same signals 11

2.3.3 Sensitizing cells preserve weak signals, adapting cells preserve

strong signals . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3.4 Ideal normalization and contrast estimation . . . . . . . . . . 18

2.3.5 Estimation of contrast in an uncertain environment . . . . . . 18

2.3.6 Variability and threshold correspond in the two populations . 19

2.3.7 Sensitizing cells decrease activity but convey more information 20

2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.5 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.5.1 Experimental preparation . . . . . . . . . . . . . . . . . . . . 26

2.5.2 Linear-Nonlinear models . . . . . . . . . . . . . . . . . . . . . 26

ix

2.5.3 Adaptive index . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.5.4 Receptive fields . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.5.5 Discriminability . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.5.6 Models of contrast normalization . . . . . . . . . . . . . . . . 29

2.5.7 Information theory . . . . . . . . . . . . . . . . . . . . . . . . 30

2.5.8 Sensitization model . . . . . . . . . . . . . . . . . . . . . . . . 31

3 Predictive sensitization 34

3.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.3.1 Center-surround adaptive fields . . . . . . . . . . . . . . . . . 37

3.3.2 A model unifies the three adaptive fields . . . . . . . . . . . . 40

3.3.3 Subcellular sensitizing and adapting subunits . . . . . . . . . 43

3.3.4 Adaptation and sensitization in a rapidly changing environment 44

3.3.5 Feature detection in Fast O↵ cells . . . . . . . . . . . . . . . . 48

3.3.6 Encoding a signal in a noisy environment . . . . . . . . . . . . 48

3.3.7 Sensitization maintains the location of an object . . . . . . . . 55

3.3.8 Inhibition is necessary for sensitization and the establishment

of the adaptive field . . . . . . . . . . . . . . . . . . . . . . . . 58

3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.4.1 Adaptive and receptive fields . . . . . . . . . . . . . . . . . . . 64

3.4.2 Integration of inhibition and excitation . . . . . . . . . . . . . 65

3.4.3 A functional role for adapting inhibition . . . . . . . . . . . . 65

3.4.4 Di↵erent levels of sensitization in di↵erent cell types . . . . . . 66

3.4.5 Updating the prior probability of a stimulus . . . . . . . . . . 67

3.4.6 Integrating information at the bipolar cell synaptic terminal . 67

3.4.7 The retinal neural code and the statistics of objects . . . . . . 69


3.5.1 Electrophysiology . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.5.2 Cell classification . . . . . . . . . . . . . . . . . . . . . . . . . 71

x

3.5.3 Receptive fields and sensitivity . . . . . . . . . . . . . . . . . 72

3.5.4 Adaptive field model . . . . . . . . . . . . . . . . . . . . . . . 73

3.5.5 Temporal adaptive field . . . . . . . . . . . . . . . . . . . . . 77

3.5.6 Signal detection model . . . . . . . . . . . . . . . . . . . . . . 77

3.5.7 Duration of sensitization . . . . . . . . . . . . . . . . . . . . . 78

4 Optimal dynamic range placement 79

4.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.3.1 Histogram equalization does not predict distinct thresholds . . 83

4.3.2 Binary response model for maximizing information . . . . . . 83

4.3.3 Low threshold cells should have less noise . . . . . . . . . . . . 85

4.3.4 Di↵erent amounts of noise produce di↵erent optimal coding

strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.3.5 Fast O↵ cells optimally space their response functions . . . . . 88

4.3.6 Model fits data across contrasts . . . . . . . . . . . . . . . . . 90

4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

4.4.1 Limitations of the model . . . . . . . . . . . . . . . . . . . . . 93

4.4.2 Redundant versus distributed encoding . . . . . . . . . . . . . 93

4.4.3 Information maximization after signal detection . . . . . . . . 94

4.4.4 Optimal population encoding . . . . . . . . . . . . . . . . . . 95



4.5.2 Linear-Nonlinear models . . . . . . . . . . . . . . . . . . . . . 96

4.5.3 Histogram normalization for multiple neurons . . . . . . . . . 97

4.5.4 Threshold model for contrast processing . . . . . . . . . . . . 98

4.5.5 Detectability . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

5 Mechanism of sensitization 100

5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

5.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

xi

5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109



5.5.2 Receptive fields and nonlinearities . . . . . . . . . . . . . . . . 113

5.5.3 Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

6 Conclusions 115

6.1 Generalization of work . . . . . . . . . . . . . . . . . . . . . . . . . . 115

6.2 Future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

A Publications 121

A.1 Journal Articles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

A.2 Refereed conference articles and abstracts . . . . . . . . . . . . . . . 121

References 123

xii

List of Figures

2.1 Adaptation and sensitization in separate neural populations . . . . . 8

2.2 Linear-Nonlinear (LN) model of ganglion cell firing rate . . . . . . . . 9

2.3 Fraction of sensitizing cells correlates across species with loss of sensi-

tivity in adapting cells . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4 Sensitization occurs during a range of stimulus conditions . . . . . . . 10

2.5 Adaptation and sensitization to changes in luminance . . . . . . . . . 11

2.6 Sensitizing and adapting populations encode common stimulus features 12

2.7 Cell classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.8 Mammalian sensitizing cells are composed of various cell classes . . . 14

2.9 Sigmoid fits for nonlinearities . . . . . . . . . . . . . . . . . . . . . . 14

2.10 Improvement of discriminability in a combined population of sensitiz-

ing and adapting cells . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.11 Correlations between adapting and sensitizing cells . . . . . . . . . . 16

2.12 Sensitizing cells specialize to encode weak signals; adapting cells encode

strong signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.13 Noise and placement of threshold . . . . . . . . . . . . . . . . . . . . 20

2.14 Sensitizing and adapting cells increase information transmission using

opposing changes in firing rate . . . . . . . . . . . . . . . . . . . . . . 21

2.15 Information transmission in sensitizing cells increases when firing rate

decreases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.16 Model of sensitization . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.1 Three di↵erent adaptive fields in the retina . . . . . . . . . . . . . . . 38

3.2 Sensitivity changes underlie activity changes in the adaptive field . . 40

xiii

3.3 Amount of adapting inhibition can determine the type of adaptive field 42

3.4 Changes in sensitivity within the receptive field center . . . . . . . . . 45

3.5 Temporal adaptive fields during rapidly changing contrast . . . . . . 46

3.6 Distinct cell types for object motion sensitivity and global sensitization 49

3.7 Fast-o↵ adapting cells are object motion sensitive . . . . . . . . . . . 49

3.8 Sensitization reflects an increased prior expectation of a signal . . . . 51

3.9 Variability in O↵ bipolar cells and changes in ganglion cell responses

during sensitization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.10 Sensitization predicts future object location . . . . . . . . . . . . . . 56

3.11 Sensitization requires GABAergic transmission . . . . . . . . . . . . . 59

3.12 Sensitization does not require Glycine receptors or the On pathway . 60

3.13 Depolarization of bipolar cells during sensitization . . . . . . . . . . . 61

4.1 Adapting and sensitizing fast O↵ cells coordinate the encoding of the

input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.2 Binary model for information maximization . . . . . . . . . . . . . . 84

4.3 Lower threshold response function optimally has less noise . . . . . . 86

4.4 Distinct population coding regimes . . . . . . . . . . . . . . . . . . . 87

4.5 Fast o↵ cells optimally space their response functions . . . . . . . . . 89

4.6 Model fits to the data . . . . . . . . . . . . . . . . . . . . . . . . . . 91

4.7 Detecting a signal in the presence of noise . . . . . . . . . . . . . . . 92

5.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5.2 Adaptation in sustained O↵ amacrine cells . . . . . . . . . . . . . . . 105

5.3 Amacrine transmission is depressed at the transition to low contrast . 107

5.4 Amacrine transmission changes during low contrast . . . . . . . . . . 108

5.5 High contrast current in a single amacrine cell is su�cient to cause

sensitization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

5.6 Simplified model for sensitization . . . . . . . . . . . . . . . . . . . . 111

5.7 A diverse set of amacrine cells . . . . . . . . . . . . . . . . . . . . . . 112

xiv

Chapter 1

Introduction

1.1 Background

The computational perspective provides a useful framework for understanding the

nervous system. It focuses on the way in which the brain transforms an input to

an output, providing multiple clear avenues of inquiry. The brain is composed of

many complicated dynamic and nonlinear parts. To understand relevant functions of

such a complicated system an understanding of its native inputs is critical. Along

similar lines, such a complicated system can produce many di↵erent types of output;

it therefore also becomes critical to carefully choose outputs relevant to the system.

Then once the input and output are defined many tools and techniques exist, but in

no way guarantee success, to decipher the algorithm that converts the inputs to the

outputs.

The retina provides an excellent substrate for understanding neural computations.

A major strength of studying the visual system is our knowledge, at least in the

absolute sense, of the input to the system. Photons provide the natural input, and

the visual system maintains exquisite sensitivity to photons (Hecht et al., 1942; Baylor

et al., 1984). Furthermore, much work has been done to understand the structure of

natural visual scenes (Field, 1987; Ruderman and Bialek, 1994; van Hateren and

Ruderman, 1998; Simoncelli and Olshausen, 2001; Geisler, 2008), and the way in

which an animal experiences that visual input (Yarbus, 1967; Martinez-Conde and

1

2 CHAPTER 1. INTRODUCTION

Macknik, 2008; Rucci et al., 2007; Rucci, 2008).

The retina contains five di↵erent classes of cells. Photoreceptors transform light

into electrical activity. Bipolar cells are excitatory interneurons that receive input from

photoreceptors and provide a direct pathway to ganglion cells, the output neurons

of the retina. Horizontal cells are inhibitory interneurons in the outer retina that

inhibit the photoreceptor signal. And amacrine cells are a diverse class of inhibitory

interneurons in the inner retina that receive input from bipolar cells and inhibit

bipolar and ganglion cells (Dowling, 1987; Masland, 2001).

By removing the retina from an animal we can record from many ganglion cell

at once while presenting a visual stimulus (Meister et al., 1994; Segev et al., 2004).

This is a perfect set up for computational studies since we precisely control the input

and measure the output of a practically intact neural circuit. Additionally, in recent

years, this extracellular recording set-up was combined with intracellular recording

to allow for perturbations of the di↵erent cells in the retina; thereby, enabling an

understanding of the way in which the retina performs a given computation (Ge↵en

et al., 2007; Baccus et al., 2008; de Vries et al., 2011; Manu and Baccus, 2011).

In my studies I have focused on adaptation. Compared to the range of their

inputs neurons have a limited dynamic range for their outputs. This mismatch is

quite apparent in the visual system where we can detect ten orders of magnitude by

using neurons that can only provide outputs over two to three orders of magnitude

(Rieke and Rudd, 2009). One strategy that neurons use to handle this problem is

that they change their dynamic range to match the range of the inputs, becoming

less sensitive when there is a large range of inputs, and more sensitive when there is a

smaller range of inputs. Because this is such a general problem, neurons throughout

the brain will adapt (Smirnakis et al., 1997; Kohn and Movshon, 2003; Nagel and

Doupe, 2006; Maravall et al., 2007; Kobayashi et al., 2010).

1.2 Summary of thesis work

In this thesis, I introduce the phenomenon of contrast sensitization, show its functional

relevance for retinal visual processing, derive a theoretical basis to justify sensitization

1.2. SUMMARY OF THESIS WORK 3

and some of its functional consequences, and elucidate the mechanism by which the

retina performs sensitization.

Chapter 2 characterizes the discovery of sensitization in the retina of multiple

species. The discovery of sensitization sheds light on an interesting encoding scheme—

coordinated dynamic encoding—whereby the retina distributes the encoding of it

inputs between two populations of neurons. These two populations coordinate their

encoding by representing very similar features of the visual world, but then specialize

in encoding di↵erent components of those features. One population sensitizes and

maintains a lower threshold to encode weaker parts of the input, while the other

population adapts and maintains a higher threshold to encode stronger parts of the

input. Both of these populations alone fall victim to saturating parts of their nonlinear

response function, but combined the two populations can encode the input over a far

broader range because they coordinate the placement of their response functions such

that when one saturates the other does not.

Chapter 3 discusses the adaptive field, which is the spatio-temporal structure that

cause a neuron to adapt. Once we saw in Chapter 2 that the retina has two opposing

forms of plasticity, namely adaptation and sensitization, I drew a parallel to a more

well know opponency in the retina: the On and O↵ pathway. On and O↵ channels are

combined within the receptive field of ganglion cells to enable biphasic spatio-temporal

processing. I report that the retina also combines adaptation and sensitization into

biphasic adaptive fields. Further drawing upon the comparison to the receptive field,

where inhibition is necessary for the biphasic filtering, I created a model that used

adapting inhibition to create the biphasic adaptive field. Using the adaptive field,

Chapter 3 shows that sensitization can function to store information. Whereas the

receptive field removes correlations in the input through predictive encoding, the

adaptive field uses those correlations to forms predictions about the world to encode

during a time of uncertainty.

Chapter 4 studies the way in which a population of neurons should place their

dynamic ranges to maximally transmit information about their input. I develop a

simple model to determine the optimal placement of dynamic ranges that maximize

the information about the input. I then go on to show that the fast O↵ populations in

4 CHAPTER 1. INTRODUCTION

the retina optimally space their response functions, given the noise in their responses

and an overall metabolic constraint to enforce sparse encoding. Furthermore, I show

that there are two regimes for optimal population encoding, distributed encoding and

redundant encoding. The On population has responses consistent with their optimally

choosing redundant encoding, a finding that has the potential to explain the greater

homogeneity in the On population.

Chapter 5 focuses on the way in which the retina performs the computations

of sensitization. Using pharmacology, and combined intracellular and extracellular

recording, I show that inhibition is both necessary and su�cient for sensitization.

Furthermore, I go on to show that inhibitory dynamics underly the role of inhibition

in sensitization.

In Chapter 6 I conclude by showing the seeds of similar computations in other

parts of the brain, and highlight some implications of this work for future research

directions.

Chapter 2

Coordinated dynamic encoding in

the retina using opposing forms of

plasticity

This chapter has been published in Nature Neuroscience as “Coordinated Dynamic

Encoding in the Retina Using Opposing Forms of Plasticity,” with author list: Kastner

DB, Baccus SA.

2.1 Summary

The range of natural inputs encoded by a neuron often exceeds its dynamic range. To

overcome this limitation, neural populations divide their inputs among di↵erent cell

classes, as with rod and cone photoreceptors, and adapt by shifting their dynamic

range. We report that the dynamic behavior of retinal ganglion cells in salaman-

ders, mice and rabbits is divided into two opposing forms of short-term plasticity in

di↵erent cell classes. One population of cells exhibited sensitization—a persistent ele-

vated sensitivity following a strong stimulus. This newly observed dynamic behavior

compensates for the information loss caused by the known process of adaptation oc-

curring in a separate cell population. The two populations divide the dynamic range

of inputs, with sensitizing cells encoding weak signals and adapting cells encoding

5

6 CHAPTER 2. COORDINATED DYNAMIC ENCODING

strong signals. In the two populations, the linear, threshold and adaptive proper-

ties are linked to preserve responsiveness when stimulus statistics change, with one

population maintaining the ability to respond when the other fails.

2.2 Introduction

Adaptive systems adjust their response properties to the statistics of the recent in-

put (Laughlin, 1981). However, a fundamental tradeo↵ exists between optimizing for

the current environment, and being able to respond reliably when the environment

changes. Due to statistical limitations of how long it takes to estimate the recent

stimulus distribution (DeWeese and Zador, 1998; Wark et al., 2009), the timescale of

adaptation greatly exceeds the integration time of the response in many sensory sys-

tems (Laughlin, 1981; Smirnakis et al., 1997; Fairhall et al., 2001; Nagel and Doupe,

2006; Maravall et al., 2007). As a consequence, when stimulus statistics change sud-

denly, as often occurs in natural scenes (Frazor and Geisler, 2006), sensory neurons

often fall below threshold or saturate, until they successfully measure and adapt to

the statistics of the new environment.

In the retina, a transition from a high to a low contrast environment reveals this

tradeo↵, when the decreased sensitivity caused by high contrast prevents the neuron

from firing for some time after the contrast decreases (Smirnakis et al., 1997; Baccus

and Meister, 2002; Rieke and Rudd, 2009). Adapting primate retinal ganglion cells

are known to recover their activity after high contrast with a prolonged time constant

of ⇠ 6 s (Solomon et al., 2004). However, human psychophysical performance recovers

faster at early timescales (<1 s), matching an ideal observer model, indicating that

some adapting neural pathway can signal quickly even after exposure to high contrast

(Snippe and van Hateren, 2003). We recorded from retinal ganglion cells in amphib-

ian and mammalian retina during sudden changes in the statistics of the stimulus

to examine how neural populations maintain responsiveness when the environment

changes.

2.3. RESULTS 7

2.3 Results

2.3.1 Adaptation and Sensitization in retinal ganglion cells

We measured the average firing rate response of salamander, mouse, and rabbit gan-

glion cells to a contrast transition by presenting a spatially uniform visual stimulus.

The intensity was drawn from a Gaussian white noise distribution with a constant

mean and a standard deviation that alternated between high and low temporal con-

trasts (Figure 2.1a). Even after a short high contrast presentation, many ganglion

cells failed to respond for seconds after the transition to low contrast as their fir-

ing rate slowly recovered, consistent with previously reported properties of contrast

adaptation (Smirnakis et al., 1997; Brown and Masland, 2001; Fairhall et al., 2001;

Baccus and Meister, 2002; Maravall et al., 2007) (Figure 2.1a,b).

We found, however, that some neurons responded rapidly after a transition to low

contrast (Figure 2.1a), even after a long high contrast presentation (Figure 2.1b).

These cells exhibited an elevated response following high contrast that persisted for

several seconds, gradually decreasing during low contrast. This decay had an average

(± standard deviation) time constant of 2.4±1.1 s in salamanders, 1.3±0.3 s in mice,

and 4.1± 2.7 s in rabbits.

To measure how the sensitivity of the two populations changed during low con-

trast, we computed a linear-nonlinear (LN) model of each neuron’s firing rate (Baccus

and Meister, 2002) (see methods) (Figure 2.2). We compared the nonlinearities com-

puted early (Learly

) and late (Llate

) after the transition to low contrast (bars in Figure

2.1a). For the two populations of ganglion cells, the change in firing rate arose from

a change in average sensitivity, defined as the average slope of the nonlinearity (Fig-

ure 2.1c). For salamanders, cells that elevated their activity at the transition to low

contrast doubled their average sensitivity (2.1± 0.3) during Learly

relative to Llate

. In

part, a change in threshold underlaid this change in average sensitivity. Because the

presence of a strong stimulus elevated the sensitivity to a subsequent weak stimulus,

we term this property sensitization, by analogy to behavioral sensitization (Pinsker

et al., 1973).

Sensitizing cells were found in salamanders (Figure 2.1a,c) (32%, 80 out of 250


Figure 2.1: Adaptation and sensitization in separate neural populations. (a) Stimulus inten-sity alternating between high and low contrast during a single trial (top), for salamander(left) and mouse (right). Firing rate response for adapting (middle) and sensitizing (bot-tom) cells, averaged over all trials, each with a di↵erent stimulus sequence. Color indicatesresponse to low contrast. (b) Average time to first spike after a transition from high tolow contrast (n = 2 � 12 cells). (c) Nonlinearities of an LN model (see methods) for cellsin (a) calculated during intervals indicated by bars in (a) for salamander (left) and mouse(right). The interval L

early

was defined as 0.5 � 2 s after the transition to low contrast,and L

late

was 10� 16 s for salamander and 10� 15 s for mouse. (d) Adaptive indices (seemethods) for 190 ganglion cells from 16 salamander retinas. The distribution is significantlybimodal (Hartigans dip test, p < 0.05). (e) High contrast (35%) was presented for 1, 2 or 5s, followed by low contrast (3%) for 15 s. The average change in firing rate between L

early

and Llate

is shown normalized by the average rate for low contrast in all conditions (n = 5cells). Black line is an exponential fit to the data. (f) For the same cells, the adaptive indexwas computed separately for changing contrast at a fixed luminance, and compared to theadaptive index when changing the mean luminance a factor of 16 at a fixed contrast of 10%(see Figure 2.5).

2.3. RESULTS 9

Figure 2.2: Linear-Nonlinear (LN) model of ganglion cell firing rate. For a fast O↵-typeganglion cell, the stimulus, s(t), was convolved with a linear filter, F (t), to yield the filteredstimulus, g(t). The filtered stimulus was then transformed by the nonlinearity, N(g), to yieldthe predicted response, r0(t). The linear filter in all conditions was biphasic, and lasted lessthan 0.5 s (Baccus and Meister, 2002).

cells), mice (Figure 2.1a,c) (12%, 5 out of 41 cells), and rabbits (21%, 8 out of 39

cells) (Figure 2.3a,b). A similar ratio of salamander ganglion cells has been reported in

abstract form to respond to contrast decrements (C.A. Burlingame, A.Y. Dymarsky,

M.J.Berry II, Soc Neurosci. Abstr. 506.11, 2007). Recording from many cell types

in the salamander, we found that adapting and sensitizing cells formed two distinct

classes (Figure 2.1d). For each species, we used the nonlinearities during Learly

and Llate

to compute the average loss of sensitivity. The sensitivity loss in adapting cells during

Learly

correlated with the fraction of sensitizing cells in the species (Figure 2.3c),

suggesting that sensitizing cells compensate for the sensitivity loss due to adaptation.

Sensitization occurred over a broad range of spatial frequencies and stimulus sizes

(Figure 2.4). By measuring sensitivity after di↵erent high contrast durations, we found

that after 0.55 s of high contrast, a cell reached 63% of its peak sensitization (⌧ = 0.55

s) (Figure 2.1e). Thus, significant sensitization is expected even during brief fixations.

After the transition to low contrast, increased activity was not instantaneous, but

reached a peak in 0.98 ± 0.03 s. This delay may reflect the statistical limitation

necessitating su�cient temporal integration for any system to adapt to a contrast

decrement (DeWeese and Zador, 1998; Fairhall et al., 2001; Snippe and van Hateren,

2003).

We tested whether the two forms of plasticity generalized to statistics other than


Figure 2.3: Fraction of sensitizing cells correlates across species with loss of sensitivity inadapting cells. (a) Example response of a sensitizing cell from rabbit. High contrast (25%)and low contrast (4%) were both presented for 30 s over 27 trials. (b) Nonlinearities for cellin (a) calculated during the times indicated by the corresponding colored bars in (a). L

early

,0.5� 4 s after the transition to low contrast; L

late

, 15� 30 s. (c) The fraction of sensitizingcells in each species plotted against the average decrease in sensitivity during L

early

relativeto L

late

.

Figure 2.4: Sensitization occurs during a rangeof stimulus conditions. (a) The response of asalamander sensitizing cell to stimuli with dif-ferent spatial frequencies. Stimuli alternated be-tween high contrast (35%) and low contrast(5%) and were composed of 12 µm bars (left), 50µm bars (center), or a uniform field (right). Col-ored regions indicate responses to low contrast.Average adaptive indices for the three condi-tions were 0.45±0.01, 0.27±0.01 and 0.23±0.01,respectively (n = 4 cells). (b) The response of asensitizing cell to di↵erent size stimuli. Stimuliwere composed of 50 µm bars that covered thewhole retina, >2mm (left), or a 200 µm square.Adaptive indices for the two conditions were0.27± 0.07 and 0.49± 0.03, respectively (n = 3cells).

2.3. RESULTS 11

contrast by changing the mean luminance while keeping the contrast fixed. Each cell

type showed consistent sensitizing or adapting behavior for changes in both stimulus

parameters (Figure 2.5, and Figure 2.1f).

Figure 2.5: Adaptation and sensitization tochanges in luminance. (a) Stimulus during a sin-gle trial (top), and average response over 64 tri-als for example salamander adapting (middle)and sensitizing (bottom) cells at a fixed con-trast of 10% during high and low luminance,which di↵ered by a factor of 16. (b) Nonlinear-ities for cells in (a) calculated during the timesindicated by the corresponding colored bars in(a). L

early

, 0.5 � 3 s after the transition to lowluminance; L

late

, 10� 20 s.

2.3.2 Adapting and sensitizing populations encode the same

signals

Although adaptation and sensitization slowly modulated the average firing rate, reti-

nal ganglion cells encode visual information on a much finer timescale using repro-

ducible firing events—intervals of high firing probability lasting <0.1 s in duration

(Baccus and Meister, 2002). We compared firing events for adapting and sensitizing

cells recorded simultaneously by repeating an identical stimulus sequence during Learly

and Llate

. During Llate

, 94% of adapting cell firing events occurred synchronously with

a sensitizing cell firing event (Figure 2.6a,b). Consistent with the changing nonlin-

earities, during these individual common firing events the activity of adapting cells

during Learly

decreased by 41± 3% relative to Llate

(n = 28), whereas the activity of

sensitizing cells increased by 93 ± 8% (n = 12). Thus, the two populations coordi-

nated their encoding such that they responded to the same visual stimuli, with the

representation shifting more to the sensitizing population during Learly

.

To examine the specific messages encoded by sensitizing and adapting cells, we


Figure 2.6: Sensitizing and adapting populations encode common stimulus features. (a)Average response of salamander adapting and sensitizing cells to 26 trials of the samestimulus repeated during L

early

and Llate

after 4 s of high contrast (35%). Low contrast was3� 5%. Firing rate binned at 10 ms. (b) Absolute di↵erence in time between events in allpairs of fast O↵-type adapting cells (n = 28) and sensitizing cells (n = 12). Events definedas times when a cell’s firing rate, binned at 10 ms, exceeded 20 Hz. (c) Average temporal(top) and spatial (bottom) filters for adapting (n = 142), and sensitizing (n = 48) fastO↵ cells, mapped in one dimension. Curves obscure the error bars located at the peak andtrough of the temporal filters and along the spatial filters. Spatial filters normalized to theirpeaks. (d) Fractions of adapting and sensitizing cells of di↵erent cell types, as classifiedby a cell’s temporal filter (n = 209 fast O↵, 16 medium O↵, 20 slow O↵, 9 On) (Figure2.7). (e) Spatial receptive field centers of fast O↵ adapting and sensitizing cells recordedsimultaneously. Receptive fields displayed at one standard deviation of a 2-D Gaussian fit.(f) Histogram of spacing (see methods) between nearest neighbors of fast O↵ adapting(n = 615) and sensitizing (n = 171) cells.

2.3. RESULTS 13

Figure 2.7: Cell classification. (a)Temporal filters obtained from a sin-gle salamander retina. (b) Filtersfrom (a) projected onto the first andsecond principal components of allfilters. (c) Filters from (a) projectedonto the second principal componentplotted against each cell’s adaptiveindex. Cells that did not respondduring low contrast do not appearon the plot because their adaptiveindex is undefined. Cells were clas-sified based upon their grouping inplots (b) and (c). There were 4 broadcategories of cells as classified bytheir filter alone. Within the fast O↵population most analyses for adapt-ing cells were performed on the firstgroup (red).

measured how the plasticity of a cell corresponded to its linear spatio-temporal re-

ceptive field (Figure 2.6c,d). For all salamander O↵-type cells—⇠90% of the cells

in the salamander retina (Segev et al., 2006)—the adaptive index divided each cell

type into two groups, composed of both adapting and sensitizing cells. Within a cell

class, the spatial receptive fields of adapting and sensitizing cells overlapped (Figure

2.6e), but maintained a minimum spacing between members of the same class (Fig-

ure 2.6f) (Huberman et al., 2008). This indicates that a mixed group of cells with

highly similar linear receptive fields (Segev et al., 2006), splits into two classes with

di↵erent short-term plasticity, each of which appears to tile the retina. Thus, adapt-

ing and sensitizing populations represent the same stimuli. In mice, sensitizing cells

also comprised di↵erent cell types, including both On and O↵ classes (Figure 2.8a).

In addition, some adapting and sensitizing cells in mice and rabbits had very similar

temporal properties (Figure 2.8b).

Because sensitizing cells compensate for the loss of sensitivity in the adapting

population during low contrast, we tested whether the reverse was true during high


Figure 2.8: Mammalian sensitizing cells are composed of various cell classes. (a) Temporalfilters from four sensitizing mouse ganglion cells shown in di↵erent colors. (b) Example tem-poral filters from mouse (left) and rabbit (right) with similar properties between adaptingand sensitizing cells. In mice, 3 out of 18 On cells, and 2 out of 18 O↵ cells sensitized. Inrabbits 1 out of 10 On cells, and 7 out of 18 O↵ cells sensitized. Temporal kernels could notbe classified for three of the rabbit cells.

contrast. During Hearly

, 0.5�5 s after a transition to high contrast, the nonlinearity of

sensitizing cells saturated (Figure 2.9), reaching 98± 1% of their estimated maximal

firing rate, and their sensitivity dropped to 10± 4% of the peak sensitivity (n = 3).

Adapting cells did not saturate, however, and only reached 79± 4% of their maximal

rate while retaining 63±8% of their peak sensitivity (n = 11). Thus, adapting cells

compensated for saturation in the sensitizing population at the transition to high

contrast.

Figure 2.9: Nonlinearities and sigmoid fits for exam-ple adapting (top) and sensitizing (bottom) cells. Usingthis sigmoid, we estimated maximal firing rate and thepeak sensitivity, which is the slope at the midpoint.

2.3. RESULTS 15

2.3.3 Sensitizing cells preserve weak signals, adapting cells

preserve strong signals

To measure the functional benefit of having the two opposing forms of plasticity,

we quantified the discriminability, d0, in the combined population of sensitizing and

adapting cells after a decrease in contrast (see methods). This measure derives from

the Fisher information, an upper bound on the information available by any unbiased

decoding scheme (Dayan and Abbott, 2009). Discriminability, and Fisher informa-

tion, increases with the slope of the nonlinearities at each input (Figure 2.10a), but

decreases with the variability of the response at that input. It also depends on corre-

lations between cells, which can either increase or decrease information (Abbott and

Dayan, 1999). We used simultaneously recorded populations of adapting and sensitiz-

ing cells to account for the nonlinearities, variability, and covariance as a function of

distance between cells (Figure 2.11) (see methods). Discriminability in the adapting

population alone decreased 44.2±1.9% during Learly

relative to Llate

. However, for the

combined population of sensitizing and adapting cells, discriminability only decreased

16.8±2.3% during Learly

. Thus, the addition of sensitizing cells to the population sub-

stantially reduced the loss of discriminability when the contrast of the environment

changed.

Figure 2.10: Improvement of discriminabilityin a combined population of sensitizing andadapting cells. (a) Nonlinearities for adapting(n = 21) and sensitizing (n = 13) cells duringLearly

(left) and Llate

(right). (b) Discriminabil-ity between nearby stimuli, d0(g), as a functionof the stimulus (see methods) in the full popu-lation minus d0(g) for the adapting populationalone (blue) or minus d

0(g) for the sensitizingpopulation alone (red) during L

early

(left) andLlate

(right). All values were normalized by thearea of the total d0 in the full population duringLlate

.


Figure 2.11: Correlations betweenadapting and sensitizing cells. (a)The covariance of an example pairof sensitizing cells is shown as afunction of the filtered stimulus g.In addition, a model of this co-variance is shown, computed as thegeometric mean of the two vari-ances weighted by the correlationcoe�cient between the two cells(see methods). (b) Correlation co-e�cient as a function of distanceduring L

late

within the adaptingand sensitizing populations, andbetween populations. Lines are ex-ponential fits to the data.

We then examined this improvement in discriminability in the full population at

each separate stimulus, and found that the addition of sensitizing cells to a popula-

tion of adapting cells enhanced the discriminability of weak signals (Figure 2.10b).

The improvement produced by including sensitizing cells during Learly

was 1.8 times

the improvement during Llate

. Discriminability improved most in the region of the

reduced threshold of the nonlinearities of sensitizing cells, indicating that this re-

duction during Learly

further enhanced the encoding of weak signals. Conversely, the

addition of adapting cells to a population of sensitizing cells enhanced discriminabil-

ity of strong signals (Figure 2.10b). As expected, this contribution of adapting cells

increased during Llate

as their threshold decreased and sensitivity increased.

The dynamics of adapting and sensitizing cells decayed towards a steady-state

response that depended on the contrast. To understand the endpoint of this adap-

tive process, we measured the steady-state nonlinear response curve from LN models

computed across a ten-fold range of contrasts (Figure 2.12a). Compared to adapt-

ing cells, sensitizing cells had a threshold closer to the mean (Figure 2.12a,b). Thus,

across all contrasts the two populations divided the range of inputs, with sensitizing

cells encoding weak signals, and adapting cells encoding strong signals.

2.3. RESULTS 17

Figure 2.12: Sensitizing cells specialize to encode weak signals; adapting cells encode strongsignals. (a) Twelve di↵erent contrast levels (3 � 36%) were randomly interleaved for atleast 110 s and three repeats, and the first 10 s of data in each contrast was discarded.Nonlinearities are shown for an adapting (top) and sensitizing (bottom) cell for the di↵erentcontrasts. Each row is a di↵erent nonlinearity, displayed in a color scale. Black dots indicateone standard deviation above the mean for each contrast level. Nonlinearities calculated fromthe data (left), and as predicted using a model described in panel (c) (right). (b) Normalizednonlinearities from cells in panel (a). For each contrast, the nonlinearity was scaled alongthe abscissa by the input standard deviation (top) or shifted by a common factor (↵) andthen scaled along the abscissa by the contrast (bottom). (c) Model M

↵

. Input values werepassed through a threshold function, which shifted the mean value by a factor, ↵, thenwere rescaled by the contrast (�), and then passed through a secondary nonlinearity withthreshold ✓ to recreate the range of nonlinearities shown in (a). The secondary nonlinearity isthe average nonlinearity for a cell after shifting by ↵ and rescaling. (d) Nonlinearities N

i

(g)were computed for each 3 s bin. For each bin, an estimate of the contrast was determined asthe contrast, �, for which the steady-state nonlinearity of the model M

↵

(�) had the smallestmean-squared di↵erence to N

i

(g). Low contrast (5%) followed 40 s of high contrast (35%).


Consistent with this division of labor, sensitizing cells had a larger center and

weaker surround than did adapting cells (Figure 2.6c). This di↵erence likely enables

sensitizing cells to improve their signal to noise ratio for weak inputs by spatial

averaging, as occurs for ganglion cells during low luminance conditions (Enroth-Cugell

and Robson, 1966; Srinivasan et al., 1982).

2.3.4 Ideal normalization and contrast estimation

To explain the relationship between contrast and the steady-state dynamic range of

adapting and sensitizing cells, we considered that an ideal encoder that maximizes

information from a stimulus distribution should change its sensitivity inversely with

the contrast (Laughlin, 1981). This ideal normalization is thought not to occur in

the retina because ganglion cells reduce their sensitivity by a fraction less than the

change in contrast. This can be seen by comparing nonlinearities whose input has

been normalized by the contrast (Figure 2.12b top) (Smirnakis et al., 1997; Chander

and Chichilnisky, 2001).

We found, however, that a model, M↵

(see methods), using ideal normalization

does account for steady-state adaptation, causing the normalized curves to nearly

overlay, if one considers that the rescaling occurs after a threshold (Figure 2.12b

bottom). This type of normalization could occur if the stimulus passes through a

threshold, such as from voltage-dependent Ca channels in bipolar cell presynaptic

terminals (Mennerick and Matthews, 1996), and then rescaling occurs about that

threshold (Figure 2.12c).

2.3.5 Estimation of contrast in an uncertain environment

A change in stimulus statistics, as has recently occurred during Learly

, necessarily

brings uncertainty as to the new range of inputs (DeWeese and Zador, 1998; Fairhall

et al., 2001; Wark et al., 2009). As seen in the di↵erent dynamics of their firing rates

(Figure 2.1a) and nonlinearities (Figure 2.1c), the two populations make di↵erent

choices during that time of uncertainty, and then adjust their response to the new

contrast. Thus, we can view the initial placement of the nonlinearity as corresponding

2.3. RESULTS 19

to an initial estimate of the contrast.

The model M↵

represents an idealized relationship between contrast and the op-

timized response of a cell to that contrast. We therefore used the model as a lookup

table to identify the contrast estimate given the nonlinearity of a cell at di↵erent times

during low contrast (Figure 2.12d). We mapped nonlinearities for each cell at di↵erent

time intervals to a given estimated contrast by finding the most similar nonlinearity

in the steady-state model M↵

. During Learly

, adapting cells overestimated the contrast

at 1.6± 0.1 times the actual value (n = 12), and sensitizing cells underestimated the

contrast at 0.5± 0.1 times the actual value (n = 6).

2.3.6 Variability and threshold correspond in the two popu-

lations

We next sought to explain why sensitizing cells raised their threshold during prolonged

exposure to the low contrast environment, rather than maintaining a continued higher

firing rate during low contrast. For optimal encoding of an input, the level of noise

can influence the placement of threshold, with higher noise necessitating a higher

threshold (Field and Rieke, 2002). Sensitizing cells had lower variability than adapting

cells as measured by the Fano factor, or variance to mean ratio, by a factor of 1.86±0.17 (Figure 2.13a). This may occur in part due to their di↵erent receptive field sizes,

which would predict, assuming independent noise from photoreceptors, that their

variability would di↵er by the ratio of the receptive field areas, which was 2.07± 0.06

(26 sensitizing and 74 adapting cells).

We then examined the parameters of the model M↵

, which resembles an ideal ob-

server model of human perception having ideal contrast normalization with a thresh-

old set by internal noise (Snippe and van Hateren, 2003). Compared to adapting cells,

sensitizing cells had a lower initial threshold, ↵ (by a factor of 1.96) and a lower final

threshold, ✓, (by a factor of 3.6) (Figure 2.13b), possibly constrained by the di↵erent

variability in the two populations. Because of this connection between variability and

threshold, and the defined relationship of the steady-state threshold with contrast

(Figure 2.12ac), we considered that after a change in contrast, the threshold might


Figure 2.13: Noise and placement ofthreshold. (a) Variance and mean ofthe spike count during L

late

from re-peated stimuli (Figure 2.6a) calcu-lated every 100 ms. Black lines arelinear fits to the data. Results arefrom 28 adapting cells and 12 sen-sitizing cells recorded from 3 reti-nas. The Fano factor is 1.43 ± 0.08for adapting and 0.77± 0.06 for sen-sitizing cells. (b) Value of ↵ plot-ted against the threshold ✓ from themodel in Figure 2.12c.

then become optimized in the steady state to convey greater information about the

current stimulus.

2.3.7 Sensitizing cells decrease activity but convey more in-

formation

These observations led us to propose that during low contrast, from Learly

to Llate

, in-

formation transmission improved for both adapting and sensitizing cells, even though

the firing rates of the two populations moved in opposite directions. We thus mea-

sured the mutual information during Learly

and Llate

for adapting and sensitizing cells

by presenting pulses of eight di↵erent intensities during Learly

and Llate

(Figure 2.14a).

As expected, adapting cells conveyed less information during Learly

than sensitizing

cells, and increased their information transmission between Learly

and Llate

. Remark-

ably, we found that sensitizing cells also conveyed more information during Llate

than

Learly

(Figure 2.14b) even though their activity decreased during Llate

(Figure 2.15a).

Thus, the increase in threshold for sensitizing cells from Learly

and Llate

improves in-

formation transmission. This increase in mutual information was consistent with the

population measurement of discriminability (Figure 2.10b), in that the sensitizing

population alone lost 8.4 ± 4.0% of its discriminability during Learly

. Thus although

both sensitizing and adapting cells lose information at the transition to low contrast,

2.3. RESULTS 21

sensitizing cells lose much less.

This loss of information in the sensitizing population despite the increase in firing

rate can be explained by comparing the variability during Learly

and Llate

. A lower

threshold during Learly

exposed an increase in noise at the weakest stimuli for sensi-

tizing cells (Figure 2.14c), but not for adapting cells (Figure 2.15c), confirming that

subthreshold noise limits the steady-state placement of threshold. Previously, it has

been shown that higher firing rate correlates with greater information transmission

(Wessel et al., 1996; Reinagel and Reid, 2000). Here, however, the decay in activity

in sensitizing cells actually improves the encoding of the low contrast stimulus.

Figure 2.14: Sensitizing and adapting cells increase information transmission using opposingchanges in firing rate. (a) Stimulus used in the calculation of mutual information and thestimulus specific information (SSI) for low contrast. 20 s of identical high contrast pulseswere followed by L

early

, which was 2 s of 8 randomly presented low contrast pulses. ForLlate

, every 180 s, 44s seconds of continuous, randomly organized, low contrast pulses waspresented. (b) Mutual information during L

late

versus Learly

. Llate

occurred from 22� 44 safter high contrast, and L

early

occurred from 0.5 � 2 s after high contrast. All sensitizingcells had a higher firing rate during L

early

than Llate

(Figure 2.15a). A bin size of 150 mswas used, but the increase of information during low contrast is independent of bin size(Figure 2.15b). (c) Average mean and variance during L

early

(lighter colors, thicker lines)and L

late

(darker colors, thinner lines) for the sensitizing cells in (b), shown as a functionof the stimulus pulse amplitude. (d) Stimulus specific information, I

SSI

, for each of the 8di↵erent low contrast stimuli. In (c) and (d), flash amplitude is the Michelson contrast,(I

max

� I

min

)/(Imax

+ I

min

), of the 8 brief flashes in the low contrast stimulus.


Figure 2.15: Information transmission in sensitizing cells increases when firing rate decreases.(a) Firing rates during L

early

and Llate

for the sensitizing cells from Figure 2.14b. Lowcontrast stimuli were eight randomly presented low contrast pulses of di↵erent amplitudespresented either after high contrast pulses (L

early

) or in a prolonged presentation (Llate

) asdescribed in the legend of Figure 2.14. (b) Average mutual information during L

early

andLlate

for the sensitizing cells in Figure 2.14b calculated across a range of bin sizes. (c) Meanand variance of firing rate averaged across adapting cells from Figure 2.14b during L

early

(lighter colors, thicker lines) and Llate

(darker colors, thinner lines). For Learly

, the curvefor variance obscures that of the mean rate. Flash amplitude is the Michelson contrast. (d)Examples of the bias correction for finite data Strong et al. (1998) (see methods) for mutualinformation (left) and stimulus specific information measurements (right). The informationmeasurements were computed on all of the data, and the data divided into x parts, wherex is the value on the abscissa. The average value is plotted for all fractions of the data,and a second-order polynomial fit was used to extrapolate the curve to the case of infinitedata. For the stimulus specific information, I

SSI

, during Llate

is shown for all of the di↵erentintensity values in di↵erent colors.

2.4. DISCUSSION 23

To further examine how encoding changed for individual stimuli, we computed

the stimulus-specific information (Butts, 2003) (see methods), during Learly

and Llate

.

This measure reflects the contribution of each specific stimulus to the mutual infor-

mation. During both Learly

and Llate

, adapting and sensitizing cells favored di↵erent

ends of the input signals (Figure 2.14d), with sensitizing cells conveying the greatest

amount of information about the weakest stimuli during Learly

. This was consistent

with the measure of discriminability, which showed that the additional discriminabil-

ity conveyed by the two populations separated during Learly

(Figure 2.10b). However,

across all stimuli, information transmission improved from Learly

to Llate

. Thus, after

the initial opposing thresholds chosen by sensitizing and adapting cells, both popu-

lations improved their information transmission with more prolonged exposure to a

steady environment.

2.4 Discussion

These results give an explanation for the opposing dynamics of sensitizing and adapt-

ing cells. A decrease in contrast creates the greatest ambiguity as to the statistics of

the stimulus, because the new range of inputs only contains weak signals that fall

within the most probable values of the previous distribution (DeWeese and Zador,

1998; Fairhall et al., 2001). The addition of sensitizing cells to the population im-

proves the encoding of weak signals, with the greatest improvement being after the

contrast decreases (Figure 2.10b). However, neither population perfectly encodes the

new distribution after the contrast decreases (Figure 2.14b,d), a condition compelled

by the uncertainty that accompanies a transition to an environment of weak signals

(DeWeese and Zador, 1998; Fairhall et al., 2001). But by positioning their sensitivity

at di↵erent sides of the steady-state value, sensitizing and adapting cells bracket the

target sensitivity by underestimating or overestimating, respectively, the steady-state

sensitivity (Figure 2.12d). Thus, during the time of greatest statistical uncertainty

the two populations span the range of inputs. Because this initial position deviates

from optimal, both sensitizing and adapting cells then increase their information

transmission by adopting their steady-state positions (Figure 2.14b,d). Therefore,


the coordinated dynamics of adapting and sensitizing cells (Figure 2.1a) represent a

tradeo↵ between the immediate encoding of an uncertain distribution and the delayed

optimization for that distribution.

Dynamic changes within the circuitry of the inner retina underlie contrast adap-

tation (Rieke, 2001; Baccus and Meister, 2002; Kim and Rieke, 2003; Manookin and

Demb, 2006). Two adapting pathways, one excitatory and one inhibitory could com-

bine to produce sensitization (Figure 2.16). In this scheme, high contrast causes in-

hibitory transmission to adapt. Then, at the transition to low contrast, the residual

lowered inhibition raises sensitivity (Figure 2.16b,c). This model of sensitization in-

dicates that sensitizing cells receive a negative version of an adapting cell’s response.

This causes the two populations to encode di↵erent signals, in particular during the

time when each population has the highest likelihood of failing to encode the stimulus.

The model also indicates that the source of increased variability during sensitization

lies prior to the initial threshold in the excitatory pathway, as decreased inhibition

prior to this threshold could result in greater transmission of noise.

A neuron with a response curve that spans its distribution of inputs will encode

those inputs e�ciently (Laughlin, 1981). However, to perform this task dynamically

would require that the neuron maintain its threshold to encode the weakest signals,

and its maximal response to encode the strongest, making both ends of the response

curve vulnerable to saturation should the stimulus distribution change. Here, we have

shown that the retina divides this problem in two, with linear filtering, threshold

placement, and dynamic plasticity combining to encode a specific range of inputs.

Low threshold cells with weaker surrounds sensitize to reliably encode weak signals.

High threshold cells with stronger surrounds adapt to reliably encode strong signals.

When one population saturates, the other compensates. The ability to coordinate

opposing forms of dynamic encoding allows a neural population to avoid the inherent

losses of any single type of plasticity.

2.4. DISCUSSION 25

Figure 2.16: Model of sensitization. (a) Sensitization results from the di↵erence betweentwo adapting pathways, one excitatory and one inhibitory. In each pathway, the stimulusis passed through a linear filter, L, a threshold, N , and then an adapting block, A. Theadapting block is a feedforward module. In the inhibitory pathway, the input, u(t), is con-volved with an exponential filter, F

A

, yielding F

A

⇤u (see methods). The input, u(t), is thendivided by the filtered input, F

A

⇤u, such that the output of the adapting block, v(t), has asmaller amplitude than the input, u(t). A temporal filter, L

Q

, and saturating function, NQ

,is applied to the inhibitory pathway before the two pathways are combined. (b) Response ofthe model to an input that repeated, and was identical during L

early

and Llate

. (c) Averageresponses over many white noise sequences, shown at di↵erent stages in the model. (v) Inthe inhibitory pathway, the response decreases during high contrast, and recovers duringlow contrast. (w) The synaptic functions decrease the response modulation during highcontrast. (y) The decrease in inhibition at the transition to low contrast elevates activity inthe excitatory pathway. (z) The final adapting block, A

E

, in the excitatory pathway yieldsadaptation during high contrast, and preserves sensitization during low contrast.


2.5 Materials and Methods

2.5.1 Experimental preparation

We recorded from retinal ganglion cells of larval tiger salamanders, mice, and rabbits

using an array of 60 electrodes (Multichannel Systems) as described (Baccus and

Meister, 2002). Ringer solution (124 mM NaCl, 2.6 mM KCl, 2 mM CaCl2, 2 mM

MgCl2, 1.25 mM NaH2PO4, 26 mM NaHCO3, 22.2 mM glucose) perfused the mouse

retina at 32� 35�C and the solution maintained a pH of 7.35� 7.4 by aeration with

95/5% O2

/CO2

. Ames medium perfused the rabbit retina at 37�C.

A video monitor projected the visual stimuli at 30 Hz using Psychophysics Toolbox

(Brainard, 1997; Pelli, 1997) in Matlab (Mathworks). Stimuli were uniform field with

a constant mean intensity, M , of 8 � 10 mW/m2 and were drawn from a Gaussian

distribution unless otherwise noted. Contrast is defined as � = W/M , where W is the

standard deviation of the intensity distribution, unless otherwise noted. To measure

changes in firing rate for adapting and sensitizing cells (Figure 2.1a), for salamander,

80 trials were presented, alternating between 4 s high (35%) and 16 s low contrast

(5%). For mouse, 104 trials were presented of 15 s high (30%) and 15 s low contrast

(9%). For the measurement of the average time to the first spike after the transition

to low contrast (Figure 2.1b), results were pooled over 5 experiments, with >50 trials

for each cell. To measure the development of sensitization (Figure 2.1e), conditions

were interleaved in blocks of 17 trials for a total of 102 trials in each condition.

2.5.2 Linear-Nonlinear models

LN models (Figure 2.2) consisted of the light intensity passed through a linear tem-

poral filter, which describes the average response to a brief flash of light, followed

by a static nonlinearity, which describes the threshold and sensitivity of the cell. To

compute the model, the stimulus, s(t), was convolved with a linear temporal filter,

F (t), which was computed as the time reverse of the spike triggered average stimulus,

such that

2.5. MATERIALS AND METHODS 27

g(t) =

ZF (t� ⌧)s(⌧)d⌧. (2.1)

A static nonlinearity, N(g), was computed by comparing all values of the firing

rate, r(t), with g(t) and then computing the average value of r(t) over bins of g(t). The

filter, F (t), was normalized in amplitude such that it did not amplify the stimulus,

i.e. the variance of s and g were equal (Baccus and Meister, 2002). Thus, the linear

filter contained only relative temporal sensitivity, and the nonlinearity represented the

overall sensitivity of the transformation. Adapting and sensitizing cells were equally

well fit by an LN model. Model and data had a correlation coe�cient of 56± 2% for

adapting cells, and 61 ± 3% for sensitizing cells. The sigmoidal function used to fit

the nonlinearities was

y = x0

+m

1 + exp⇣

x

1

/

2

�x

r

⌘ , (2.2)

where x0

is the basal firing rate, m is the maximal firing rate, x1

/

2

is the x value at

50% of maximal firing, and r controls the maximal slope.

2.5.3 Adaptive index

The adaptive index was r

early

�r

late

r

early

+r

late

, where rearly

and rlate

are the firing rates during a

3 s window beginning during Learly

and Llate

, respectively. Only cells that responded

during rearly

and rlate

were included.

2.5.4 Receptive fields

Spatio-temporal receptive fields were measured in one or two dimensions by the stan-

dard method of reverse correlation (Chichilnisky, 2001) of the spiking response with

a visual stimulus consisting of either lines or squares. The spatio-temporal recep-

tive field was approximated as the product of a spatial profile and a temporal filter

(Olveczky et al., 2003). The normalized distance between receptive fields (Figure 2.6f)

was the spacing, S = d/(r1

+ r2

), where d is the distance between the center of the


two cells, and r1

and r2

are the radii of the two cells along the line connecting their

centers.

2.5.5 Discriminability

The average discriminability between nearby stimuli (Dayan and Abbott, 2009) as a

function of the stimulus was estimated as:

d0(g) =p

IF

(g), (2.3)

where IF

, the Fisher information, was computed as,

IF

(g) = N0(g)TQ(g)�1N0(g) +1

2Tr[Q0(g)Q�1(g)Q0(g)Q�1(g)]. (2.4)

Total discriminability was computed as d0 =Rd0(g)dg. The vector N0(g) is the deriva-

tive of the nonlinearity for a population of cells with respect to the filtered stimulus

g, Q(g) is the covariance matrix as a function g, and the function Tr is the trace of

a matrix (Abbott and Dayan, 1999). Nonlinearities, N(g), were sigmoidal fits to the

measured nonlinearities. The diagonal terms of Q(g), which were the variance of each

cell as a function of the stimulus g, were empirically well fit by a combination of mul-

tiplicative noise � that depended on g, and additive noise � that was independent of

g. This relationship was fit to the data (Figure 2.14c and Figure 2.15c) for sensitizing

and adapting cells during Learly

and Llate

,

Qii

(g) = �Ni

(g) + �. (2.5)

Only sensitizing cells had significant additive noise. The o↵-diagonal terms of Q(g),

the covariance between cells, were well fit by the geometric mean of the two variances

weighted by distance (Figure 2.11a),

Qij

= c(dij

)qQ

ii

(g)Qjj

(g). (2.6)


The correlation coe�cient c(dij

) decayed exponentially as a function of distance be-

tween two cells (Figure 2.11b). Di↵erent functions c(dij

) were fit during Learly

and

Llate

for pairing within and between adapting and sensitizing cells. The fractional loss

in discriminability during Learly

was 1� (d0early

/d0late

). Distance values dij

were taken

from a complete population of sensitizing and adapting cells spanning ⇠1 mm (Figure

2.6e). Error was computed by multiple random draws from a set of 21 adapting and

13 sensitizing cells.

2.5.6 Models of contrast normalization

Nonlinearities, N�

(g), were computed across 12 steady-state contrasts ranging from

3� 36%. The basic model of normalization by the contrast, M�

, was computed as:

M�

= N(g

�), (2.7)

where � is the contrast, and a single function N() was chosen to minimize the error

between model and data, E�

, defined as the average rms di↵erence between the model

and the set of nonlinearities, N�

. The model of normalization following a threshold,

M�

, was computed as:

M↵

= N

✓U↵

(g)

�

◆, (2.8)

where U↵

is a threshold function. In practice, because the threshold of U↵

was nearly

always lower than that of N , U↵

could be substituted with a simpler form having a

single parameter, ↵,

M↵

= N

✓g � ↵

�

◆. (2.9)

The nonlinearity N() and ↵ were similarly chosen to minimize the error, E↵

. The

model normalizing each curve separately, Mfull

, was computed as:

Mfull

= N

✓g � ↵(�)

c(�)

◆, (2.10)


where in addition to a single N(), a separate ↵ and c were chosen for each N�

to

minimize the error, Efull

. For all models sigmoid fits to the data were used for N�

.

We compared the relative performance of M↵

to M�

and Mfull

by computing (E�

�E

↵

)/(E�

�Efull

). Relative toM�

, the single parameter modelM↵

captured 92.6±1.0%

for adapting cells (n = 40) and 85.6± 1.8% for sensitizing cells (n = 12), of the error

reduction produced by Mfull

, which contained 22 parameters.

Thresholds were computed from a fit to a nonlinearity using the equation:

N(x) =

(0 if x < ✓

ax� ✓ if x � ✓, (2.11)

where ✓ is the threshold, and a is the slope above threshold. The line above threshold

was fit below saturating levels of the nonlinearity.

2.5.7 Information theory

To gather su�cient data to compute the mutual information after a transition to low

contrast, Learly

intervals occurred in di↵erent periods than Llate

. To gather data for

Learly

, the stimulus alternated between 20 s of identical high contrast pulses and 2

s of low contrast containing 8 randomly chosen stimulus intensities. To gather data

for Llate

, the stimulus consisted of a continuous 44 s sequence of random low contrast

pulses. Learly

and Llate

conditions were alternated every 180 s. The response to stimulus

pulses separated by 0.5 s was defined as a series of spike counts in bins of duration

150 ms (Figure 2.14a), or in durations ranging from 10�150 ms (Figure 2.15b). Each

response spanned a window of 150 ms, which included all spikes from a given pulse

of the stimulus. Mutual information was computed by taking the di↵erence between

the total response entropy, H(R), and the noise entropy, H(R|S), where the entropy

(H) is

H(X) = �X

x

p(x)log2

p(x). (2.12)


The stimulus specific information (ISSI

) was computed as:

ISSI

(s) =X

r

p(r|s){H(S)�H(S|r)}. (2.13)

This measure is the average reduction of uncertainty gained from a measurement of

the set of responses given a particular stimulus s (Butts, 2003). The weighted average

ISSI

over all stimuli is the mutual information between stimulus and response. All

information measurements were corrected for limited data by computing the infor-

mation for fractions of the data and then extrapolating the result to infinite data

(Strong et al., 1998; Gollisch and Meister, 2008) (see Figure 2.15d).

2.5.8 Sensitization model

The model for sensitization was generated to reproduce the qualitative behavior of

sensitizing cells. Excitatory and inhibitory adapting pathways were linked by a synap-

tic pathway. A prime candidate for the proposed inhibitory pathway could be the sig-

nal passed through amacrine cells, inhibitory interneurons in the retina (Baccus and

Meister, 2002). Variables correspond to symbols in Figure 2.16. The biphasic linear

filter for both pathways matched the time to peak of sensitizing cells,

g(t) =

ZL(t� ⌧)s(⌧)d⌧. (2.14)

For the inhibitory pathway, a linear-threshold function contained a threshold set at

the mean of the input g(t),

u(t) = NI

(g) =

(0 if g < hgig(t)� hgi if g � hgi

, (2.15)

Brackets, h...i, denote the average quantity. Adaptation occurred through a feedfor-

ward divisive operation. This adaptation could either occur at the level of a bipolar

or amacrine cells (Baccus and Meister, 2002). The input u(t) was convolved with an

exponential filter, FA

, and then u(t) was divided by the result. A constant term in


the denominator set the magnitude of adaptation,

v(t) = AI

(u(t)) =u(t)

2 +RFA

(t� ⌧)u(⌧)d⌧. (2.16)

The time constant of FA

, representing the timescale of integration of the contrast,

was 2 s,

FA

(t) = 0.5e�t

2s (2.17)

The connection between the two pathways contained a temporal filter LQ

defined as

an alpha function with a time to peak of 150 ms,

LQ

(x) = 2x

.15

exp��x�.15

.15

�

wL

(t) =RLQ

(t� ⌧)v(⌧)d⌧. (2.18)

This delay could result from the action of metabotropic GABA receptors (Maguire

et al., 1989). The connection between the two pathways also contained a saturating

nonlinearity NQ

,

w(t) = NQ

(wL

(t)) =0.3

1 + exp⇣

0.03�w

L

(t)

0.01

⌘ , (2.19)

the e↵ect of which was to diminish the modulation of inhibitory transmission at

high contrast, and amplify the modulation at low contrast. This saturation could

arise from either synaptic depression or receptor desensitization (Li et al., 2007).

An alternative source of the inhibitory pathway could be that adaptation is in the

bipolar cell, and the delay and saturation (LQ

and NQ

) are produced by the filtering

and membrane properties of an intervening amacrine cell (Baccus and Meister, 2002).

The two pathways combined linearly,

x(t) = g(t)� w(t), (2.20)

The pathways combined prior to the excitatory pathway threshold indicating that the

amacrine cell might synapse presynaptically onto a bipolar cell terminal. The nonlin-

earity, NE

, in the excitatory pathway was a linear-threshold function with threshold


↵, representing the initial threshold ↵ in the model M↵

in Figure 2.10,

z(t) = NE

(x(t)) =

(0 if x(t) < hx(t)i+ ↵

x(t)� (hx(t)i+ ↵) if x(t) � hx(t)i+ ↵, (2.21)

with ↵ set to 0.025. Finally, the excitatory input y(t) was passed through another

stage of divisive adaptation, and the result thresholded by an output nonlinearity NF

.

The threshold ✓ represented the final threshold ✓ of the model M↵

from Figure 2.10,

z(t) = NF

(AE

(y(t))) = NF

⇣y(t)

3+

RF

A

(t�⌧)y(⌧)d⌧

⌘

NF

(x) =

(0 if x < ✓

x if x � ✓

. (2.22)

✓ was set to 0.005. Error indicates standard error of the mean, computed across cells,

unless otherwise noted.

Chapter 3

Spatial segregation of adaptation

and predictive sensitization in

retinal ganglion cells

This chapter has been accepted to Neuron as “Spatial segregation of adaptation and

predictive sensitization in retinal ganglion cells,” with author list: Kastner DB, Baccus

SA.

3.1 Summary

Sensory systems change their sensitivity based upon recent stimuli to adjust their

response range to the range of inputs, and to predict future sensory input. Here we

report the presence of retinal ganglion cells that have antagonistic plasticity, showing

central adaptation and peripheral sensitization. Ganglion cell responses were captured

by a spatiotemporal model with independently adapting excitatory and inhibitory

subunits, and sensitization requires GABAergic inhibition. Using signal detection

theory we show that the sensitizing surround conforms to an optimal inference model

that continually updates the prior signal probability. This indicates that small recep-

tive field regions have dual functionality—to adapt to the local range of signals, but

34

3.2. INTRODUCTION 35

sensitize based upon the probability of the presence of that signal. Within this frame-

work, we show that sensitization predicts the location of a nearby object, revealing

prediction as a new functional role for adapting inhibition in the nervous system.

3.2 Introduction

Visual scenes have correlations over space and time that arise from the properties

of environmental conditions, objects, eye movements, and self motion (Field, 1987;

Ruderman and Bialek, 1994; Frazor and Geisler, 2006). Because of this statistical

regularity, it has long been thought that the visual system might improve its e�ciency

and performance by adjusting its response properties to the recent history of visual

input (Barlow et al., 1957; Blakemore and Campbell, 1969; Laughlin, 1981).

In early stages of sensory systems, studies of how stimulus statistics influence

the neural code have focused mainly on adaptation, which also occurs throughout

the brain (Smirnakis et al., 1997; Nagel and Doupe, 2006; Maravall et al., 2007;

Tobler et al., 2005; Kohn and Movshon, 2003). Given the recent stimulus distribution,

response properties change over multiple time scales to encode more information and

remove predictable parts of the stimulus (Fairhall et al., 2001; Hosoya et al., 2005;

Wark et al., 2009; Ozuysal and Baccus, 2012). A primary concept underlying studies

of adaptation is that early sensory systems should transmit as much information as

possible for further processing in the higher brain (Atick, 1992; van Hateren, 1997).

Studies in the higher brain and in behavior often take a di↵erent point of view:

the goal is to generate a behavior given a stimulus (Kersten et al., 2004; Yuille and

Kersten, 2006; Kording and Wolpert, 2006; Schwartz et al., 2007b). Accordingly, such

studies highlight the benefit of predicting future stimuli, using inference about the

prior probability of future sensory input for choosing appropriate actions.

Recent results indicate that many ganglion cells encode specific features with a

sharp threshold, implying that these ganglion cells make a decision as to the presence

of a feature (Olveczky et al., 2003; Zhang et al., 2012). If so, one might expect that

plasticity in the retina also take advantage of the principles of signal detection and op-

timal inference. At the photoreceptor to bipolar synapse, even though at the dimmest

36 CHAPTER 3. PREDICTIVE SENSITIZATION

light level the threshold of the synapse is close to the optimal level to perform signal

detection, it does not appear that any adjustment due to the prior probability of a

signal occurs (Field and Rieke, 2002). This problem, however, has not been explored

at the level of ganglion cells. Given the complex circuitry of the inner retina (Roska

and Werblin, 2003) and the di↵erent types of ganglion cell plasticity (Hosoya et al.,

2005; Olveczky et al., 2007; Kastner and Baccus, 2011), we examined this plasticity

in the context of both signal transmission and signal detection.

Here we systematically mapped the spatial arrangement of plasticity in retinal

ganglion cells, finding that many ganglion cells adapted to a localized stimulus, but

sensitized in the surrounding region. The spatiotemporal properties of this plasticity

were captured by a computational model having independently adapting excitatory

subunits, producing localized adaptation, and larger adapting inhibitory subunits,

producing sensitization.

Using knowledge of the detailed computation, we then combined signal detection

theory and optimal inference to qualitatively account for several properties of sensiti-

zation. This indicated that sensitization creates a regional prediction of future input

based upon prior information of local signal correlations in space and time. We then

test this theory in a more natural context by showing that object motion sensitive

ganglion cells use sensitization to predict the location of a camouflaged object.

Finally, we show that sensitization requires GABAergic inhibition, and that di↵er-

ent levels of inhibition can account for di↵erences in sensitization between ganglion

cell types. Together these results show how two functional roles of plasticity are

combined in a single cell—to adapt to the range of signals, and predict when those

signals are more likely to occur. Furthermore, these results establish a functional role

for adapting inhibition in predicting the likelihood of future sensory input based upon

the recent stimulus history.

3.3 Results

We first measured the spatiotemporal region whose statistics control the sensitiv-

ity of a cell—the adaptive field. Previous measurements of spatial properties of the

3.3. RESULTS 37

adaptive field focused primarily on fast adaptation—changes in sensitivity occurring

within the integration time of a cell. These fast, suppressive e↵ects in the retina and

lateral geniculate nucleus extend beyond the receptive field center (Victor and Shap-

ley, 1979; Werblin, 1972; Olveczky et al., 2003; Bonin et al., 2005; Solomon et al.,

2002). Considerably less e↵ort has been devoted to measurements of the adaptive

field with changes in sensitivity lasting longer than the integration time of the cell.

Recent results have shown that delayed changes in sensitivity in salamanders, mice,

and rabbits have two opposing signs, adaptation and sensitization (Kastner and Bac-

cus, 2011). The spatial extent of adaptation has been measured as it pertains to

mechanisms of adaptation within the circuit, indicating that small regions of the gan-

glion cell receptive field adapt somewhat independently (Brown and Masland, 2001).

Spatial properties of sensitization have not been measured.

To measure prolonged changes in sensitivity at di↵erent spatial locations, we pre-

sented a low contrast flickering checkerboard. Every 20 s, one region of space changed

to high contrast for 4 s (Figure 3.1a,b). The high contrast stimulus was presented at

di↵erent retinal locations, allowing for the creation of a spatial map of slow changes

in sensitivity. We compared the firing rate during two time intervals after the high

contrast spot disappeared: Learly

, 0.5 to 3 s after the transition to all low contrast, and

Llate

, 13.5 to 16 s after the transition to all low contrast, a time that approximated

the steady state.

3.3.1 Center-surround adaptive fields

Fast O↵-type adapting and sensitizing cells are two defined cell types that each form

an independent mosaic in the salamander retina (Kastner and Baccus, 2011). In

response to a spatially global transition between high and low contrast, defined as

the standard deviation of the intensity computed over time, adapting cells decrease

their sensitivity following a high contrast stimulus, whereas sensitizing cells increase

their sensitivity.

Fast O↵ cells that adapted to a global contrast change also adapted when the high

contrast spot was directly over their receptive field center. However, when the high


contrast spot neighbored their receptive field center they sensitized, increasing their

response during Learly

relative to Llate

(Figure 3.1c,d). Thus, the adaptive field of this

type of cell exhibited spatial antagonism, showing central adaptation but peripheral

sensitization.

Sensitizing cells also had a spatially varied response to a local high contrast spot.

During Learly

, these cells sensitized both in their central and surround region (Figure

3.1c,d). However, when the firing rate was examined at an even earlier time, from

0�0.5 s after the transition from high contrast (L0�0.5

), sensitizing cells also adapted

in their center. Thus both cell types had an adapting center and sensitizing surround,

although with apparently di↵erent dynamics in their adaptation. In comparison, On-

type cells had a spatially monophasic adaptive field, adapting both in the central and

surround regions. This was the case for all On cells examined (Figure 3.1c,d).

Although a change in firing rate reveals an overall change in the response of a

Figure 3.1 (facing page): Three di↵erent adaptive fields in the retina. (a) A single frame ofthe stimulus when a high contrast square was presented. Boxes were either 300 µm or 200µm on each side. (b) Temporal sequence of the binary stimulus in the di↵erent regions. Highcontrast was 100% and lasted 4 s in a single region, indicated by the black box in panel (a).Low contrast was 5%. Contrast was defined to be: C = I

max

�I

min

I

max

+I

min

, with I

max

and I

min

beingthe maximum and minimum intensity values. (c) Response of an adapting On (left), fast-O↵adapting (middle), and fast-O↵ sensitizing (right) cell to the adaptive field stimulus. PSTHsare shown with the high contrast region (square) located at two positions relative to thereceptive field center (circle), and show the average response for >60 stimulus sequences.Data binned at 0.5 s. Colored responses indicate when all regions were low contrast. Blackindicates the time of the local high contrast. (d) Adaptive indices for all cells. The color ofeach point in the polar plot indicates the cell’s adaptive index when the adapting square wasat that location. The origin indicates the cell’s receptive field center. The adaptive index is:A =

r

early

�r

late

r

early

+r

late

, where r

early

is the average firing rate during L

early

, and r

late

is the average

firing rate during L

late

. Data comes from 9 adapting On, 21 sensitizing, and 74 adapting O↵cells. For sensitizing cells, adaptive fields are shown during L

early

(top), and during L

0�0.5

, 0 � 0.5 s after high contrast (bottom) (e) Average adaptive index for each cell type as afunction of distance from the cell’s center. Results were averaged across angles in (d), andcolors correspond to (c). Solid black lines are single or di↵erence of Gaussian fits to thedata. For sensitizing cells, the larger standard deviation (s.d.) was 0.41 mm. For adaptingO↵-cells, the smaller s.d. was 0.11 mm and the larger s.d. was 0.30 mm. For adapting Oncells, a single Gaussian was used with an s.d. of 0.32 mm. In (e), error values are s.e.m. andwere computed across cells contributing to each point.

3.3. RESULTS 39

c

a

Inte

nsity

4 s

Learly Llateb

300 µmd

e 0.50

-0.5

Adap

tive

Inde

x

0.50Distance (mm)

Learly

L0 - 0.5


cell, we tested whether changes in firing rate observed following a local high contrast

stimulus were accompanied by spatial changes in visual sensitivity. We computed the

sensitivity at each spatial location during Learly

and Llate

using a spatiotemporal filter

representing the receptive field (see methods). In all cell types, a prolonged adaptive

change in sensitivity underlied the changes in activity as measured using a spatiotem-

poral linear-nonlinear (LN) model (Figure 3.2a,b). Therefore, three di↵erent popu-

lations of cells—fast-O↵ adapting cells, fast-O↵ sensitizing cells and On cells—had

distinct spatiotemporal adaptive properties, with O↵ cells exhibiting center-surround

adaptive fields.

Adapting Off!Sensitizing!

b

-0.6-0.3

00.3

∆ se

nsiti

vity

0.50Distance (mm)

a Adapting On!

Figure 3.2: Sensitivity changes underlie activity changes in the adaptive field. (a) Sensitivitywas measured in each spatial region using a spatiotemporal linear-nonlinear (LN) model (seemethods). Average di↵erence in sensitivity at each location for each cell type, normalizedby the average sensitivity at each location during L

late

. The map of � sensitivity for eachcell was centered on the location of the high contrast region. Data comes from 7 adaptingOn, 43 adapting O↵, and 10 sensitizing cells. (b) Average di↵erence in sensitivity betweenL

early

and L

late

for each cell type as a function of distance from the cell’s center. Datafrom panel (a) were averaged across angles. Colors correspond to labels above figures in(a). Error values (s.e.m.) are obscured by the data points, and were computed across cellscontributing to each point.

3.3.2 A model unifies the three adaptive fields

To gain insight into both the computation and potential mechanisms that underlied

the construction of the adaptive field, we modeled the center-surround adaptive field

3.3. RESULTS 41

by extending a previous model that produced sensitization using an adapting in-

hibitory pathway (Kastner and Baccus, 2011). In this model, adapting excitation and

inhibition combine, such that a high contrast stimulus causes inhibitory transmission

to adapt, thus reducing inhibition and generating a residual sensitization after the

high contrast ceases.

To extend the previous model, we added adapting spatial subunits for both excita-

tory and inhibitory pathways (Figure 3.3a). Excitatory subunits, representing bipolar

cells, had receptive fields smaller than that of the ganglion cell, and inhibitory sub-

units were three times larger than excitatory subunits (Figure 3.3a). This size ratio

was taken from a di↵erence of Gaussians fit to the center-surround adaptive field (Fig-

ure 3.1e). Based upon the earlier model, inhibition was delivered prior to a strong

threshold, as occurs at the presynaptic terminal of the bipolar cell (Heidelberger and

Matthews, 1992). The ganglion cell then received a spatially weighted average of the

excitatory subunit outputs (Figure 3.3b). Most parameters of the model were taken

from previous full-field experiments with fast-O↵ sensitizing cells (Kastner and Bac-

cus, 2011). Two spatial parameters, representing the scale of excitatory and inhibitory

subunits, were calculated from the spatial adaptive field averaged across a popula-

tion of only fast-O↵ adapting cells, which had center-surround adaptive fields (Figure

3.1e).

Using a stimulus similar to that shown in Figure 3.1a,b, the model produces

an output that either adapts or sensitizes depending upon the location of the high

contrast (Figure 3.3c), consistent with the responses of cells with center-surround

adaptive fields. Thus, a di↵erent spatial scale of adapting excitation and inhibition

yield a center-surround adaptive field, just as a di↵erent scale for simple excitatory

and inhibitory inputs yield a center-surround receptive field (Thoreson and Mangel,

2012). Because the three types of adaptive fields had distinct properties, one might

expect that di↵erent circuitry would be required to generate the di↵erent adaptive

fields. However, we tested whether we could generate the di↵erent adaptive fields

simply by changing the parameters of the model, but not the circuitry. We were

able to reproduce all three adaptive fields by simply changing the strength of the

inhibitory weighting onto the excitatory subunits (Figure 3.3d). The adaptive fields


Excitatory

Inhibitory

Ganglion

cell

subunits

subunits

a b

c

d

−

wI

Inhibitory!

Excitatory!

wE

-0.5

0

0.5

Adap

tive

inde

x

wmax

Adapting!Sensitizing!

Figure 3.3: Amount of adapting inhibition can determine the type of adaptive field. (a)Spatial scale of the subunits in a model of a ganglion cell with a center-surround adaptivefield (see methods). Colored bars show the di↵erent locations used for the high contrast.Line thickness indicates the weight of a given subunit onto the ganglion cell. (b) Boththe inhibitory and excitatory subunits are composed of spatio-temporal receptive fields,threshold nonlinearities, and adaptive blocks (arrow in circle). The inhibitory populationwas spatially weighted (w

I

) before inhibiting an excitatory subunit, with a weighting equalto the spatial overlap between each excitatory and inhibitory subunit. The excitatory pop-ulation was likewise spatially weighted (w

E

) and then passed through a threshold to createthe output of the model. The average responses for two excitatory subunits are shown inresponse to a spot centered over the ganglion cell receptive field (colored bar in panel (a)matching the low contrast response). Markers in the top right corner of the two subunitresponses correspond to their weighting, w

E

, in the model output and their spatial locationin (a). (c) Output of the model (top) for three di↵erent locations of high contrast corre-sponding to the colored bars in (a) that match the low contrast responses. Example dataPSTHs from fast-O↵ adapting cells are shown below for comparison. (d) Adaptive indicesfrom models with di↵erent maximal inhibitory weighting (w

max

) (see methods). The valueof the adaptive index is plotted for when the high contrast spot was located directly aboveor just neighboring the ganglion cell receptive field. Line colors correspond to the bars in(a). Green and purple icons represent the type of adaptive fields measured during L

early

that correspond to that range of wmax

.

3.3. RESULTS 43

of sensitizing cells resulted from the strongest adapting inhibition, center-surround

adaptive fields resulted from intermediate adapting inhibition, and a monophasic

adaptive field, showing adaptation, resulted from the weakest adapting inhibition.

Thus, all the three adaptive fields, as well as intermediate examples that we did not

encounter experimentally, could arise solely by changing the strength of inhibition

from a single population of amacrine cells onto di↵erent bipolar cells.

This adaptive field (AF) model predicts several distinct features of the data. Sen-

sitizing cells produce less sensitization when they are directly centered under a high

contrast spot than when the spot is slightly o↵set from the receptive field center

(Figure 3.1e, 3.2a,b, and 3.3d). The model also predicts that when the high contrast

region is further removed from the receptive field center, the cell had a larger steady

state response at low contrast than high contrast, but an elevated response at the

transition to both low and high contrast (Figure 3.3c). This occurs because in the

periphery of the receptive field center the weight of inhibition is greater than exci-

tation by virtue of the greater spatial spread of inhibition (Figure 3.3a). However, a

delay in inhibitory transmission causes excitation to be transiently greater than inhi-

bition at the transition to high contrast. Thus, a model with independently adapting

excitation and inhibition predicts multiple distinct spatiotemporal properties of the

adaptive field.

3.3.3 Subcellular sensitizing and adapting subunits

The AF model contains subunits that independently undergo plasticity, with the

final response exhibiting the summed adaptive behavior of each subunit. Because

these subunits are smaller than the receptive field center, the model predicts that

individual regions of the response of the cell may sensitize, even when the overall

firing rate response adapts (Figure 3.3b). We tested whether the AF model, fit to a

coarser spatial stimulus (Figure 3.1), would predict changes in sensitivity at a high

spatial resolution within a single cell without reoptimizing the model. We stimulated

the retina with a low contrast white noise stimulus composed of concentric flickering

annuli centered on a single ganglion cell (Figure 3.4a,b). In the central 200 µm, every


20 s the stimulus turned into a uniform circle that flickered with high contrast for 4

s. The diameter of the high contrast spot was smaller than the receptive field center

of a cell.

We measured the subcellular changes in sensitivity following high contrast using

a spatiotemporal LN model of the receptive field similar to Figure 3.2a, except that

each spatial region represented an annulus. This allowed for a higher resolution mea-

surement with respect to distance. We then compared the sensitivity during Learly

and

Llate

at each spatial location (Figure 3.4c). Cells with a center-surround adaptive field

showed negative changes in sensitivity within the receptive field center below the high

contrast, and positive changes in sensitivity next to the location of the high contrast,

just as predicted by the AF model (Figure 3.4c). Thus, even though the AF model

parameters were fit using di↵erent experimental data (full field and checkerboard

changes in contrast), the model predicted subcellular adaptation and sensitization

using concentric annuli. Previously, it was shown that adaptation occurs at a subcel-

lular scale (Brown and Masland, 2001). The present result shows that interneurons

contribute spatially localized plasticity both for adaptation and sensitization within

the adaptive field.

3.3.4 Adaptation and sensitization in a rapidly changing en-

vironment

In the AF model, excitatory and inhibitory subunits adapted independently. To fur-

ther explore this property, we tested whether the model fit to the localized step change

in contrast (Figure 3.1a,b) predicted the response when all regions were activated to-

gether by a uniform field stimulus whose contrast changed with a broad temporal

bandwidth. Such rapid changes in contrast are found during natural viewing condi-

tions where the eye is moved frequently (Frazor and Geisler, 2006). We presented a

uniform field Gaussian stimulus where the temporal contrast (standard deviation of

intensity) changed randomly every 0.5 s (Figure 3.5a). The value of the contrast was

drawn from a uniform distribution. We then computed a temporal filter representing

the average e↵ect of a brief increase in contrast by correlating ganglion cell spiking

3.3. RESULTS 45

a b

c

1

0.5

0

Nor

mal

ized

sens

itivi

ty/a

rea

0.20Distance (mm)

Figure 3.4: Changes in sensitivity within the receptive field center. (a) A single frame of thestimulus used to map changes in sensitivity at a high resolution, composed of concentricannuli with radii increasing by 50 µm that were modulated independently with Gaussianwhite-noise having a 5% contrast. In the central 200 µm, the stimulus alternated between16 s of the 5% low contrast stimulus, and 4 s of a uniform circle that flickered with a 100%Michelson contrast. (b) Normalized spatial sensitivity of an adapting O↵ cell during L

late

,computed as the rms value of the spatiotemporal receptive field at each distance for thestimulus in (a). Because annuli had a di↵erent area unlike a checkerboard stimulus, thesensitivity at each distance was normalized by the area of the annulus that contributed tothat point in the receptive field. The vertical dotted line shows the point of zero crossing,which was used to define the center of the receptive field. (c) Average di↵erence between thespatial sensitivity during L

early

and L

late

for adapting O↵ cells (left) (n = 7) and the modelfrom Figure 3.3 (right). The spatial sensitivities during L

early

and L

late

were normalizedby the maximum sensitivity during L

late

. Positive values indicate regions that were moresensitive during L

early

compared to L

late

, while negative values indicate regions that wereless sensitive during L

early

compared to L

late

. The solid vertical line shows the extent of thecentral circle, which was the only location that experienced the high contrast. The dottedvertical line shows the average point where the total sensitivity within the receptive fieldcrossed zero, indicating the border between receptive field center and surround, as shownfor a single cell in (b).


with the random sequence of contrast (Figure 3.5b). This temporal filter represented

the temporal adaptive field, which is the spatial average of the spatiotemporal adap-

tive field. Note that this computation measures the average contribution of both

increases and decreases in contrast, analogous to how the linear receptive field aver-

ages over both increases and decreases in intensity. All of these functions had a large

peak in the first time bin, from 0 � 0.5 s, something expected since higher contrast

invariably produces a higher firing rate. To examine the temporal adaptive field, we

therefore focused on the component of the temporal filter outside of the first 0.5 s

bin, representing how the recent history of contrast outside the integration time of

the cell influenced the firing rate.

-1

0

Filte

r (s-1

)

42Delay (s)

42

Data AF Modelc

Inte

nsity

Con

trast

1 s

b

4

2

0

-2

Filte

r (s-1

)

420Delay (s)

SensitizingAdapting OffAdapting On

a

Figure 3.5: Temporal adaptive fields during rapidly changing contrast. (a) Experimentaldesign. The spiking response of ganglion cells was recorded in response to a Gaussian whitenoise stimulus, where the contrast, �(t), changed randomly every 0.5 s drawn from a uniformdistribution between 0 and 35% contrast. (b) Example temporal adaptive fields, whichwere calculated as the spike triggered average of the contrast, �(t). (c) Average temporaladaptive fields for ganglion cells (left), and the output of the AF model from Figure 3.3(right), computed with no refitting of AF model parameters for the rapidly changing contraststimulus. In the data figure, the width of the lines indicates the s.e.m. For the model, threeinhibitory weightings (Figure 3.3d) were chosen to represent the three di↵erent types ofspatial adaptive fields. The x-axis begins at 0.5 s to highlight the slower changes due tochanging contrast. All filters are normalized in amplitude to have the same rms value.

3.3. RESULTS 47

The three types of cells had distinct temporal adaptive fields (Figure 3.5b,c).

Adapting On cells had a slow negative monophasic filter, indicating that a brief in-

crease in contrast decreased activity between 0.5�3 s. Sensitizing cells had a biphasic

filter, such that elevations of contrast initially decreased activity, but only for a du-

ration of up to 1 s. With a delay of ⇠1 s, contrast on average increased activity, and

the e↵ect then decayed away after ⇠3 s.

Adapting O↵ cells had a temporal adaptive field that was negative and monopha-

sic, but with a more rapid decay than that of adapting On cells, indicating that an

increase in contrast caused a decrease in activity between ⇠0.5 and 1.5 s (Figure 3.5c).

After ⇠1 s the temporal filter of the adaptive O↵ cell was between those of the other

two cells. Just as with the spatial adaptive field, where adapting O↵ cells showed a

mixture of adaptation and sensitization, the temporal adaptive field of adapting O↵

cells appeared to be a mixture of the time courses of the two extremes. Although

sensitization did not completely cancel adaptation, adaptation was reduced at later

times.

We then evaluated whether the AF model could reproduce the di↵erent tempo-

ral adaptive fields using the same stimulus that changed in contrast with a broad

bandwidth (Figure 3.5a). For each of the three types of cells, we used a model with

a di↵erent strength of adapting inhibition. Even though the model parameters were

adjusted only using the spatial map of the adaptive field (Figure 3.1), we found that

the model reproduced the di↵erent average temporal adaptive fields in the three pop-

ulations, indicating that the same circuitry that underlies the spatial adaptive field

can su�ciently account for the temporal adaptive field. In particular, for adapting

O↵ cells with center-surround adaptive fields, the temporal filter in the model was

approximately an average of the filters of adapting On and sensitizing cells. Thus, a

model of the adaptive field fit to responses from a step change in contrast, captures

the adaptive dynamics during rapidly changing contrast.

Although the full spatio-temporal model (Figure 3.3) produces more complex be-

havior, such as asymmetric responses at increases and decreases in contrast, the com-

bined e↵ects of the subunits in the spatiotemporal model predict the response to

dynamically varying contrast. Because the model with independent subunits fit to


local adaptation predicts the sum total adaptation for spatially global stimuli, we

conclude qualitatively that excitatory and inhibitory subunits within the adaptive

field adapt independently.

3.3.5 Feature detection in Fast O↵ cells

Having characterized the combined spatiotemporal computation of adaptation and

sensitization, we then considered the functional relevance of the sensitizing region of

the adaptive field. Many sensory neurons encode specific visual features using a high,

sharp threshold, and signal when the stimulus matches that feature (Ringach and

Malone, 2007). In the retina, for example, object motion sensitive (OMS) (Olveczky

et al., 2003) and W3 cells (Zhang et al., 2012) selectively report the presence of

di↵erential motion.

We measured both di↵erential motion sensitivity and sensitization in the same

cells. We found that fast-O↵ adapting cells were object motion sensitive (OMS) cells,

suppressed by motion in the distant periphery, whereas fast-O↵ sensitizing cells were

not (Figure 3.6 and 3.7). Although they receive di↵erent levels of peripheral inhibi-

tion, the two cell types fire synchronously in response to a stimulus with no spatial

structure, and thus respond to the same local stimulus features (Kastner and Baccus,

2011). Consistent with a role as a feature detector, the nonlinearity of O↵-cells was

more strongly rectified than that of On cells using a previously described index of

rectification. This index measures the logarithm of the ratio of the maximum slope

of the nonlinearity to the slope at zero input (Chichilnisky and Kalmar, 2002). O↵

cells had an index of 2.2 ± 0.1 (n = 80), whereas On cells had an index of 1.3 ± 0.2

(n = 9), meaning that relative to the slope at an input of zero (the average input),

O↵ cells increased their slope ⇠8 times more than On cells.

3.3.6 Encoding a signal in a noisy environment

To better understand the function of sensitization, we formalized the apparent role

of fast O↵ cells as feature detectors using a simple model of optimal signal detection

that changes with stimulus history. In a signal detection problem, the position of

3.3. RESULTS 49

a b Global!

Background!Object!

Differential!

Figure 3.6: Distinct cell types for object motion sensitivity and global sensitization. (a)Schematic diagram of the stimulus to test for object motion sensitivity. A central objectregion was shifted either together with the background (global motion), or at a di↵erent time(di↵erential motion). (b) Histogram of the response ratio between global and di↵erentialmotion for adapting (n = 59) and sensitizing (n = 16) fast-O↵ cells.

a b c

Figure 3.7: Fast-o↵ adapting cells are object motion sensitive. (a) The average response of anadapting O↵ (top) and sensitizing (bottom) cell to a stimulus that changed back and forthbetween high (35%) and low (5%) contrast placed over the receptive field center. PSTHsbinned at 0.5 s show the average over 50 trials, each with a di↵erent stimulus sequence.(b) Spatial receptive fields of the cells in (a) relative to the location of the object region(box). (c) Average response to 10 repeats of alternating global and di↵erential motion (seemethods) for the same cells in (a).


the optimal threshold function depends upon the distributions of signal and noise,

as has been examined at the photoreceptor to bipolar cell synapse (Field and Rieke,

2002). Although the threshold at the photoreceptor to bipolar cell synapse does not

appear to change according to prior information about the probability of photons, we

considered that changes in the response function of ganglion cells reflects the changing

likelihood of a signal.

By recording intracellularly from O↵-type bipolar cells in response to a repeated

5% Gaussian white noise stimulus, we found that the noise was 0.44 ± 0.12 (n = 5,

mean ± s.d.) times the standard deviation of the recorded membrane potential fluc-

tuations (Figure 3.8a and 3.9). Thus, for weak, low contrast, signals the probability

distribution of an input, v, given the presence of a signal, p(v|s), greatly overlaps with

the probability distribution of that same input in the presence of only noise, p(v|⌘).This overlap creates a benefit from a careful threshold placement to discriminate

between the two conditions. Although both positive and negative signals are distin-

guishable from noise, because many ganglion cells have monotonic response curves,

we focused our analysis on positive signal deviations.

The probability that a particular voltage arises from the signal distribution de-

pends upon the prior probability, p(s), of the presence of a signal. Thus, when p(s)

increases, the optimal threshold decreases (Field and Rieke, 2002). What then would

lead to an increase in the prior signal probability? For the visual system, an important

source of prior information comes from the strong spatial and temporal correlations

present in natural visual stimuli (Geisler and Perry, 2009). Objects do not suddenly

disappear, therefore once they are detected they are highly likely to be present nearby

in space. We incorporated this natural visual prior into a spatiotemporal version of

an optimal inference model (Figure 3.8b), similar to that used previously (DeWeese

and Zador, 1998; Wark et al., 2009). The model has two steps. First, at each point in

time and space, a new measurement of intensity, vx,t

, combines with the prior prob-

ability of a signal, p(sx,t

), at that location to yield a new posterior estimate of signal

probability, p(s|vx,t

) (see methods). Second, at each point in time, the prior, p(sx,t+1

),

is updated from the posterior at the previous point in time p(s|vx,t

), smoothed by

a Gaussian function, h(x) (see methods), representing the di↵usion of an object or

3.3. RESULTS 51

edge due to the random walk movement of fixational eye movements. The integral of

h(x) was less than 1, reflecting the occasional possibility of saccadic eye movements

that redirect gaze to a di↵erent image location. When presented with a brief strong

stimulus (35% contrast) on a background of weak input (5% contrast), this optimal

model was biased in space and time to predict an increased probability that a signal

was present outside of the spatial range of the object, even after the object was no

longer detectable (Figure 3.8c). This optimal behavior was qualitatively similar to

the sensitizing field we observed in O↵-type ganglion cells (Figure 3.1).

We compared how the changes in the response function during sensitization corre-

spond with changes expected from the framework of ideal signal detection. The e↵ect

of a changing prior value, p(s), on the posterior probability, p(s|v), depends upon the

Figure 3.8 (facing page): Sensitization reflects an increased prior expectation of a signal.(a) Conditional probability of an input, v, given either signal, s, (5% contrast) or noise, ⌘(0% contrast). Thick line p(v|s) is the distribution of measured voltages from an O↵-typebipolar cell responding to a 5% contrast Gaussian white noise stimulus. Thick line p(v|⌘) isthe estimated noise measured from repeated presentations of the same stimulus. Thin linesare Gaussian fits to the data. (b) Schematic diagram of a recursive model whereby a one-dimensional spatiotemporal input, v

x,t

, illustrated as a bright stimulus at one point in space,x, is combined with a prior stimulus probability, p(s

x,t

), to yield a posterior, p(sx,t

|vx,t

).The colored curves indicate p(s

x,t

|vx,t

) as a function of vx,t

given di↵erent values of p(sx,t

).The posterior p(s

x,t

|vx,t

) is then smoothed by a spatial filter, h(k), to yield a new prior,p(s

x,t+1

). The integral of h(k) was 0.96, reflecting the fact that signals may disappear dueto saccadic eye movements. To convert the posterior probability to a firing rate, p(s

x,t

|vx,t

),is passed through a rectifying function, N(), which was normalized by the average ganglioncell firing rate. (c) Top, posterior probability, p(s

x,t

|vx,t

), at each point in space and timein the inference model in panel (b), in response to a stimulus that changed between 5%contrast and a 35% contrast bar applied at the region and time interval indicated by thethick black lines. Bottom, average time course of p(s

x,t

|vx,t

) at the spatial location indicatedby the arrow. The average is taken over 1000 trials of di↵erent intensity sequences but thesame change in contrast, analogous to experiments in Figure 3.1 where firing rate changesare computed over the same change in contrast but di↵erent intensity sequences. (d) Top,average posterior, hp(s|S)i, in the center of the object during L

early

and L

late

. Bottom, firingrate nonlinearities for a ganglion cells compared with the model firing rate output duringL

early

and L

late

. (e) Comparison of slope (top) and midpoint (bottom) of sigmoid fits todata and model nonlinearities during L

early

and L

late

. The abscissa is in units of s.d. at 5%contrast. Also compared are the change in nonlinearity slope and midpoint between L

early

and L

late

(�) for the data and model. The dotted line is the identity.


Data

210Model

321

Midpoint

Slope

LearlyLlateΔ

2

0Nor

mal

ized

firin

g ra

te

20Input v (σ)

1

0.5

0

< p(s

|v)>

LearlyLlate

DataModel

e c d

0.5

0

Con

ditio

nal

prob

abilit

y

210Input v (σ)

p(v|η)p(v|s)

a

2

0

Norm

alizedfiring rate

10.50p(s|v)

Nonlinearity Np(p(s|v))

0.10

-5 0 5Spatial offset k

Spatial filter h(k)

p(sx,t|vx,t)p(sx,t+1)

1

0.6

0.2

Posterior p(s|v)210

Input (v)

p(s)0.80.60.40.2

b

3.3. RESULTS 53

shapes of p(s|v) and p(v|⌘). For the case where p(v|s) and p(v|⌘) are both Gaussian

with a di↵erent width, when p(s) decreases, the slope decreases, the threshold de-

creases and the baseline increases, reflecting the increased bias towards the presence

of the signal (Figure 3.8b).

After a transition to low contrast, sensitization, by definition, consists of a decrease

in threshold (Kastner and Baccus, 2011). By intracellularly recording from sensitizing

ganglion cells we found that an increased baseline of the nonlinearity accompanied

the decreased threshold during Learly

(Figure 3.9b). This depolarization was 35±18%

of the membrane potential standard deviation during Llate

(n = 3). Finally, even

though sensitization decreases the threshold during Learly

, it also decreased the slope

in the spiking nonlinearity as measured from extracellular recordings (Figure 3.9c).

This indicates that sensitization di↵ers from changes in sensitivity due to adaptation,

where the slope increases when the threshold decreases (Baccus and Meister, 2002).

The decrease in slope occurs because of the bias conferred by an increased p(s). When

a signal is more likely, a greater influence on p(s|v) comes from the prior p(s), and a

smaller influence comes from the new input, v. In the extreme, when p(s) = 1, the

posterior will always be 1, and the cell should always fire, regardless of the input, v.

In fact, this reduced dependence on the current input is consistent with a decrease

in mutual information between stimulus and response during the higher firing rate of

Learly

reported previously for sensitizing cells (Kastner and Baccus, 2011).

During Learly

, sensitization displays all three properties—decreased threshold, in-

creased baseline observed in the subthreshold membrane potential, and decreased

slope—expected from an ideal model of signal detection. Thus, changes in the re-

sponse curve during sensitization are of the same type found in an ideal model of

signal detection when the probability of the signal increases.

We then compared the output of the optimal model more quantitatively to the

change in firing rate seen in the nonlinearities from Learly

and Llate

. Low values of input

should yield near zero firing rate in ganglion cells, owing to the apparent pressure to

convey information about the stimulus using few spikes (Pitkow and Meister, 2012).

To convert the prior probability, p(s|v), to a firing rate, we used a spiking nonlinearity

(Figure 3.8b) optimized to map p(s|v) to the firing rate averaged over all cells during


5 %!

35 %!

b 4

3

Slop

e L early

43Slope Llate

-65

-60

-55

Out

put (

mV)

-2 0 2Input (!)

LearlyLlate

a

c

Figure 3.9: Variability in O↵ bipolar cells andchanges in ganglion cell responses during sen-sitization. (a) Top, intracellular recording froman O↵-type bipolar cell responding to a Gaus-sian white noise contrast (5%). Di↵erent col-ored traces show two repeats of the same stimu-lus sequence. Bottom, response at 35% contrast.(b) Nonlinearity of the membrane potential of asensitizing ganglion cell recorded intracellularlyduring L

early

and L

late

for a switch between 35%and 5% contrast. (c) Slope of spiking nonlinear-ities during L

early

and L

late

for sensitizing gan-glion cells recording extracellularly.

both Learly

and Llate

conditions, i.e., only a single function was used for all cells and

all conditions. This function had a sharp threshold corresponding to approximately

a p(s|v) of ⇠0.5. Thus, a comparison of ganglion cell firing with the optimal signal

detection model allowed us to interpret that the cell fired when it was more likely

than not that a signal was present.

After finding the best single spiking nonlinearity we then chose a single parameter

corresponding to the standard deviation of the noise distribution, p(v|⌘), for each

cell. This noise level was chosen to match the model to the response curve of Llate

alone. We then examined how closely the model matched the nonlinearity during

Learly

. We found that the optimal signal detection model predicted the magnitude of

the change in both midpoint and slope of the nonlinearity between Learly

and Llate

(Figure 3.8d,e).

In the signal detection model, the time course that the signal probability increased

was faster than when it decayed, di↵ering by a factor of 3 (Figure 3.8c). This temporal

asymmetry reflects the fact that it is easier to detect an increase in contrast than a

decrease in contrast (DeWeese and Zador, 1998). After a decrease in contrast, most

intensity values lie in the center of a previous higher contrast distribution, whereas

after an increase in contrast, extreme intensity values are quickly encountered that

are inconsistent with a previous lower contrast value. This asymmetry corresponded

3.3. RESULTS 55

to our measurements, as sensitization decayed with a tau 4.4 times longer than sen-

sitization developed (2.4 versus 0.55 s) (Kastner and Baccus, 2011). Therefore, both

qualitatively and quantitatively, sensitization within the adaptive field conforms to

an optimal model of signal detection in the presence of background noise.

3.3.7 Sensitization maintains the location of an object

We thus propose that the sensitizing field provides a bias for the detection of a signal

based upon the prior probability of that signal conditioned on the stimulus history.

We tested this idea in a more natural context relating to the motion of objects,

which represents an important source of signals in the visual scene. In a natural

environment, objects do not suddenly disappear, therefore once detected they are

highly likely to be present nearby in space. We thus presented a stimulus where

changes in spatiotemporal contrast were generated by changes in the velocity of object

motion on a background in the presence of fixational eye movements. We chose the

spatial texture of the object and background to be identical, and thus the object

was camouflaged and could only be detected by its motion. A camouflaged object

presents a di�cult signal detection problem for the visual system (Cuthill et al., 2005;

Stevens and Cuthill, 2006). When the object moved, it stimulated the retina with both

di↵erential motion and an increase in spatio-temporal contrast; however, once the

object ceased its di↵erential motion relative to the background, it was undetectable

relative to the background, and thus any information about its location could only

arise as a prediction based upon prior measurements.

The stimulus was a textured background of vertical lines with an intensity drawn

randomly from a Gaussian distribution that jittered in one dimension to mimic fix-

ational eye movements (Olveczky et al., 2003; Martinez-Conde and Macknik, 2008)

(Figure 3.10a). Every 8 s, three neighboring bars, representing an object, moved co-

herently for 250 ms at a speed of 1.1 mm/s (for a total distance of 275 µm), 9 times

greater than the average speed of the background. This prolonged period was used

only to provide a steady baseline for the measurement, as experiments changing con-

trast every 0.5 s (Figure 3.5) show that sensitization occurs even in a rapidly changing


environment. Thus the object part of the stimulus changed its spatio-temporal con-

trast by virtue of its changing motion—with fast motion representing high contrast,

and background motion representing low contrast.

a

b

2

1

Norm

alize

d ra

te

-1 0 1-1 0 1 -1 0 1Distance from center (mm)

SensitizingAdapting On Adapting Off

Figure 3.10: Sensitization predicts future object location. (a) Camouflaged stimulus (top),shown in space (vertical axis) and time (horizontal axis), was composed of 50 µm bars, of15% contrast. The dashed vertical line indicates the time the object stopped moving rel-ative to the background. Average firing rate response of sensitizing cells (n = 7, bottom),normalized for each cell by the average steady state response for that cell during jitteringbackground motion, 5 � 8 s after the object stopped moving. (b) Average normalized re-sponse for adapting On-type (left) (n = 5), adapting O↵-type cells (OMS cells, middle)(n = 39) and sensitizing cells (right) (n = 7), where each cell experienced >1000 repeats ofthe stimulus. Firing rate in (a) and (b) is shown as a function of distance from the centerof the object’s trajectory during the time interval ‘Early’ in (a), 0.5� 1.25 s after the ob-ject stopped moving relative to the background. Positive and negative locations reflect cellswith receptive field centers on either side of the object. Error was s.e.m. and was computedacross the number of trials contributing to each spatial bin.

We measured the spiking responses of the di↵erent populations of ganglion cells

to the camouflaged object located at many di↵erent positions on the retina. We

computed the average firing rate of each population as a function of the distance

3.3. RESULTS 57

between the cell and the center of the object’s trajectory. As expected, when the

object moved, cells responded strongly in the location of the moving object (Figure

3.10a).

After the object stopped its di↵erential motion, disappearing into the background,

a population of On-type cells decreased their activity within 0.5 mm of the object,

consistent with their monophasic adaptive fields (Figure 3.10b). However, sensitizing

cells showed persistent elevated activity in the location where the object recently

moved (Figure 3.10a,b). This activity was significantly (p < 0.002) above the steady

state response for 2.8 s after the object stopped its motion relative to the background.

We compared the duration of this elevated activity to the duration of the immediate

response, defined as the time that cells under the moving object first fell below the

baseline firing rate, reflecting the end of the linear filter and the onset of brief, local

adaptation. Sensitizing cells showed elevated activity for 21 times longer than the

immediate response to the fast motion, which was 133 ms. Thus, sensitizing cells

functionally stored the location of the previously moving object with locally increased

activity.

Adapting O↵ cells had diminished activity in the immediate location where the

object had stopped, indicated by a distance of zero in Figure 3.10. However, adjacent

to the location of the moving object these cells increased their activity (Figure 3.10b).

Like sensitizing cells, this increased activity remained significantly (p < 0.005) above

the steady state response for 2.8 s after the object stopped moving, 12 times longer

than the immediate response to the fast motion, which was 233 ms. When one con-

siders the total magnitude of the peripheral increase in activity from sensitization,

as measured by the area under the curve (Figure 3.10b), this was at least as large

as (1.1 times) as the central decrease in activity caused by adaptation. These results

were consistent with the center-surround organization of their adaptive fields (Figure

3.1d,e). Therefore, following the motion of a camouflaged object, adapting O↵ cells

stored and transmitted a prediction of the location of the boundaries of the object

after it ceased to move.


3.3.8 Inhibition is necessary for sensitization and the estab-

lishment of the adaptive field

Guided by the presence of inhibitory pathways in the AF model (Figure 3.3), we tested

whether inhibitory neurotransmission was necessary for sensitization. We measured

the responses of sensitizing cells to a stimulus that changed globally between high

and low contrast before, during, and after the application of 100 µM picrotoxin,

a drug that inhibits ionotropic GABAergic receptors, one of the major inhibitory

pathways of the inner retina. Picrotoxin abolished the ability of these cells to respond

during Learly

(Figure 3.11a), and turned the sensitizing response into an adapting

response, as measured by the adaptive index (Figure 3.11b). The change of plasticity

during pharmacologic block was specific to picrotoxin because sensitization persisted

in the presence of strychnine, a glycinergic antagonist, and APB, which blocks the

On pathway in the retina (Figure 3.12). Thus, GABAergic transmission underlies

sensitization, and enables sensitizing ganglion cells to respond quickly after a decrease

in contrast.

In the AF model, inhibition combines with the excitatory pathway prior to the

threshold of the excitatory pathway (Figure 3.3b). This is necessitated because inhi-

bition delivered after the threshold would produce a vertical shift during sensitization

instead of a horizontal shift (Kastner and Baccus, 2011). Such connectivity is most

consistent with amacrine cells inhibiting bipolar cell terminals. Salamander retinal

bipolar cell terminals express GABAC

receptors that can be blocked by Picrotoxin,

but not by Bicuculline, which block GABAA

receptors found on amacrine and gan-

glion cells (Lukasiewicz et al., 1994). Therefore our model predicts that sensitization

should persist in the presence of Bicuculline, and indeed this was the case (Figure

3.11a,b).

Previous studies have shown that intracellular recordings of bipolar cells can reveal

e↵ects of inhibition at their synaptic terminals, in particular those bipolar cells that

are likely to convey input to OMS cells (Olveczky et al., 2007). If one interprets

the excitatory subunits of the AF model to be bipolar cells, the model predicts that

during Learly

, bipolar cell terminals receive less steady inhibition than during Llate

.

3.3. RESULTS 59

c

a b

0.40.20

Adap

tive

inde

x

0.60.30Distance (mm)

-0.5

0

75 µM200 µM

d

Figure 3.11: Sensitization requires GABAergic transmission. (a) The stimulus changed backand forth for 80 trials between a global high contrast (35%) for 4 s and a global low contrast(3%) for 16 s (top). Ganglion cells were continuously recorded and drug was added to thesolution after 30 min, and then washed out of the solution 1 h later. Top, example averageresponses for sensitizing cells during the 30 minutes prior to drug addition (left), and from 30min to 1h after the drug addition (right), for a cell in 100 µM picrotoxin. Bottom, same fora di↵erent sensitizing cell in 200 µM bicuculline methiodide. (b) Average adaptive indicesfor sensitizing cells in picrotoxin (top)(n = 4) or bicuculline (bottom)(n = 5). Error bars,which show the s.e.m., are obscured by the data. (c) The response of a cell with a centersurround adaptive field to the stimulus from Figure 3.1a,b before and during the addition of75 µM picrotoxin. High contrast stimulus was positioned in the sensitizing region of the cell.Each histogram comes from 60 repeats of the stimulus, with di↵erent intensity sequencespresent on each trial. (d) Average adaptive indices as a function of distance for fast-O↵adapting cells (top) (n = 68) and sensitizing cells (bottom) in control solution and 75 µM(n = 12, closed circles) or 200 µM (n = 6, open circles) picrotoxin. Colored circles show theresponses before the addition of the drug, and black circles show the responses after thedrug had been washed in for 20 min. Error bars are s.e.m.


b a

c

Figure 3.12: Sensitization does not require Glycine receptors or the On pathway. (a) Thestimulus changed back and forth between a global high contrast (35%) for 4 s and a globallow contrast (5%) for 16 s (top). Ganglion cells were continuously recorded and drug wasadded to the solution after 30 min, and then washed out of the solution 1 h later. Exampleresponses for sensitizing cells during the 30 minutes prior to drug addition (left), and from30 min to 1h after the drug addition (right) for cells in 20 µM strychnine (middle) and 15 µML-APB (bottom). Each histogram comes from >60 repeats of the stimulus, with di↵erentintensity sequences presented on each trial. (b) Average adaptive indices for sensitizing cellsin strychnine (top) (n = 5) and L-APB (bottom) (n = 4). Error bars (s.e.m.), are obscuredby the data. (c) Stimulus (top) and average response for >27 trials of a sensitizing cell(bottom) to two di↵erent changes in contrast, 35 to 5% (left) and 100 to 7% (right).

3.3. RESULTS 61

As previously reported (Rieke, 2001; Baccus and Meister, 2002) we found that some

bipolar cells had a hyperpolarized membrane potential during Learly

compared to Llate

.

However, we also found bipolar cells with a depolarized membrane potential during

Learly

compared to Llate

(Figure 3.13a,b).

Inte

nsity

5 s2 mV

100 Hz40 ms

Ganglion cell responsewhen bipolar cell:

depolarizedhyperpolarized

-1

0

Δ po

tent

ial (

mV)

100Flash amplitude

bipolar cells with:afterdepolarizationafterhyperpolarization

a b

c d

10

0

Rat

e (H

z)de

pola

rized

100Rate (Hz)

hyperpolarized

AdaptingSensitizing

0.4 s

…! …!

Figure 3.13: Depolarization of bipolar cells during sensitization. (a) Top. Stimulus that con-sisted of biphasic flashes that changed from high (100%, black) to low (7%, blue) contrast.The low contrast stimulus was composed of 9 randomly interleaved intensity flashes. Insetshows transition from high to low contrast, colors indicate di↵erent flash amplitudes. Eachflash amplitude was repeated a total of 3 times at each time point. Bottom. Average re-sponse of a bipolar cell. (b) Change in membrane potential between L

early

(0.8� 3.2 s afterhigh contrast) and L

late

(12 � 16 s after high contrast) at each flash amplitude averagedover bipolar cells that showed an afterdepolarization (n = 4 cells) or afterhyperpolarization(n = 3 cells) following high contrast. (c) Average response of a ganglion cell simultaneouslyrecorded with the bipolar cell from (a) to a low contrast flash while a +500 pA or -500 pApulse was injected into the bipolar cell. (d) Changes in the firing rate of all simultaneouslyrecorded adapting O↵ (n = 4) and sensitizing (n = 6) ganglion cells within 0.2 mm of thefour bipolar cells that showed an afterdepolarization.

Although the existence of bipolar cells that depolarize during Learly

is consistent

with the AF model, these bipolar cells must connect to fast O↵ adapting and sensitiz-

ing cells. Therefore, while recording intracellularly from these bipolar cells that display


a afterdepolarization we simultaneously recording extracellularly from ganglion cells

(Asari and Meister, 2012). Injecting depolarizing and hyperpolarizing current into

these bipolar cells changed the response of all neighboring adapting and sensitizing

O↵ ganglion cells (Figure 3.13c,d). The current injection changed the response of the

ganglion cells from 7.4± 1.5 Hz when the bipolar cell was depolarized to 4.3± 1.3 Hz

when the bipolar cell was hyperpolarized (p <0.0003), indicating that these bipolar

cells reside within the fast O↵ ganglion cell circuitry.

The AF model predicts that all three types of adaptive field can be generated using

the same circuitry by changing the strength of adapting inhibition (Figure 3.3d). We

therefore tested whether a lower concentration of picrotoxin would transform a center

surround adaptive field into a monophasic adapting adaptive field, and transform

the sensitizing adaptive field into a center-surround adaptive field. For cells with a

center-surround adaptive field, 75 µM picrotoxin caused the surround of a cell to

change from sensitizing to adapting (Figure 3.11c,d). Thus, GABAergic transmission

was also necessary for sensitization in cells with a center-surround adaptive field.

In addition, when the high contrast region was close to the receptive field center of

the cell, at an average distance of 100 µm, inhibition acted to oppose adaptation,

as the adaptive index was greater in the absence of inhibition (�0.47± 0.05 control,

�0.59± 0.06 picrotoxin, p < 0.0125).

We then examined the e↵ect of 75 µM picrotoxin on sensitizing cells. We found

that cells located closer to the high contrast region changed from sensitizing to adapt-

ing, whereas those further away from the high contrast region still sensitized, but to

a lesser degree (Figure 3.11d). Sensitization was completely abolished at all distances

by added 200 µM picrotoxin (Figure 3.11d). Thus, a partial block of GABAergic

transmission transformed the sensitizing adaptive field into a center-surround adap-

tive field (Figure 3.11d). This confirms that a combination of adapting excitation and

inhibition constructs the adaptive field. As predicted by the AF model (Figure 3.3d),

reductions in the strength of one broad class of inhibition changed the adaptive field

from sensitizing to center-surround and then to adapting.

One potential concern with experiments using picrotoxin is that an increased firing

rate might cause increased adaptation to mask intact sensitization. In picrotoxin, the

3.4. DISCUSSION 63

high contrast response increased on average by 38 ± 18%, and the steady state low

contrast response increased by 123± 14%. However, an increased firing rate can also

occur with stronger stimuli in control solution. Therefore we compared the response

of individual sensitizing cells (n = 8) to two di↵erent contrast transitions (35 � 5%

versus 100�7%) (Figure 3.12c). Sensitizing cells increased their high contrast response

by 61 ± 17% in 100% contrast compared to 35% contrast. They also increased their

steady state low contrast response by 153 ± 51% in 7% contrast compared to 5%

contrast. Even with a firing rate higher than in picrotoxin, sensitizing cells continued

to sensitize under the higher contrast condition, as the adaptive index was 0.36±0.06

for 35 to 5% contrast, and 0.21± 0.01 for 100 to 7% contrast (Figure 3.12c).

3.4 Discussion

Here we have studied multiple aspects of how adaptation and sensitization combine

in single ganglion cells. As to the general phenomenon, Fast O↵-type retinal ganglion

cells have center-surround adaptive fields, showing central adaptation but peripheral

sensitization (Figure 3.1). Furthermore, spatial antagonism of plasticity occurs at a

subcellular scale (Figure 3.4) and sensitization occurs in a rapidly changing contrast

environment (Figure 3.5). As to the computation, a model with independently adapt-

ing excitatory and inhibitory subunits explains the spatiotemporal plasticity within

the adaptive field (Figure 3.3�3.5). The model further shows that di↵erent types of

adaptive fields can be explained by di↵ering strength of inhibition. As to the un-

derlying mechanisms, a membrane potential depolarization underlied sensitization of

the firing rate (Figure 3.9b). Sensitization also requires GABAergic inhibition, but

not transmission through GABAA

receptors (Figure 3.11). Certain bipolar cells ex-

perience a depolarization following high contrast and also connect to ganglion cells

that show sensitization (Figure 3.13). Furthermore, partial blockade of GABAergic

transmission supports the idea that di↵erent levels of inhibition can produce di↵erent

types of adaptive fields. As to the functional relevance of sensitization, one popula-

tion of cells with center-surround adaptive fields are object motion sensitive cells, thus

conforming to the notion of a feature detector (Figure 3.6). Fast-O↵ sensitizing cells,


although they are not OMS cells, have a similarly sharp threshold and respond to the

same local features as fast-O↵ adapting cells (Kastner and Baccus, 2011). Finally, as

to a theoretical understanding of these results, the sensitizing e↵ect on nonlinearities

is consistent with a simple model showing that inhibition acts as a bias in the detec-

tion of an e↵ective stimulus (Figure 3.8). Furthermore, the spatiotemporal sensitizing

field conforms to a recursive inference model that updates the prior probability of

a signal, predicting a sensitizing surround larger than the immediate response to a

stimulus. Testing this idea with a stimulus representing a camouflaged object, we

showed that sensitization enables the prediction of a future object position (Figure

3.10).

3.4.1 Adaptive and receptive fields

The most basic stimulus we used to characterize the adaptive field (Figure 3.1) is sim-

ilar in nature to the stimulus first used to describe the receptive field (Ku✏er, 1953;

Barlow, 1953), except that in our case we used changing spots of contrast instead

of flashing spots. Even though the classical receptive field incompletely describes the

response of a cell, part of its usefulness comes from the fact that, to some extent,

di↵erent spatial regions provide an independent contribution to the response of the

cell. Similarly, our measurements of the adaptive field indicate that excitatory and

inhibitory subunits contribute, to some extent, independently towards adaptation

and sensitization, respectively. Toward that end, we confirmed that the adaptive field

could be used to explain and interpret responses to di↵erent (global stimuli) and

more ecological stimuli (moving objects). We thus expect that the basic model of the

adaptive field o↵ered here should prove useful in an analysis of other visual stimuli.

Recently it was shown that at the level of the ganglion cell membrane potential, all

adaptive properties for a uniform stimulus could be explained by a model of synaptic

adaptation (Ozuysal and Baccus, 2012). If local sites of adaptation contribute inde-

pendently, this implies that spatiotemporal plasticity may be explained substantially

by knowledge of the local adaptive properties of synapses and of anatomical circuitry.

3.4. DISCUSSION 65

3.4.2 Integration of inhibition and excitation

A number of papers have described the di↵erent spatiotemporal properties of local

inhibition integrated with local excitation (Munch et al., 2009; Russell and Werblin,

2010; Manu and Baccus, 2011; de Vries et al., 2011; Bolinger and Gollisch, 2012; Asari

and Meister, 2012; Garvert and Gollisch, 2013). The integration of inhibition and

excitation at di↵erent spatial and temporal scales thus appears to be a common theme

to generate diversity among ganglion cell types, depending upon the combination of

all properties, including linear spatiotemporal filtering, nonlinearities, and dynamic

adaptation. Recent studies of responses across either shorter timescales or in the

steady state (Bolinger and Gollisch, 2012; Garvert and Gollisch, 2013), likely study

populations overlapping with those that we have studied here; however it is di�cult

to make a direct correspondence as the previous studies did not examine plasticity

over the timescales studied here. Because our main results are confined to identified

cell types known to form two separate mosaics (fast O↵ cells) (Kastner and Baccus,

2011), future results can compare di↵erent phenomena as we have done here with

object motion sensitivity and sensitization.

3.4.3 A functional role for adapting inhibition

A strong parallel exists between the role of inhibition in the receptive field, and the role

of adapting inhibition in the adaptive field. Just as the receptive field surround relies

on inhibition with a wider spatial extent than excitation (Thoreson and Mangel, 2012),

our AF model (Figure 3.3) and pharmacological experiments (Figure 3.11) indicate

that di↵erent levels of adapting inhibition produce the various spatial adaptive fields.

Although adaptation in inhibitory amacrine cells was known to exist (Baccus and

Meister, 2002), it lacked any apparent role in the plasticity of ganglion cells (Brown

and Masland, 2001; Rieke, 2001; Manookin and Demb, 2006; Beaudoin et al., 2007).

Our results and model show that by opposing excitatory adaptation and producing

sensitization, inhibitory synaptic transmission plays a critical role in retinal plasticity.

When GABAergic transmission was blocked, sensitizing cells adapted and failed


to signal at the transition to low contrast. Thus at the transition to low contrast, ac-

tivity was lowered in the absence of inhibition. This confirms the previously proposed

active role of inhibition in preserving sensitivity at the transition to a low contrast

environment (Kastner and Baccus, 2011). Because GABAergic amacrine cells in the

salamander are known to be sustained cells, this e↵ect is also consistent with the

role of these amacrine cells in generating ganglion cell activity through disinhibition

(Manu and Baccus, 2011).

However, it is likely that the classical linear surround and sensitization arise from

di↵erent sources of inhibition. Fast-O↵ adapting cells have a stronger inhibitory sur-

round than sensitizing cells (Kastner and Baccus, 2011), yet sensitizing cells appear to

have stronger input from adapting inhibition (Figure 3.11). This suggests that some

part of the inhibition that produces the linear receptive field surround is distinct from

the GABAergic inhibition that produces sensitization. Accordingly, we found a min-

imal correlation between the strength of the linear surround and the adaptive index

within adapting O↵ (r2 = 0.051) and sensitizing (r2 = 0.009) cells.

3.4.4 Di↵erent levels of sensitization in di↵erent cell types

Three di↵erent cell types showed di↵erent levels of sensitization, with On cells show-

ing no sensitization, and OMS cells showing intermediate sensitization. One possible

functional explanation for this observation is that On cells have a more shallow re-

sponse curve than o↵ cells (Chichilnisky and Kalmar, 2002; Zaghloul et al., 2003). As

such, they act less as a feature detector and therefore may have less of a benefit from

sensitization. Although fast-O↵ adapting cells are OMS cells, and sensitizing cells are

not (Figure 3.6 and 3.7), the two cells do respond to the same local temporal features

(Kastner and Baccus, 2011). Because OMS cells receive information from the wider

surround, indicating whether a di↵erential motion signal is present, they may rely

less on prior information in the form of sensitization.

3.4. DISCUSSION 67

3.4.5 Updating the prior probability of a stimulus

Models that use ongoing inference to adjust the prior probability are consistent with

behavior (Kording and Wolpert, 2006; Schwartz et al., 2007b), but a similar question

has not been explored in early sensory systems. Furthermore, previous theoretical

work has suggested that an optimal model that updated its prior probability is in-

consistent with observed physiological data precisely because such a model would not

predict adaptation (‘repulsion’) of a tuning curve, but an opposite e↵ect (‘attrac-

tion’) (Stocker and Simoncelli, 2006). In fact, in the primate LGN and primary visual

cortex, stimulus-specific enhancement of sensitivity from peripheral stimuli has been

shown and has been explained by a model containing adaptation of an inhibitory

surround pathway analogous to what we have proposed (Camp et al., 2009; Wissig

and Kohn, 2012). As to whether this behavior might be consistent with updating of a

prior stimulus probability, it has been noted that during low contrast or noisy stim-

uli, prior information would become particularly important, but these conditions have

not been thoroughly explored (Schwartz et al., 2007b), most likely because conditions

of strong stimuli are often more amenable to experimentation. In fact, we observed

sensitization under conditions of weak stimuli, when prior information from nearby

or previous strong stimuli is most critical in detecting signals in a noisy environment.

3.4.6 Integrating information at the bipolar cell synaptic ter-

minal

Several lines of evidence suggest that sensitization first arises in the bipolar cell presy-

naptic terminal, although a definitive confirmation must come from more mechanistic

future experiments. Sensitization produces a horizontal shift on the ganglion cell non-

linearity (Kastner and Baccus, 2011). For such a shift to occur a steady change in

inhibition must be delivered prior to a strong threshold, as occurs at the bipolar

cell terminal (Heidelberger and Matthews, 1992). Furthermore, although GABAergic

transmission is required (Figure 3.11), transmission through GABAA

receptors is not.

This shows that GABAergic transmission directly onto ganglion cells is not required

for sensitization (Figure 3.11), and indicates a requirement for transmission through


GABAC

receptors on bipolar cell terminals. Although a more direct test would involve

a specific blocker of GABAC

receptors, these may not be specific in salamanders (Ichi-

nose and Lukasiewicz, 2005). Finally, recordings from a subset of bipolar cells show a

depolarization after high contrast. These bipolar cells also connect to fast O↵ adapt-

ing and sensitizing cells (Figure 3.13). Although one may consider the possibility that

depolarization in bipolar cells reflects an intrinsic change in conductance instead of

changing inhibitory input, the spatial extent of sensitization (space constant of 0.41

mm for sensitizing cells) appears too large to arise from bipolar cells alone.

The bipolar cell synaptic terminal is also thought to be the site of contrast adap-

tation (Manookin and Demb, 2006; Jarsky et al., 2011; Ozuysal and Baccus, 2012).

Accordingly, we have seen that adaptation and sensitization combine at a scale smaller

than the ganglion cell receptive field (Figure 3.4). Previous studies of the OMS circuit

likewise indicate that the synaptic terminal does not simply relay the local photore-

ceptor input, but performs an integration of local and distant signals (Olveczky et al.,

2007; Baccus et al., 2008).

The depolarizing o↵set observed in bipolar cells that connect to sensitizing gan-

glion cells could underlie the shift in threshold, and potentially the decrease in slope

seen during sensitization. Inactivation of voltage dependent ion channels or synaptic

depression at the bipolar cell terminal could potentially decrease the slope of the

nonlinearity when the bipolar cell is depolarized, although future studies must be

performed to identify the biophysical mechanisms underlying the observed changes

in sensitivity. Studies of GABAergic receptors on bipolar cell terminals indicate that

transmission through GABAC

receptors does indeed undergo depression, with a re-

covery time constants of seconds, somewhat longer than the time course of recovery

of depression of excitatory transmission at the terminal (Li et al., 2007; Sagdullaev

et al., 2011).

The threshold at the bipolar cell terminal plays a key role in establishing certain

ganglion cells as feature detectors. Taking the functional point of view that the steady

level of inhibition is related to the prior probability of a signal (Figure 3.8), the bipolar

cell terminal adapts to the range of local signals, and steady presynaptic inhibitory

input provides information about the likelihood of those signals. One may wonder

3.4. DISCUSSION 69

why the retina performs the inference produced by sensitization, as opposed to only

occurring in the higher brain. The sharp threshold of ganglion cells acting as feature

detectors again provides the answer. If a signal fails to cross this threshold, it cannot

be detected by a later brain region no matter what future computation is performed.

Consistent with this idea, previous results indicate that sensitization preserves signals

that would otherwise be lost in cells with less sensitization (Kastner and Baccus,

2011). Thus, for the brain to take the greatest advantage of prior knowledge about

simple spatiotemporal correlations, the sensitizing signal must be delivered prior to

this threshold.

3.4.7 The retinal neural code and the statistics of objects

The detection, classification, and representation of objects is a di�cult task that oc-

curs throughout the visual hierarchy (Logothetis and Sheinberg, 1996). In the retina,

the neural code takes advantage of the distinct statistics of objects to encode an

object’s location and trajectory. For example, the trajectory of an object necessar-

ily di↵ers from background motion due to eye movements, a property used by OMS

cells to detect the presence of objects (Olveczky et al., 2003). Object motion is often

smooth, a property the retina uses to anticipate the location of a moving object,

(Berry et al., 1999), and signal a deviation from a smooth trajectory (Schwartz et al.,

2007a).

An additional important statistical property of an object is that its identity re-

mains constant, a property that underlies the cognitive representation of object per-

manence (Bower, 1967; Shinskey and Munakata, 2003). Thus object constancy pro-

vides the basis for an inference about the source of a visual stimulus.

However, objects present the retina with signals of vastly di↵ering strengths de-

pending upon motion, ambient lighting, or context. Adaptation to these changing

properties provides one strategy to reduce the e↵ects of environmental conditions

(Olveczky et al., 2007; Wark et al., 2009). Nevertheless, in cases of very large changes

in visual input, such as when an object stops moving, cells will fall below threshold

notwithstanding adaptation (Olveczky et al., 2007; Kastner and Baccus, 2011).


With respect to the problem of maintaining a continuous representation of an

object, a camouflaged object presents a particularly di�cult stimulus to the visual

system. Motion reveals the object, causing it to pop out from its surroundings, a

property that may arise in the retina due to OMS cells (Olveczky et al., 2003). Yet,

once the object stops, it nearly disappears into its surroundings. In this case, the visual

system has no choice but to rely upon prior information to represent the object, as

occurs higher in the brain (Graziano et al., 1997). Because of the di↵erent histories

of the motion trajectories of the object and the background, and because of the

property of object constancy, sensitization helps preserve an object’s location across

changes in object motion, thus contributing to the stable representation of objects.

Because a saccadic eye movement will change the location of an object on the retina,

it is expected that this preservation of object location will function within a saccadic

fixation. Across a saccade, the spatial scale of prolonged plasticity will relate to both

the size of the object and the saccade. Further experiments will be necessary to

determine how the present image is influenced by adaptive plasticity from a previous

fixation.

Although a number of sophisticated computations have been described in the

retina, these properties are typically studied in isolation (Rieke and Rudd, 2009; Gol-

lisch and Meister, 2010; Schwartz and Rieke, 2011). Here we have shown that several

computations—adaptation, sensitization and object motion sensitivity—combine to

enable a prolonged representation of an object in the retina. The basic principles

of adaptation and prediction are common to all sensory regions of the brain. Similar

synaptic mechanisms have been proposed to accomplish adaptation both in the retina

and in the cortex (Jarsky et al., 2011; Ozuysal and Baccus, 2012; Chance et al., 2002).

Given the simple underlying mechanism of adaptation of inhibitory transmission that

we propose to generate predictive sensitization, one might expect that similar pro-

cesses underlie prediction elsewhere in the nervous system.



3.5.1 Electrophysiology

Retinal ganglion cells of larval tiger salamanders of either sex were recorded using

an array of 60 electrodes (Multichannel Systems) as described (Kastner and Baccus,

2011). A video monitor, which had a frame rate of 60 Hz, projected the visual stimuli

at 30 Hz controlled by Matlab (Mathworks), using Psychophysics Toolbox (Brainard,

1997; Pelli, 1997). The video monitor was calibrated using a photodiode to ensure

the linearity of the display. Stimuli had a constant mean intensity of 10 mW/m2.

Contrast was defined as the standard deviation divided by the mean of the intensity

values, unless otherwise noted.

Simultaneous intracellular and multielectrode recordings were performed as de-

scribed (Manu and Baccus, 2011). Sensitizing ganglion cells were identified by their

level in the retina, spiking response and sensitizing behavior. O↵-type bipolar cells

were identified by their flash response, receptive field size, and level in the retina.

3.5.2 Cell classification

For all experiments, all ganglion cells (>250 cells in >45 retinas) were classified as pre-

dominantly On-type or O↵-type based upon their linear temporal filters computed by

reverse correlation to a spatial visual stimulus. They were further classified as adapt-

ing or sensitizing by whether a spatially global high contrast stimulus subsequently

decreased or elevated the firing rate response to low contrast, as previously described

(Kastner and Baccus, 2011). Sixty percent of the cells we recorded from were fast-

O↵ cells (adapting or sensitizing) or On cells. Other cell types could not be sampled

in large enough numbers to assign them to distinct classes, and therefore were not

included.

Additionally, for experiments in Figures 3.6 and 3.10, cells were classified as object

motion sensitive (OMS) cells using a stimulus similar to one previously described

(Olveczky et al., 2007). A striped grating shifted ⇠25 µm back and forth over the

retina with a frequency of 0.5 Hz. A central 800 µm object region moved coherently


with the background (global motion) or out of phase with the background (di↵erential

motion) with the condition changing every 6 s. The ratio of the average firing rate

during global vs. di↵erential motion was computed.

3.5.3 Receptive fields and sensitivity

To compute sensitivity at each spatial location, a spatiotemporal LN model was com-

puted by correlating the spiking response with a visual stimulus consisting of binary

squares (Figure 3.1) such that

F (x, y, ⌧) =1

T

ZT

0

s(x, y, t� ⌧)r(t)dt, (3.1)

where F (x, y, ⌧) is proportional to the linear response filter at position (x, y) and

delay ⌧ ; s(x, y, t) is the stimulus intensity at position (x, y) and time t, normalized to

zero mean; r(t) is the firing rate of a cell; and T is the duration of the recording. For

stimuli containing Gaussian white-noise annuli (Figure 3.4), the filter had one spatial

dimension and was normalized by the area of the annulus at each distance to account

for the di↵erence in area of di↵erent annuli. The filter had a significant amplitude

for a duration of ⇠0.5 s, shorter than the time intervals of Learly

and Llate

used to

calculate the LN model. Then the predicted linear response, g(t), was computed by

convolving the stimulus with the linear response filter such that

g(t) =

ZT

0

s(x, y, ⌧)F (x, y, t� ⌧)dxdyd⌧. (3.2)

The filter was initially normalized in amplitude so that the standard deviation of g(t)

and s(x, y, t) were equal (Baccus and Meister, 2002). A static nonlinearity, N(g), was

then computed as the average value of the response r(t) over bins of g(t). Model and

data had a correlation coe�cient of 0.52 ± 0.03 for the ganglion cells contributing

to Figure 3.4. This correlation was comparable to our previous work (Kastner and

Baccus, 2011).

To measure the sensitivity within each spatial region between Learly

and Llate

the


nonlinearities were fit to a sigmoid function,

y = x0

+m

1 + exp⇣

x

1

/

2

�x

r

⌘ , (3.3)

where x0

is the basal firing rate, x0

+m is the maximal firing rate, x1

/

2

is the x value

at the midpoint of the range of firing rates, and r�1 controls the maximal slope.

This equation was also used to report parameters of nonlinearities in Figure 3.8e and

3.9c. For sensitivity measurements, the nonlinearity measured during Learly

was scaled

along the x-axis to match the nonlinearity from Llate

. The factor needed to scale the

two nonlinearities together was then multiplied into the linear filter computed during

Learly

(Kim and Rieke, 2001). This placed the sensitivity in the magnitude of the

linear filter at each spatial location. The spatial sensitivity was computed to be the

root-mean-squared value of the temporal filter in a given region in space. For Figure

3.2 the sensitivity di↵erence was the di↵erence between the spatial sensitivity between

Learly

and Llate

in all regions of space that had a temporal filter with a sensitivity

value that deviated by four standard deviations from the temporal filters in all regions

of space.

For all cells, a receptive field was independently measured using reverse correla-

tion to a binary checkerboard stimulus, and the spatio-temporal receptive field was

approximated as the product of a spatial profile and a temporal filter (Olveczky et al.,

2003).

3.5.4 Adaptive field model

The model of Kastner and Baccus (2011) was extended by replicating the model’s

structure as a set of excitatory and inhibitory subunits, along with the two new spa-

tial parameters that described the size of the subunits. The output of the inhibitory

subunits were linked by a synaptic pathway to the excitatory subunits. Then exci-

tatory subunits were spatially weighted and passed through a threshold to produce

the final output. A prime candidate for the proposed inhibitory pathway could be the

signal passed through amacrine cells, inhibitory interneurons in the retina (Baccus,


2007).

All subunits contained separable spatiotemporal filters, F (x, ⌧). For each subunit,

the stimulus was convolved with the spatio-temporal filter,

g(t) =

ZT

0

s(x, ⌧)F (x, t� ⌧)dxd⌧. (3.4)

The temporal component of all subunit filters was identical, and modeled as a biphasic

function (di↵erentiated Gaussian) that roughly matched the peak time of fast-O↵

adapting and sensitizing cells. The spatial component of each filter was modeled as a

Gaussian with standard deviation, �, and subunits within a type were separated by

2�, representing tiling of the subunits. Because the extent of sensitization was roughly

three times that of adaptation in center-surround cells (Figure 3.1e), the inhibitory

spatial filters were three times the size of the excitatory spatial filters.

In the inhibitory subunits gI

(t) was then passed through a linear-threshold func-

tion, which was the same for all inhibitory subunits,

hI

(t) = NS

(gI

) =

(0 if g

I

< hgI

i+ 0.025

gI

(t)� (hgI

i+ 0.025) if gI

� hgI

i+ 0.025. (3.5)

This same nonlinear function, NS

(), was also used for excitatory subunits as described

below. Brackets h...i denote the average quantity, which for all g was constant because

the stimulus mean did not change.

After the threshold in each subunit, adaptation occurred through a feedforward

divisive operation, such that the response of the subunit was divided by the mean

value of its recent history weighted by an exponential filter of two seconds. This was

chosen for simplicity, although more accurate models exist of adaptation (Jarsky et al.,

2011; Ozuysal and Baccus, 2012). This adaptation could either occur at the level of

a bipolar or amacrine cell synaptic terminals (Baccus and Meister, 2002; Sagdullaev

et al., 2011). For all excitatory and inhibitory subunits the same adaptive filtering

was used. The input, h(t), was convolved with an exponential filter, FA

, and then h(t)

was divided by the result. A constant term in the denominator set the magnitude of


adaptation,

mI

(t) = A(h(t)) =h(t)

2 +RFA

(t� ⌧)(⌧)d⌧, (3.6)

where m(t) is the output of the subunit. The time constant of FA

, representing the

timescale of integration of the contrast, was 2 s,

FA

(t) = 0.5e�t

2s . (3.7)

For inhibitory subunits, the output mI

(t) passed to excitatory subunits through a

synaptic temporal filter LQ

defined as an alpha function with a time to peak of 150

ms,

LQ

(x) = 2x

0.15

exp⇣

�(⌧�0.15

0.15

⌘

n(t) =RLQ

(t� ⌧)mI

(⌧)d⌧. (3.8)

This synaptic delay could result from the action of metabotropic GABA receptors

(Maguire et al., 1989). The connection between the inhibitory subunits and an exci-

tatory subunit also contained a saturating nonlinearity, NQ

,

pI

(t) = NQ

(n(t)) =0.3

1 + exp⇣

0.03�n(t)

0.01

⌘ , (3.9)

the e↵ect of which was to diminish the modulation of inhibitory transmission at high

contrast, and amplify the modulation at low contrast. Thus, pI

(t) represented the

unweighted inhibitory synaptic input to an excitatory subunit. This saturation could

arise from either synaptic depression or receptor desensitization (Li et al., 2007). An

alternative source of the inhibitory pathway could be that adaptation is in the bipolar

cell synaptic terminal that forms the input to an amacrine cell, and the delay and

saturation (LQ

and NQ

) are produced by the filtering and membrane properties of

the intervening amacrine cell (Baccus and Meister, 2002).

In narrow field amacrine cells, neural processes produce both input and output.

Thus, the weighting wI,E

of the connection between each inhibitory and excitatory


subunit was equal to the overlap between the spatial filters of the subunits,

wI,E

=X

x

FI

(x)FE

(x), (3.10)

as shown in Figure 3.4b, where wI,E

computed as the dot product between the two

spatial filters.

For each excitatory subunit, all inhibitory subunits were linearly combined,

qE

(t) = gE

(t)� wmax

X

j

wI

pI

(t), (3.11)

with a scaling of wmax

to increase or decrease the magnitude of the inhibition in

the model (Figure 3.3d). The pathways combined prior to the excitatory pathway

threshold indicating that the amacrine cells might synapse presynaptically onto a

bipolar cell terminal.

Within the excitatory subunit, qE

(t), was then passed through the same linear-

threshold function NS

() and adapting function A() as in the inhibitory pathway.

The excitatory subunits were then combined linearly according to

r(t) =X

i

wE

A(NS

(qE

(t))) (3.12)

Each excitatory subunit was weighted by wE

according to the overlap between the

subunit’s spatial filter and the ganglion cell spatial filter, which was also three times

as large as an excitatory subunit. This size was chosen because for cells with a center-

surround adaptive field (Figure 3.1e), the receptive field center was approximately

the size of sensitizing surround of the adaptive field (Figure 3.4c). The output was

then passed through another linear threshold function

u(t) = NF

(r(t)) =

(0 if r(t) < ✓

r(t)� ✓ if r(t) � ✓. (3.13)

Where ✓ was a function of the total magnitude of the inhibition, used to provided a

comparable steady state response across all inhibitory magnitudes used. This ensured


that the only di↵erences seen in the adaptive index were due to changes in the strength

of the plasticity and not due to changes in thresholds at steady state.

3.5.5 Temporal adaptive field

To measure the temporal adaptive field we presented a stimulus whose contrast was

drawn randomly from a uniform distribution of 0 � 35% contrast every 0.5 s. The

intensities presented for each contrast were randomly drawn from a Gaussian distri-

bution defined by the contrast of that time point. Since the intensities were randomly

drawn, as the input for the filter we computed the contrast from the mean, M , and

standard deviation, W , of the sequence of intensities that were actually presented,

which were 0� 66%. The contrast, �, was � = W/M .

3.5.6 Signal detection model

The probability, p(v|s), of an input, v, given a signal, s, was taken from a Gaussian

fit from the distribution of bipolar cell membrane potentials at 5% contrast. The

probability of an input, v, given that no signal was present, p(v|⌘), was estimated as

a Gaussian distribution from repeated presentation of the same 5% contrast stimuli.

For the model, the average ratio of the s.d. of a Gaussian fit to p(v|⌘) and p(v|s) wasthe only parameter taken from the data. For the recursive spatiotemporal inference

model at each time point the posterior probability, p(sx,t

|vx,t

) was computed from

Bayes’s rule as

p(sx,t

|vx,t

) =p(v

x,t

|sx,t

)p(sx,t

)

p(vx,t

|sx,t

)p(sx,t

) + p(vx,t

|⌘)(1� p(sx,t

)). (3.14)

The denominator, p(v), reflected the fact that p(s) + p(⌘) = 1 (either a signal is

present or it is not). The prior probability, p(sx,t

), was updated from the previous

posterior probability at each time point by convolving a Gaussian smoothing filter,

h(k), with p(sx�k,t�1

|vx�k,t�1

) according to

p(sx,t

) =

Zh(k)p(s

x�k,t�1

|vx�k,t�1

)dk. (3.15)


The average posterior, hp(s|v)i, during Learly

and Llate

was computed. To convert

the posterior probability to an average firing rate, a nonlinear function, N(hp(s|v)i),was computed to map hp(s|v)i in the center of the object to a firing rate nonlinear-

ity averaged over all ganglion cells at both Learly

and Llate

. This function captured

the average relationship between signal probability and firing rate for all cells and

conditions. Then to assess whether the optimal model could reproduce the changing

nonlinearities between Learly

and Llate

, a single parameter representing the standard

deviation of the noise distribution p(v|⌘) was fit. This parameter varied across cells

and ranged between 4.0 and 4.3% contrast, and was optimized only to make the

output of the model approximate the nonlinearity during Llate

. Then, we examined

whether the model’s firing rate output, N(hp(s|v)i), during the time interval Learly

matched the measured nonlinearity during Learly

. Nonlinearities for data and model

were compared using Equation 3.3.

3.5.7 Duration of sensitization

For experiments in Figure 3.10, the significance of the response of a population of cells

was assessed in the spatial region that gave the largest response. The number of trials

contributing to the calculation of significance for the sensitizing and adapting OMS

O↵ cells was 1000 and 8000, respectively, averaged across 7 retinas. Significance was

measured using Student’s t-test by comparing the distribution of values at a given

time point to the distribution of values from 5� 8 s after the object stopped moving.

Chapter 4

Optimal dynamic range placement

by coordinated populations of

ganglion cells

This chapter is in preparation as “Optimal dynamic range placement by coordinated

populations of ganglion cells,” with author list: Kastner DB, Baccus SA, Sharpee TO.

4.1 Summary

Neural circuits use populations of neurons to encode their inputs. Although there

have been various theoretical motivations for population encoding there have been

few comparisons of theory to data. Here we focus on fast O↵ retinal ganglion cells,

a set of cells made up of two distinct populations of neurons. These neurons have

been shown to encode very similar features of the visual scene, allowing us to focus

exclusively on their dynamic range placement. We develop a simple model, based

upon binary neural encoders, constrained by neural noise and metabolic e�ciency.

We show that these populations of neurons optimally place their dynamic ranges

to maximize the amount of information they encode about the input distribution.

We also find that there are two distinct regimes for optimal population encoding.

At low noise the optimal solution distributes the encoding with distinct thresholds,

79

80 CHAPTER 4. OPTIMAL DYNAMIC RANGE PLACEMENT

while at high noise the optimal solution redundantly encodes the input. On cells have

response functions consistent with their using redundant encoding, explaining their

greater homogeneity.

4.2 Introduction

Neurons have a limited dynamic range, placing a premium on the way in which

a neuron encodes its inputs. In select circumstances it has been shown that neurons

approach the optimal positioning of their dynamic range to maximally transmit infor-

mation about their inputs (Laughlin, 1981; Brenner et al., 2000; Pitkow and Meister,

2012). Furthermore, neurons dynamically change their response range in ways con-

sistent with optimal behavior (DeWeese and Zador, 1998; Kastner and Baccus, 2011;

Sharpee et al., 2006; Wark et al., 2009). However, neural circuits use populations

of neurons to encode their inputs. In fact, both optimal information transmission

(Nikitin et al., 2009) and metabolic e�ciency (Laughlin et al., 1998) theoretically

motivate the use of population encoding in neural circuits. Yet, whether or not popu-

lations of neurons perform optimally within neural circuits remains poorly explored.

The salamander retina contains two populations of ganglion cells that encode

the same features of the visual world, but do so with distinct thresholds (Kastner

and Baccus, 2011). These two populations show distinct forms of plasticity upon

a change in the contrast distribution. Sensitizing cells maintain a lower threshold,

encoding weaker signals, and adapting cells maintain higher thresholds, encoding

stronger signals. We sought to determine whether this coordination of signal strengths

could be a consequence of maximizing the information these two populations can

provide about the input.

Toward that end we developed a simple model to determine the spacing of response

functions for two neurons that maximizes the amount of information they provide

about the input. Since ganglion cells produce sparse and noisy responses (Pitkow and

Meister, 2012), the model found the spacing of the response function that maximized

the information given constraints put on the overall rate of the response functions,

and the noise of the individual response functions. With those constraints in place,

4.3. RESULTS 81

we show that, across a large range of contrasts distributions, adapting and sensitizing

cells space their response functions very close to the optimal spacing that maximizes

information. Furthermore the model predicts two distinct regimes for population en-

coding, one using response functions with di↵erent thresholds, and one using identical

response functions, redundantly encoding the input. We show that whereas the O↵

population in salamanders conformed to the former option, the homogeneity within

the On population in salamanders behaves consistently with the prediction for redun-

dant encoding.

4.3 Results

To measure dynamic ranges we recorded the responses of ganglion cells to Gaussian

white noise across multiple contrast distributions (Figure 4.1a). That enabled the

fitting of a linear-nonlinear model to the response of each ganglion cell at each contrast

(see methods). The linear component of the model represents the feature to which the

cell has the greatest sensitivity, on average, while the static-nonlinearity of the model

captures the dynamic range of the cell in each contrast condition (Chichilnisky, 2001).

In salamanders, all O↵ cell types split into adapting and sensitizing populations, and

the two fast-O↵ populations tile the retina, indicating that they are distinct cell types

(Kastner and Baccus, 2011). Because they form distinct cell types, here we will focus

on the dynamic range placement of the fast-O↵ adapting and fast-O↵ sensitizing cells.

As previously reported (Kastner and Baccus, 2011), sensitizing cells maintain

lower thresholds across the entire range of recorded contrast distributions (Figure

4.1b,c). To gain further insight into encoding with populations of cells, we wished to

understand the positioning of response functions for two cells that would maximize

the amount of information transmitted about the input distribution.


c

a b 60300R

ate

(Hz)

0.20 0.40Input

0.60

Sensitizing!Adapting!

32

x 1/2

/ σ

0.30.2Contrast (σ)

Figure 4.1: Adapting and sensitizing fast O↵ cells coordinate the encoding of the input. (a)Stimulus (top) and average response of fast O↵ sensitizing (middle) and adapting (bottom)cells recorded in three di↵erent contrast distributions (12, 24, 36%). The cells were recordedsimultaneously. 9 di↵erent contrasts were presented from 12 � 36% in 3% intervals. Eachcontrast was presented for > 110 s. The contrasts were randomly interleaved and repeated.Each contrast was presented for > 600 s. (b) Nonlinearities for the adapting and sensitizingcells shown in (a). Black lines are sigmoid fits to the data. The first 10 s of each repeat wasnot included in the LN model calculation. (c) Average values for all sensitizing (n = 11)and adapting (n = 36) cells at each contrast, �. The x1

/

2

values were normalized by � tomake it easier to see the di↵erences across all contrasts. s.e.m. values are obscured by thedata points.

4.3. RESULTS 83

4.3.1 Histogram equalization does not predict distinct thresh-

olds

Histogram normalization has proven to be a successful framework for understanding

the optimal placement of a dynamic range in single neurons (Laughlin, 1981; Brenner

et al., 2000). By matching an equal area of the input to a comparable range of output

it ensures optimal usage of a limited dynamic range. Therefore we extended the

approach of Laughlin to the case of two response functions (see methods). However,

given the assumptions of equal Gaussian noise at each response level, the optimal

solution for this approach never splits the response ranges of the two neurons. Rather

histogram equalization extends to predict two response functions located at the same

location, and the only thing that can vary between the two responses functions is the

overall scaling.

Beyond the assumption of equal Gaussian noise at each response level, the straight-

forward solution of histogram normalization will never produce a response function

shifted away from the mean. Even in the single cell case the mean of the response

function must reside at the mean of the input distribution. This, too, provides a sig-

nificant limitation when trying to understand the sparse responses typically found in

vertebrate neural circuits, not to mention the retina.

4.3.2 Binary response model for maximizing information

Therefore we decided to take a di↵erent approach. Our approach turned out to be

similar to that in a recently published paper, which looked at the optimal response

curve for a single ganglion cell in the retina (Pitkow and Meister, 2012). We modeled

the responses of individual neurons as a binary output with a probability of spiking

defined by a sigmoid function,

y =1

1 + exp⇣

x

1

/

2

�x

b

⌘ , (4.1)

The sigmoid function had two parameters, x1

/

2

, which is the x value that leads to

a 50% spiking probability, and b, where the inverse of b corresponds to the slope of


a b

10.50p(

1|x)

-2 0 2Input (x)

0.40.20

p(x)

x1/2

0.40H

(r|x)

61

2 4 610

2

Slope (b-1)0.40.20

p(x)

-2 0 2Input (x)

10.50

p(1|x)

0.40.20

p(x)

-2 0 2Input (x)

10.50

p(1|x)

Input (x)!

c

Figure 4.2: Binary model for informationmaximization. (a) Example input distribu-tion (top), and response function (bottom).(b) Noise entropy as a function of the slopeof the sigmoid. (c) Optimal placement of thetwo response functions without (left) andwith (right) a rate constraint.

the sigmoid. Multiplying the response function by the input distribution provides the

instantaneous probability of spiking, p(1). Since there are only two possible outcomes

from a single response function, subtracting 1 from p(1), provides the probability that

the response function produced no spike, p(0). Because we used Gaussian distributions

to generate the stimuli for the data in this work, we will use Gaussian distributions

as the input distributions (Figure 4.2a); however, there is nothing in this model that

requires any specific form to the input distribution.

For two neurons, instead of there only being two possible outcomes there are now

four: when both spike, p(11), when neuron one spikes but neuron two does not, p(10),

when neuron one does not spike but neuron two does, p(01), and when neither neuron

spikes, p(00). This treats the neurons as independent without significant correlations

in their responses, a good first approximation for the fast O↵ adapting and sensitizing

cells (Kastner and Baccus, 2011).

With the ability to calculate all possible outputs for the two model response

functions, it is straightforward to compute the mutual information they provide about

the input. The mutual information is computed by subtracting the noise entropy from

the total entropy. Here the total entropy is computed by:

H(r) = �X

p(ri

)log2

p(ri

). (4.2)

The noise entropy is computed by:

H(r|x) = �Z

p(x)X

p(ri

|x)log2

p(ri

|x)dx. (4.3)

4.3. RESULTS 85

Within this framework the slope of the sigmoid introduces noise into the system

(Figure 4.2b). When the slope is infinite, the sigmoid turns into a step function with

no uncertainty as to the outcome, and the slope decreasing creates uncertainty as to

the outcome of producing a spike. When finding the optimal position of the response

functions we will impose slopes for the functions. This constraint requires there to be

a certain amount of noise in the system, a rather plausible constraint for a biological

system.

Unlike with histogram normalization, the response functions that provide the op-

timal amount of information with this binary model separate from each other (Figure

4.2c); however, the curves produced still surround the mean of the input distribution,

and are not sparse like the data (Figure 4.1b). Therefore to shift the curves away from

the mean we imposed a constraint on the average rate of the two response functions

(Figure 4.2c)

hri = p1

(1) + p2

(1). (4.4)

We can interpret this rate limitation as enforcing a metabolic constraint on the sys-

tem. Neural activity brings with it a large metabolic cost (Ames et al., 1992; At-

twell and Laughlin, 2001). This metabolic cost is so strong that it likely provided

a strong evolutionary limitation on brain size (Kotrschal et al., 2012). Furthermore,

retinal ganglion cells show responses consistent with e�ciently taking into account

that metabolic cost (Balasubramanian and Berry, 2002).

4.3.3 Low threshold cells should have less noise

Now that we have a model that has the potential to produce curves similar to the

data we wanted to understand the general behavior of the model. Toward that end

we simulated the model across a large range of noise values and average rates. For

each grouping of two slopes, which sets the noise levels in the two response functions,

and average rate there is a single spacing between the two curves that maximizes

the information that the two curves provide about the input. When we simulated the

optimal response functions in many di↵erent conditions we found that all solutions

placed the response function with the lower amount of noise, steeper slope, closer to


a b

3.53

2.5Slop

e / !

0.30.2Contrast (!)-4

-2

0

2

4

Spac

ing

( !x 1/2)

2 4 61

2 4

Slope Ratio

0.40.2

< r >


Figure 4.3: Lower threshold response function optimally has less noise. (a) Many simulationsof the binary model. Each data point shows the spacing between the two response functionsthat maximizes the information they provide about the input. For each point two slopes anda rate were randomly chosen. Spacing is defined as the x1

/

2

value from response functionone minus the x1

/

2

value from response function two. The slope ratio was taken as the slopeof response function one over the slope of response function two. (b) Average slope valuesfor the same group of cells from Figure 4.1c. The slope values were normalized by � to makeit easier to see the di↵erences across all contrasts. s.e.m. values are obscured by the datapoints.

the mean (Figure 4.3a).

These simulations provide the first prediction of the model: the lower threshold

cell should have less noise. It has previously been shown that sensitizing cells have less

noise than adapting cells (Kastner and Baccus, 2011), but this model makes a finer

prediction, the less noise should also manifest as a steeper slope of the sensitizing

response function. We, therefore, compared the slopes of the response functions of

adapting and sensitizing cells across the range of recorded contrasts. Across the full

range of contrasts, sensitizing cells maintained a steeper slope than the adapting

cells (Figure 4.3b). Just as predicted by the model, sensitizing cells have the lower

threshold (Figure 4.2c), and have less noise, as manifested by their steeper slope.

4.3.4 Di↵erent amounts of noise produce di↵erent optimal

coding strategies

In understanding the general behavior of the model, we next sought to understand

the spread that occurs in the spacing as the slopes of the response functions become

4.3. RESULTS 87

a c b 1

0.5

0Spac

ing

( ! x 1

/2)

65432Slope (b-1)

0.40.2

< r >

20

0Rat

e (H

z)

-0.5 0 0.5Input

3

2.5

Estim

ated

Slo

pe

Fast On adapting

Fast Off adaptingFast Off sensitizing

Figure 4.4: Distinct population coding regimes. (a) Many simulations of the binary modelwith the slopes and rates chosen randomly; however, the slopes of the two response functionswere the same. Each point shows the spacing that maximizes the amount of informationconveyed about the input. (b) Example nonlinearities for a fast O↵ sensitizing, a fast O↵adapting, and an On cell recorded simultaneously. (c) Average slopes for fast O↵ sensitizing(n = 95), fast O↵ adapting (n = 388), and On (n = 58) cells. For (b) and (c) the stimuluswas over 500 s of a spatial Gaussian white noise stimulus, made up of independent 50 µmbars, where each bar had a contrast of 35%.

similar (Figure 4.3a). When the slopes were the same, slope ratio of 1 in Figure

4.3a, sometimes the optimal solution placed the curves in the same location, with no

spacing between the response functions, and sometimes the optimal solution spaced

the two curves apart. To better understand what contributed to that di↵erence we

reran the simulations with two response functions that had the same slope. We found

a very sharp transition between two di↵erent coding strategies for populations (Figure

4.4a). When the noise is high, as manifested by shallow slopes, the optimal solution

places the response functions in the same location, using redundant encoding. As the

slope becomes steeper, and the noise is low enough, the optimal solutions sharply

transitions to coordinated encoding, with curves spaced apart.

This provides an explanation for a previously perplexing result. In salamanders

all O↵ populations were heterogeneous, splitting into adapting and sensitizing types;

however, the On population was homogeneous, only displaying adaptation. A possible

explanation for the homogeneity of the On population now could be that the noise

in the On population is such that the optimal coding strategy would be redundant

encoding. That predicts that the On response functions should have a shallower slope

than the fast O↵ cells, which was the case (Figure 4.4b,c).


The data from Figure 4.4b,c was collected in response to a spatial stimulus, un-

fortunately, preventing a direct comparison of the slopes measured to those used in

the simulation of the model since we cannot know the actual contrast that the cell

experienced. However, the data collected in Figure 4.1, was in response to a uniform

stimulus, where there is no uncertainty as to the contrast. Since the slope divided by

the contrasts of the fast O↵ sensitizing cells was e↵ectively a constant (Figure 4.1b),

we found the contrast that would create the best match of the data in Figure 4.4c

to that in Figure 4.1b. That transformation allowed us to compare the values of the

slopes in the data to the axis of the simulation. The fast O↵ slopes were above the

sharp threshold where coordinated encoding was optimal, and the On slopes were

below that threshold, putting them within the regime of redundant encoding.

4.3.5 Fast O↵ cells optimally space their response functions

Up until this point we have considered the general behavior of optimal response func-

tions. This model allows us to go a step further, and directly compare the placement

of the response functions of the recorded ganglion cells to the optimally placed re-

sponse functions. By fitting the data to sigmoid functions we can extract the noise

and rates that are the constraints to the model. We can then calculate the informa-

tion transmitted by a range of spacing that are all consistent with the constraints

from the sigmoid fits to the data. This creates a function that relates the transmitted

information to the spacing between the response functions. This bi-lobed function has

a maximum at the spacing that provides the maximal amount of information, and a

second local maximum at spacing that has the lower sloped response function closer

to the mean (Figure 4.5a).

Across the full range of contrasts the spacing of the data was very close to the

spacing that maximizes the information about input (Figure 4.5a). On average fast

O↵ cells had a spacing that provided > 97% of the maximum amount of information

(Figure 4.5b).

4.3. RESULTS 89

1

0.9

0.8Rel

ativ

e in

form

atio

n

-1 0 1Spacing (Δx1/2)

302010

Contrast

a b 1

0.9

0.8R

elat

ive

info

rmat

ion

0.30.2Contrast (σ)

Figure 4.5: Fast o↵ cells optimally space their response functions. (a) Each curve shows theinformation for a given spacing given the noise and rate contraint at each contrast. Theslopes used were taken from sigmoid fits to the nonlinearities of a pair of fast O↵ sensitizingand adapting cells recorded simultaneously. The rate was also taken from the sigmoid fitsafter rescaling to make the maximum 1 for each fit. The black dots are the spacing seen inthe data at each contrast. Each curve was normalized by the maximum information at thatcontrast. The curves are o↵set from each other along the y-axis to be able to see each curveindependently. (b) The average percentage of the maximum information reached for all cellpairs (n = 7) at each contrast. Colors correspond to the colors from (a). The dotted line ispositioned at 97%. s.e.m. values are obscured by the data points.


4.3.6 Model fits data across contrasts

Finally, we sought to fit the measured response functions with the model. For a

given set of two slopes and the rate constraint a single pair of response functions

maximizes the information about the input. We searched through the space of optimal

response functions to find the set that best fit the data after being normalized to a

maximum firing rate of one (Figure 4.6a). To determine how well the optimal fits

approximated the data we compared the error associated with the optimal fits to two

di↵erent error values. The minimal error would come about if the model fit the data

as well as independent sigmoid fits to the two response functions. The underlying

principle of the model is that the spacing, and thereby the half maximal points, x1

/

2

,

of the response functions were optimized to maximally transmit information about

the input. Therefore at the opposite extreme we compared the model fits to sigmoid

fits to the data that could have independent slopes, but shared the same half maximal

point, x1

/

2

. Across all cell pairs and contrasts the model fit the data well, reaching

> 65% of the error associated with the independent sigmoid fits to the response

functions, which had an extra parameter for the fit (Figure 4.6b).

For the optimal fits, the x1

/

2

and the slopes changed in a stereotyped manner

with contrast (Figure 4.6c). Previously it was shown that each individual ganglion

cell could be viewed as rescaling their response function by the contrast after an initial

threshold (Figure 2.12c)(Kastner and Baccus, 2011). Here we see that this type of

rescaling is the optimal behavior for the pair of neurons.

Up until this point we have treated each input distribution as if they were all

fundamentally identical just with di↵erent scaling factors that led to the di↵erent

contrasts. However, for the optimal model fits the fact that the rate constraints, hri,increased with increasing contrast distributions (Figure 4.6d) highlights that these

paired ganglion cells do not behave identically at each contrast. To understand the

di↵erence between the di↵erent contrasts we considered that ganglion cells do not

encode a perfectly detectable signal. Rather ganglion cells encode their input within

the context of noise.

To properly function, information processing systems, like the brain, need to be

able to detect a signal in the presence of noise (Kording and Wolpert, 2006), and the

4.3. RESULTS 91

0.60.2x 1

/20.30.2

Contrast (σ)

0.10.05

b

10.50

Rel

ativ

e er

ror

0.30.2Contrast (σ)

a

b

c

d

10.50R

ate

(Hz)

0.20 0.40Input

0.60


0.20.10<

r >

0.40.2Contrast (σ)

Figure 4.6: Model fits to the data. (a) Data (color circles) and optimal fits (black lines)for response functions for a pair of adapting and sensitizing cells at three di↵erent contrastdistributions (12, 24, 36%). (b) Average error for the seven pairs of adapting and sensitizingcells across the range of contrast distributions. (c) Average parameters for the fits to theadapting and sensitizing cells. Black lines show the fits for the model that scales by thecontrast after an initial threshold (see methods). (d) Average rate constraints for the pairs ofganglion cells across the range of contrast distributions. Black line shows the rate constraintextracted from the threshold model from (c).

92 CHAPTER 4. OPTIMAL DYNAMIC RANGE PLACEMENTPr

obab

ility

0.20Input

NoiseLow contrastHigh contrast

a b

Det

ecta

bilit

y0.40.2

Contrast (σ)

Figure 4.7: Detecting a signal in the presence ofnoise. (a) Three sample distributions: noise (grey),low contrast (green), and high contrast (purple).(b) The relative detectability of signals as a func-tion of the contrast distribution in the presenceof a fixed noise distribution (see methods for thecalculation of detectability).

retina is no exception. Already at the first synapse in the retina a threshold separates

the reliable signal from perverting noise (Field and Rieke, 2002). Indeed, discriminat-

ing a signal from noise in a dynamic environment predicts sensitization itself (Figure

3.8) and responses similar to sensitization (Stocker and Simoncelli, 2006). Therefore

we found it quite useful to consider signal detection within the framework of optimal

information processing in the retina.

Within a low contrast distribution it is quite di�cult to distinguish signal from

noise because of the large overlap between the two distributions. However, as the con-

trast increases a far greater proportion of the distribution separates from the distri-

bution of the noise (Figure 4.7a). The increase that we observed in the rate constraint

with increasing contrast (Figure 4.6d) can reflect this increasing discriminability in

the signal (Figure 4.7b).

4.4 Discussion

We presented a model that determines the dynamic range placement for populations

of neurons that maximizes the information about the input distribution. Given noise

constraints for the individual neurons and an energy constraint for the pair of neu-

rons we found that the fast O↵ adapting and sensitizing cells position their response

functions to maximize the amount of information they encode about the input. These

two populations maintain that optimal placement across a broad range of contrast

distributions. Furthermore, we found two distinct regimes for optimal population en-

coding. A low noise regime distributes the encoding of the input between low and

high threshold response functions, just as seen with the coordinated encoding within

4.4. DISCUSSION 93

the fast O↵ populations. While a high noise regime forces the response functions to

overlap and redundantly encode the input. The On population within salamanders

appears to be within this higher noise regime, explaining why it is a more homogenous

set.

4.4.1 Limitations of the model

One of the powers of the model is its simplicity. Modeling neurons as noisy binary

encoders makes the calculation of mutual information quite straightforward. However,

because the model response functions range between zero and one there is no place

within the model for the di↵erent absolute firing rates seen within the data (see

Figure 4.1b). This complicates the interpretation of the energy constraint within the

model as a simple mapping onto the spiking of individual neurons since adapting and

sensitizing cells have di↵erent maxima for their response functions. Rather it requires

a more nuanced accounting of the energy that each population expends.

The simplicity of the model also allowed us to numerically solve for the optimal

response functions, using error minimization. However, an analytic solution to the

general problem could prove useful for verification of the error minimization proce-

dures. Additionally, having an analytic solution to the problem could also make a

more comprehensive model feasible, such as fitting a single optimal model across all

contrasts.

4.4.2 Redundant versus distributed encoding

Although redundant encoding can be thought to be suboptimal at the populations

level (Puchalla et al., 2005), here we have shown that it too can be an optimal

solution for information maximization at the population level. Our finding that the

level of noise creates distinct optimal encoding regimes is reminiscent of work on

optimal transcriptional regulation (Tkacik et al., 2009). The work on transcriptional

regulation also took advantage of a simple model to show the optimal behavior of a

biological system (Tkacik et al., 2008).


To understand why the On populations falls within the regime of redundant en-

coding it is helpful to consider what we generally know about the On population. The

fact that the On and O↵ populations di↵er is not new. The On population has been

shown to more linearly encode its input (Chichilnisky and Kalmar, 2002; Zaghloul

et al., 2003), On and O↵ populations show di↵ering levels of adaptation (Chander

and Chichilnisky, 2001; Ozuysal and Baccus, 2012), and there are di↵erent numbers

of On and O↵ cells within the retina (Ratli↵ et al., 2010). By more linearly encoding

its input the On population conveys a more complete representation of the visual

world. In so doing it has a dynamic range that encodes input values through the

mean, which are also the noisiest values of the input. Therefore it might be the case

that the On population has traded higher noise levels to maintain that more linear

encoding, but in so doing those noise levels force the population into the regime of

redundant encoding that we find here.

4.4.3 Information maximization after signal detection

To have the model produce curves relatable to response functions seen in the data it

was necessary to limit the overall rate of the model (Figure 4.2c). In so doing we, as

other before us (Pitkow and Meister, 2012), placed a constraint on the overall energy

used by the neurons. However, when we considered that energy constraint across

contrasts we found that it increased with contrast (Figure 4.6d). This result allowed

us to reconsider the function of the energy constraint. As opposed to it simply being

an accounting for each and every spike, rather it can be viewed as a weighting of

spikes given their likelihood to arise from the signal rather than noise (Figure 4.7).

At lower contrasts since there is far greater overlap between the noise distribution

and the signal distribution, it would be a waste of the limited energy resources to

devote a similar amount of energy as in high contrast, when the signal distribution is

far more easily separated from the noise.

This perspective raises the possibility that there are two things at play in the

determination of dynamic range placement in the retina. The first is signal detection,

and the second is information maximization. There is an initial threshold placed

4.4. DISCUSSION 95

to separate out signal from noise (Kastner and Baccus, 2011). This threshold also

functions to limit overall metabolic cost of the response, and it does so somewhat

rationally by distributing the resources to the more informative inputs. Then there is

an optimal placement of the dynamic range to encode that more informative signal.

4.4.4 Optimal population encoding

The fast O↵ population within the salamander retina proved to be a useful population

to test our theory of optimal population encoding since within this grouping there

are two populations that encode very similar features of the visual world (Kastner

and Baccus, 2011). That allowed us to focus exclusively on dynamic range placement

for the fast O↵ adapting and sensitizing populations. To broaden the theory to less

similar initial filtering, for instance to incorporate the slower O↵ populations or the

On populations, the model will need to be extended to incorporate multidimensional

nonlinearities. This comes about because each visual filter produces a dimension upon

which the stimulus is projected to convert the input into the output. There is nothing

preventing our simple model from being extended to multiple dimensions, but such a

multidimensional approach raises the question of how to choose the optimal filtering

dimensions. Such considerations will be necessary to fully understand the way in

which the retina encodes its input.

Of course the retina is not the only neural circuit to encode with populations of

neurons. The auditory cortex also seems to have neurons split into distinct forms

of plasticity (Watkins and Barbour, 2008). The somatosensory system also might

make use of di↵erent forms of plasticity (Ganmor et al., 2010), perhaps indicating the

possibility of similar distributed encoding. It will be interesting to see if these diverse

neural circuits can also be understood from the perspective of optimal information

transmission.




We recorded from retinal ganglion cells of larval tiger salamanders using an array of

60 electrodes (Multichannel Systems) as previously described (Kastner and Baccus,

2011). A video monitor projected the visual stimuli at 30 Hz controlled by Matlab

(Mathworks), using Psychophysics Toolbox (Brainard, 1997; Pelli, 1997). Stimuli were

uniform field with a constant mean intensity, M , of 10 mW/m2 and were drawn from

a Gaussian distribution. Contrast is defined as � = W/M , where W is the standard

deviation of the intensity distribution.

4.5.2 Linear-Nonlinear models

LN models consisted of the light intensity passed through a linear temporal filter,

which describes the average response to a brief flash of light, followed by a static

nonlinearity, which describes the threshold and sensitivity of the cell. To compute the

model, the stimulus, s(t), was convolved with a linear temporal filter, F (t), which

was computed as the time reverse of the spike triggered average stimulus, such that

g(t) =

ZF (t� ⌧)s(⌧)d⌧ . (4.5)

A static nonlinearity, N(g), was computed by comparing all values of the firing rate,

r(t) with g(t) and then computing the average value of r(t) over bins of g(t). The

filter, F (t), was normalized in amplitude such that it did not amplify the stimulus,

i.e. the variance of s and g were equal (Baccus and Meister, 2002). Thus, the linear

filter contained only relative temporal sensitivity, and the nonlinearity represented

the overall sensitivity of the transformation.


4.5.3 Histogram normalization for multiple neurons

We would like to maximize the entropy of the neural response

~r = (r1

(x), r2

(x)), (4.6)

where r1

(x) is the firing rate of neuron 1 for stimulus x, and r2

(x) is the firing rate

of neuron 2 for stimulus x. The stimulus x varies between �1 and 1. Note that r1

and r2

cannot take arbitrary values because in the space of two neural responses they

form a one dimensional line obtained by varying stimulus value x.

To maximize the response entropy,

H = �Z

p(l)lnp(l)dl, (4.7)

where the variable l marks the position along the curve of ~r, we want

p(l)dl = p(x)dx, (4.8)

where the probability to be within a segment dl along the curve equals the probability

to be within interval dx on the stimulus axis. Since

dl =q

r02

1

(x) + r02

2

(x)dx, (4.9)

the entropy equations becomes,

H = �Z

p(x)lnp(x)dx+

Zp(x)ln

qr02

1

(x) + r02

2

(x)dx. (4.10)

Since the first part of Equation 4.10 does not depend upon either r1

(x) or r2

(x) we

can focus on the second part of the equation.

The variation in H when we change r1

(x) is:

�H =1

2

Zp(x)

2r01

(x)�r01

(x)

r02

1

(x) + r02

2

(x)dx, (4.11)


which is equivalent to

�H = �Z

d

dx

✓p(x)r0

1

(x)

r02

1

(x) + r02

2

(x)

◆�r0

1

(x)dx. (4.12)

Since the variation is zero if the response is maximal, Equation 4.12 is set to zero.

Correspondingly there is an equivalent equation for r2

(x), which provide the equations

p(x)r01

(x) = c1

(r02

1

(x) + r02

2

(x)) (4.13)

p(x)r02

(x) = c2

(r02

1

(x) + r02

2

(x)), (4.14)

where c1

and c2

are constants. When we divide equation 4.13 and 4.14 we get

r01

(x) = c3

r02

(x), (4.15)

where c3

is another constant, which shows that the derivatives of the two response

functions are proportional to each other, and do not split apart as seen in the data

(Figure 4.1).

4.5.4 Threshold model for contrast processing

We have previously shown that a simple model that thresholds the input prior to

scaling by the contrast was capable of capturing the response of the adapting and

sensitizing fast O↵ cells (Kastner and Baccus, 2011). That model took the form

N�

= N

✓x� ↵

�

◆, (4.16)

where N�

is the response function at a given contrast, �, N is the generic response

function, and ↵ is the threshold. We can rewrite this, given that the generic response

function is the sigmoid function (Equation 4.1).

N�

=1

1 + exp

✓x

1

/

2

�(x�↵

�

)ˆ

b

◆ . (4.17)


This then leads to how x1

/

2

and b should change as a function of contrast,

x1

/

2

(�) = �x1

/

2

+ ↵ (4.18)

b(�) = b�, (4.19)

which are the equations we used to fit the data in Figure 4.6c. We then used these

equations for the pair of cells to fit the hri data in Figure 4.6d.

4.5.5 Detectability

When there is a signal in the presence of noise the probability that any input, ⌫, is

from the signal distribution is

w(⌫) =p(s|⌫)

p(s|⌫) + p(⌘|⌫) , (4.20)

where p(s|⌫) is the probability of the signal given an input, ⌫, and p(⌘|⌫) is the

probability of the noise given an input, ⌫ (Field and Rieke, 2002). w(⌫) was calculated

for each contrast distribution with a fixed level of noise comparable to a 2% contrast

distribution. Since both the signal and noise distributions had the same mean, w(⌫)

had a minimum at the mean, which was arbitrarily placed at zero. Since we focused

on the O↵ population we only considered the function at positive input values. The

overall detectability was measured as the integral of w(⌫) for each contrast.

Chapter 5

Inhibitory dynamics underlying

contrast plasticity in the retina

This chapter is in preparation as “Inhibitory dynamics underlying contrast plasticity

in the retina,” with author list: Kastner DB, Jadzinsky PD, Panagiotakos G, Baccus

SA.

5.1 Summary

Understanding how neural circuits compute comprises a fundamental goal of neuro-

science. The more di↵erent circuit elements and cellular dynamics contribute to the

computation the more complicated it becomes to understand how the biology per-

forms the computation. Contrast plasticity in the retina provides a rich example, since

much work has been done to expose the cellular components of the computation. Yet,

the role of inhibitory dynamics in contrast plasticity remains unknown. Here we show

that sustained O↵ amacrine cells are su�cient for sensitization, a newly discovered

form of plasticity in the retina. Furthermore, we measure the changes in dynamics

at the level of the input and output of these amacrine cells to show how they create

sensitization.

100

5.2. INTRODUCTION 101

5.2 Introduction

Throughout the brain inhibition shapes neural computations (Baccus, 2007; Isaacson

and Scanziani, 2011). In the retina, inhibition suppresses and modulates excitatory

responses, as with the surround of the classical receptive field (Flores-Herr et al.,

2001; McMahon et al., 2004), the selectivity of ganglion cells to di↵erential motion

(Olveczky et al., 2003; Baccus et al., 2008), and direction selectivity (Euler et al.,

2002). However, neurons dynamically change their response properties dependent

upon the recent stimulus history. Mechanisms within excitatory neurons contribute

to these changes in the neural code. Photoreceptors and bipolar cells change their

sensitivity so as to produce luminance adaptation (Dunn et al., 2007). Bipolar and

ganglion cell dynamics provide the necessary components for contrast adaptation

within the retina (Rieke, 2001; Kim and Rieke, 2003; Manookin and Demb, 2006;

Beaudoin et al., 2007). Although inhibition is necessary for some of these dynamic

processes (Hosoya et al., 2005; Ge↵en et al., 2007; Olveczky et al., 2007)(Chapter 3),

the contribution of inhibitory dynamics remains largely unclear.

Pharmacologic experiments provide useful information for determining the neces-

sity of inhibition for retinal processing (Olveczky et al., 2003; Hosoya et al., 2005;

Bolinger and Gollisch, 2012); however they require caution when trying to decipher

mechanistic roles for that inhibition. Drug application a↵ects the entire retina. All

neurotransmission of the type a↵ected by the drug will be altered. If that neurotrans-

mitter plays diverse roles a pharmacologic blockage will alter all of them, and the

results will reflect a combination of all of those e↵ects. Furthermore, such a global

change manipulates the overall state of the retina, making it practically impossible

to tease apart whether inhibition mediates the computation of interest, or rather

just modulates the computation by generating an appropriate environment for the

true mediators of the computation of interest. Therefore, to mechanistically deter-

mine the role of inhibition in retinal processing we need more refined techniques for

manipulation of inhibitory circuitry.

Here we used paired recordings between amacrine and ganglion cells to selectively

manipulate inhibition in order to measure inhibitory dynamics and understand their

102 CHAPTER 5. MECHANISM OF SENSITIZATION

role in retinal contrast processing. Ganglion cells undergo two types of plasticity with

changes in contrast. They can show decreased or increased sensitivity after a change

from a high to a low contrast distribution, performing adaptation or sensitization

respectively. Even though amacrine cells also adapt to contrast (Baccus and Meister,

2002), and undergo synaptic depression (Sagdullaev et al., 2011), their role in retinal

contrast plasticity has remained opaque (Rieke, 2001; Brown and Masland, 2001;

Manookin and Demb, 2006; Beaudoin et al., 2007) until very recently (Chapter 3).

Here we show that amacrine cells are su�cient to cause sensitization, and we measure

the various stages of plasticity that underlie sensitization.

5.3 Results

Recently the retina was shown to process contrast with two opposing forms of plas-

ticity, adaptation and sensitization (Kastner and Baccus, 2011). Although synaptic

plasticity in excitatory neurons has been proposed to underlie adaptation (Manookin

and Demb, 2006; Jarsky et al., 2011), the circuit mechanisms underlying sensitization

remain far less understood. In response to a more local high contrast some cells vary

their form of plasticity from adaptation to sensitization based upon the location of

the cell relative to the high contrast (Figure 3.1). This suggests that intrinsic ganglion

cell properties are not solely responsible for sensitization. A membrane depolariza-

tion underlies sensitization even in cells that exclusively sensitize (Figure 3.9). Such

membrane dynamics typically indicate presynaptic computations (Carandini and Fer-

ster, 1997; Manookin and Demb, 2006). Also a computational model that combines

adapting inhibition and excitation captures the phenomenon of sensitization (Kastner

and Baccus, 2011), and suggests that di↵erences in the type of adaptive response can

be explained by di↵erences in the amount of adapting inhibition (Figure 3.3). These

results call for a further study into the role of amacrine cell dynamics in contrast

processing.

Although pharmacologic experiments place a necessary role on GABAergic inhi-

bition for sensitization (Figure 3.11) they cannot identify the way in which inhibitory

transmission shapes contrast plasticity. Blocking inhibition increases the overall firing

5.3. RESULTS 103

rates of the ganglion cells (Figure 3.11), making a comparison of the details of the

dynamics of the response of a ganglion cell between the control condition and in the

presence of drug inappropriate, since e↵ectively the strength of the overall stimulus

di↵ers between the two conditions.

Therefore we simultaneously recorded intracellularly from an amacrine cell and

extracellularly from multiple nearby ganglion cells, all while presenting a visual stim-

ulus to the retina (Figure 5.1a,b). We focused on sustained O↵ amacrine cells to see

if they could contribute the inhibition underlying the picrotoxin results (Figure 5.1c).

Sustained O↵ amacrine cells were good candidates for several reasons. First, we chose

to focus on amacrine cells in general as the source of the inhibition instead of horizon-

tal cells since the outer retina does not adapt to contrast (Baccus and Meister, 2002).

Second, sensitization persists with blockage of the On pathway, making On-O↵ cells

much less likely a candidate. Third, a model that reproduces sensitization contains a

nonlinearity between the inhibitory and excitatory pathways (Figure 2.16) that can

be understood as the inhibition working largely through disinhibition. Recently, sus-

tained O↵ amacrine cells were shown to function largely through disinhibition (Manu

and Baccus, 2011). Finally, sensitization even occurs with smaller and more local

high contrast transitions (Figure 2.4 and 3.1), making it less likely that the inhibitory

cell will have a large receptive or projective field. Sustained O↵ amacrine cells have

smaller receptive and projective fields (de Vries et al., 2011), especially when com-

pared to transient cells like the polyaxonal amacrine cell (Cook et al., 1998; Baccus

et al., 2008).

Since horizontal cells also have sustained O↵ flash responses we measured the

spatio-temporal receptive field of the interneurons (Figure 5.1d). By ensuring that an

interneuron had a surround we were able to separate amacrine from horizontal cells.

For some of the cells we confirmed that they were in fact amacrine cells by filling

and imaging them (Figure 5.1e). By verifying that an interneuron sent projections

into the inner plexiform layer we were able to distinguish an amacrine cell from a

horizontal cell. We correctly identified all of the amacrine cells that we filled (n = 4).

Some amacrine cells adapt to contrast while others do not (Baccus and Meister,

2002). Therefore we determined if sustained O↵ amacrine cells as a class adapted to


300 µm

Electrode array!

H!

G!

P! P!

A!B!B!

G!

Visual stimulus!

Mem

brane potential!

Current injection!

a b

c

d e

Ligh

t OnOff

10 mV

1 s

Figure 5.1: Experimental setup. (a) The retina is placed onto a multielectrode array, whichallows for extracellular recording from multiple ganglion cells. An interneuron is simultane-ously recorded using a sharp electrode with a resistance of 150�300 M⌦. A visual stimulusis focused onto the photoreceptors. (b) Spatial receptive fields of an amacrine (red) and gan-glion cells (black) recorded simultaneously. (c) Average response of a sustained O↵ amacrinecell to a 0.5 Hz flashing stimulus. (d) Spatio-temporal receptive field of an amacrine cell.Red indicates sensitivity below the mean, blue indicates sensitivity above the mean. (e)Image of the same amacrine cell from (d). INL is the inner nuclear layer, IPL is the innerplexiform layer, and GCL is the ganglion cell layer.

5.3. RESULTS 105

1 mV

0.4 sIn

tens

ity4 mV

5 s

LlateLearlya b c

-0.20

0.2

Δ m

embr

ane

pote

ntia

l (m

V)

100Flash amplitude

HorizontalAmacrine

Figure 5.2: Adaptation in sustained O↵ amacrine cells. (a) Visual stimulus (top) and theresponse of an example amacrine cell (bottom). High contrast was 100% Michelson contrast,and low contrast was composed of 9 di↵erent flashes randomly delivered. The high contrastwas only presented over the receptive field of the amacrine cell. The rest of space was lowcontrast. (b) Average membrane potential of the amacrine cell shown in (a) to the ninedi↵erent flashes delivered during low contrast. Times for L

early

and L

late

are shown abovethe stimulus in (a). Average di↵erence in membrane potential between L

late

and L

early

foramacrine (n = 21) and horizontal (n = 4) cells. Negative values indicate that the cell washyperpolarized during L

early

compared to L

late

.

contrast. First we created an online map of the receptive field of the amacrine cell using

a white-noise checkerboard stimulus (Figure 5.1b). This allowed us to place a local

high contrast spot over the amacrine cell and then measure its response to a stimulus

that changed from a high to a low contrast (Figure 5.2a). Sustained O↵ amacrine

cells adapted to contrast (Figure 5.2a). Their membrane potential hyperpolarized

immediately after the transition from a high to a low contrast, Learly

, compared to

later during low contrast, Llate

(Figure 5.2b,c). Consistent with a previous report

(Baccus and Meister, 2002), horizontal cells showed practically no adaptation with a,

relatively, minimal hyperpolarization (Figure 5.2c).

The adaptation seen in these amacrine cells could contribute to sensitization in

ganglion cells because this adaptation diminishes the amount of inhibition that a

ganglion cell will receive after a transition from high contrast leading to an e↵ective

increase in excitation. However, this adaptation only provides one half of the picture

of the amacrine cell dynamics. To fully implicate these sustained O↵ amacrine cells

in sensitization we need to not only characterize their input dynamics, comparable to

their receptive field, we also must characterize their output dynamics, comparable to

their projective field (Lehky and Sejnowski, 1988; de Vries et al., 2011).


To measure the output dynamics of these amacrine cells we presented a visual

stimulus to the retina that allowed for the rapid measurement of the ganglion cell

response function during Learly

and Llate

without current injected into the amacrine

cell, and while depolarizing or hyperpolarizing the amacrine cell (Figure 5.3a,b). The

slower temporal frequency of the response allowed for a rapid measurement of the

ganglion response function without having to also measure the ganglion cell filter

(Brenner et al., 2000). To be able to extract the di↵erence between amacrine cell

transmission during Learly

and Llate

we took advantage of the fact that ganglion cell

response functions are well fit by sigmoid equations (Kastner and Baccus, 2011). We

then assumed that the way in which current injected into the amacrine cell a↵ected

the ganglion cell only changed in magnitude between Learly

and Llate

. That means

that if the amacrine cell changes the threshold of a ganglion cell during Learly

, we

assume that it will also only change the threshold of the ganglion cell during Llate

,

but it can change the threshold more or less than during Learly

.

Using this assumption we were able to model the e↵ects of the hyperpolarizing

and depolarizing current during Learly

and Llate

(Figure 5.3c) (see methods). From the

model, we computed the change in the strength of transmission between Learly

and

Llate

. We found that transmission is greater during Llate

than Learly

both when we

hyperpolarized and depolarized the amacrine cell (Figure 5.3d). Therefore, not only

did the input to these amacrine cells adapt, but their output was also depressed.

In modeling the e↵ect of the current we were able to see the depressed transmission

in many amacrine-ganglion cell pairs, but it did require an assumption. Therefore we

also sought to verify the depressed transmission in a model independent way. In

most cases it is di�cult, if not impossible to just look at the response functions and

determine changes in transmission between Learly

and Llate

because of the changes

in the response functions in the control conditions (Figure 5.3b); however there are

situations when we can unambiguously say that the transmission is depressed by

high contrast. That occurs when during the control condition there is sensitization,

but during the current condition there is adaptation or no change in the response

between Learly

and Llate

. We were able to observe such e↵ects on multiple occasions

(Figure 5.4), confirming depressed transmission in a model independent way between

5.3. RESULTS 107

200

100

0

Rat

e (H

z)

100Flash amplitude

HyperpolarizationControl

LearlyLlate

200

100

0

Rat

e (H

z)

100Flash amplitude (%)

100

Learly Llate

Visu

alIn

tens

ity

Cur

rent

Inte

nsity

... ...

200 ms

...

... ...

200

100

0

Rat

e (H

z)

100Flash amplitude (%)

Depolarization!Control!Hyperpolarization!Model!

a b

c d 1

0.50Δ transmission

hyperpolarization

10.50-0.5Δ transmissiondepolarization

Flash amplitude!

Flash amplitude!

Figure 5.3: Amacrine transmission is depressed at the transition to low contrast. (a) Visualstimulus changed back and forth between high and low contrast. High contrast was 100%Michelson contrast, and low contrast was composed of 9 di↵erent flashes randomly delivered.Depolarizing (+500 pA) and hyperpolarizing (�500 pA) current was precisely delivered for200 ms starting when the visual stimulus flash went from On to o↵. Current was onlydelivered during the flashes that occurred 0.8 � 3.2 s (L

early

) and 16 � 20 s (Llate

) afterthe high contrast. The high contrast was only presented over the receptive field of theamacrine cell. The rest of space was low contrast. (b) Average response of an exampleganglion cell to the 9 di↵erent visual flashes during the 6 conditions of the experiment.(c) Same curves from (b) just with L

early

on the left and L

late

on the right for clarity.The grey curves show the output of the model, which capture the e↵ect of the current.(d) Change in transmission between L

early

and L

late

for when the current is depolarizingand hyperpolarizing (see methods). Positive values indicate that inhibitory transmission isgreater during L

late

.


200

100

0

Rat

e (H

z)

100Flash amplitude

HyperpolarizationControl

LearlyLlate

Figure 5.4: A model independent view of depressed amacrine transmission. Multiple exam-ples of response functions of ganglion cells from the experimental paradigm shown in Figure5.3.

sustained O↵ amacrine cells and ganglion cells following a transition from high to

low contrast. This increase in transmission from Learly

to Llate

is consistent with a

recovery from synaptic depression, in accordance with recent studies of amacrine cell

transmission (Sagdullaev et al., 2011).

Now that we have established that these sustained O↵ amacrine cells have both

an adapted input and a depressed output we wanted to verify that these cells were

su�cient for sensitization. To do that we designed an experiment such that only the

amacrine cell e↵ectively experiences high contrast, and we measured the response of

ganglion cells following the exposure of that single circuit element to high contrast.

The visual stimulus was comprised of exclusively low contrasts. Instead of presenting

a high contrast visual stimulus, we periodically injected a current designed to mimic

the voltage change in the amacrine cell recorded during high contrast (Figure 5.5a),

while simultaneously measuring the response of multiple ganglion cells.

5.4. DISCUSSION 109

We found that the high contrast current injected into the amacrine cell was suf-

ficient to cause sensitization in ganglion cells (Figure 5.5b-d), and this e↵ect was

specific to ganglion cells that had receptive fields within several hundred µm to the

amacrine cell. Whereas amacrine cells were su�cient for sensitization, horizontal cells

were not (Figure 5.5d). The sensitization measured here was likely due to the high

contrast current marshaling synaptic depression in the amacrine cells (Figure 5.3 and

5.4) since the high contrast current did not change the membrane potential like a

high contrast visual stimulus (Figure 5.5e). Therefore, our su�ciency measurement

here provides a minimal amount of sensitization that an individual amacrine cell can

create. We would expect individual amacrine cells to contribute even more to sensi-

tization than what we can measure here, since in response to a high contrast their

output would be further decreased by their input adaptation (Figure 5.2)

5.4 Discussion

We have found that sustained O↵ amacrine cells show adaptation at the level of their

input (Figure 5.2) and depression at the level of their output (Figure 5.3 and 5.4).

This combination of dynamics in the inhibitory signal is consistent with previous

models of sensitization (Figure 2.16 and 3.3), whereby after a high contrast stimulus

inhibition is decreased leading to an e↵ective increase in excitation, i.e. sensitization.

Furthermore, we have shown that these sustained O↵ amacrine cells are su�cient to

generate sensitization in ganglion cells.

To fully understand and explain the results in this paper we generated a sim-

plified model (Figure 5.6). We modeled the amacrine response function as a linear

transformation between its input and output. During Learly

the response function is

depolarized and less sensitive than during Llate

. This amacrine output then inhibits

the bipolar cells response more (Llate

) or less (Learly

), leading to more excitation

during Learly

. It is worth noting that it is necessary to incorporate the fact that these

sustained O↵ amacrine cells e↵ect ganglion cells largely through disinhibition (Manu

and Baccus, 2011), meaning that there is a nonlinearity between the amacrine cell and

ganglion cell output. That nonlinearity explains the larger amount of depression seen


0.020

-0.02Ad

aptiv

e in

dex

0.30.20.1Distance (mm)

AmacrineHorizontal

4

2

0

Rat

e (H

z)

100Flash amplitude

a

c

Cur

rent

inte

nsity

Visu

alin

tens

ity

4 s

Learly Llate

-0.20

0.2

Δ m

embr

ane

pote

ntia

l (m

V)

100Flash amplitude

CurrentVisual

b

d

e

Figure 5.5: High contrast current in a single amacrine cell is su�cient to cause sensitization.(a) The visual stimulus was a continuous low contrast composed of 9 di↵erent flashes ran-domly presented at 2.5 Hz (top), identical to the low contrast from Figure 5.3a. Current wasinjected into a single amacrine cell to mimic its high contrast response, which was previ-ously recorded (Figure 5.2a). The current had a maximum amplitude of 1 nA. A membranetime constant of 30 ms was assumed to convert the current into membrane voltage, but thistechnique is not particularly sensitive to the exact value of the membrane time constant(Manu and Baccus, 2011). (b) Average response of a ganglion cell to the stimulus protocolin (a). Black indicates the time of current injection, and the color indicates the time withoutcurrent injection. (c) Average response of the ganglion cell in (b) to the 9 di↵erent flashespresented in the visual stimulus during L

early

and L

late

, as indicated in (a). (d) Averageadaptive index of ganglion cells plotted relative to the distance between the ganglion cellsand amacrine cells or horizontal cells. Data comes from a total of 76 amacrine and ganglioncell pairs and 10 horizontal and ganglion cell pairs. (e) Average di↵erence in membranepotential between L

late

and L

early

for the amacrine cells (n = 21) for when they were eitherstimulated with a visual high contrast, or injected with current to mimic their high contrastresponse. Negative values indicate that the cell was hyperpolarized during L

early

comparedto L

late

. Error bars indicate s.e.m.

5.4. DISCUSSION 111

Amac

rine

outp

ut! Depolarization!

Hyperpolarization!

Learly!

Llate!

Amacrine input!

− Amacrine output!

Gan

glio

n ou

tput!

Figure 5.6: Simplified model for sensitization. Input adaptation is illustrated as an o↵-set in the amacrine input-output function between L

early

and L

late

. Synaptic depressionis illustrated as a decreased slope of the amacrine cell input-output function during L

early

compared to L

late

. The same current is delivered, but the amacrine output is less duringL

early

. Hyperpolarization shows a greater di↵erence in transmission because of the subse-quent threshold between amacrine output and ganglion cell response. This threshold can beat the bipolar cell synapse or in the ganglion cell itself.

with a hyperpolarizing than with a depolarizing current in the amacrine cell (Figure

5.3d) since hyperpolarization sends that ganglion cell into the expansive part of the

nonlinearity, whereas depolarization sends the ganglion cell into the compressive part

of the nonlinearity.

The disinhibitory nature of sustained O↵ amacrine cells also explains the increase

in response seen in the ganglion cell during the current injection during the experi-

ments to test su�ciency (Figure 5.5b). Consistent with previous results (Manu and

Baccus, 2011), a large variation current will increase the output of connected gan-

glion cells because of the intervening nonlinearity. Since hyperpolarizing current has

more of an e↵ect than depolarizing current, the nonlinearity e↵ectively causes such

a stimulus to remove inhibition. Even though the current injected into the amacrine

cell causes an increase in response in the ganglion cell during the current injection,

the increase in response in the ganglion cell alone is not su�cient to cause sensiti-

zation because some ganglion cells change their type of plasticity from adapting to

sensitizing based upon the location of a high contrast stimulus (Figure 3.1).

Throughout this work we have focused on the sustained O↵ amacrine cells as if

they were a single population of interneuron. Although the population as a whole


50 µm!

Figure 5.7: A diverse set of amacrine cells. Two fills of sustained oO↵ amacrine cells.

clearly shows the results described here it is unlikely that this is a single type of

amacrine cell. Rather it is more likely that we are dealing with multiple di↵erent types

of cells. Comparing the projection pattern of filled sustained O↵ amacrine clearly

makes the point that within the sustained O↵ population there are multiple di↵erent

amacrine cell types (Figure 5.7). It will have to be left to future work to determine the

nature of the di↵erent populations within the class of sustained O↵ amacrine cells.



Retinal ganglion cells of larval tiger salamanders of either sex were recorded using

an array of 60 electrodes (Multichannel Systems) as described(Kastner and Baccus,

2011). A video monitor projected the visual stimuli at 30 Hz controlled by Matlab

(Mathworks), using Psychophysics Toolbox (Brainard, 1997; Pelli, 1997). Stimuli had

a constant mean intensity of 10 mW/m2. Contrast was defined as either the the

standard deviation divided by the mean of the intensity values, or as the Michelson

contrast, which is C = I

max

�I

min

I

max

+I

min

, with Imax

and Imin

being the maximum and minimum

intensity values.


5.5.2 Receptive fields and nonlinearities

Spatio-temporal receptive fields were measured in two dimensions by the standard

method of reverse correlation (Chichilnisky, 2001) of the spiking response with a

visual stimulus consisting of binary squares, such that

F (x, y, ⌧) =

ZT

0

s(x, y, t� ⌧)r(t)dt, (5.1)

where F (x, y, ⌧) is the linear response filter at position (x, y) and delay ⌧ , s(x, y, t) is

the stimulus intensity at position (x, y) and time t, normalized to zero mean, r(t) is the

firing rate of a cell, and T is the duration of the recording. Then the predicted linear

response, g(t), was computed by convolving the stimulus with the linear response

filter such that

g(t) =

ZT

0

s(x, y, t� ⌧)F (x, y, t� ⌧)dxdyd⌧. (5.2)

A static nonlinearity, N(g), was then computed as the average value of the response

r(t) over bins of g(t). For all experiments a cell’s receptive field was independently

measured using reverse correlation to a binary checkerboard stimulus, and the spatio-

temporal receptive field was approximated as the product of a spatial profile and a

temporal filter (Olveczky et al., 2003).

5.5.3 Transmission

To measure changes in transmission between Learly

and Llate

the ganglion cell response

function without current was fit to a sigmoid function to interpolate between the data

points. The sigmoid function used was,

y = x0

+m

1 + exp⇣

x

1

/

2

�x

r

⌘ , (5.3)

where x0

is the basal firing rate, x0

+m is the maximal firing rate, x1

/

2

is the x value

at the midpoint of the range of firing rates, and r�1 controls the maximal slope. Then,


the ganglion response during current injection was fit such that

NC

(x) = aNI

(↵x+ �) + b, (5.4)

where NC

is the ganglion response function in the control condition, NI

is the ganglion

response function during current injection, and ↵, �, a, and b are the shifting and

scaling parameters for the x and y-axes. The shifting and scaling parameters were fit

together for all current condition between Learly

and Llate

except that the parameters

could change together such that

↵E

= m↵L

+ 1

�E

= m�L

aE

= maL

+ 1

bE

= mbL

, (5.5)

where m is the di↵erence in transmission between Learly

and Llate

, and the subscript

indicates the time during low contrast, with E for Learly

and L for Llate

. The scaling

parameters (↵ and a) need to have the addition o↵set of one because if there is no

change in those parameters due to contrast, that corresponds to a multiplication by

1.

Chapter 6

Conclusions

6.1 Generalization of work

Sensitization and coordinated dynamic encoding highlight that adaptation, although

beneficial, comes with its own costs. Neurons have limited dynamic ranges. To be

able to encode the range of inputs that they encounter they have to manipulate that

dynamic range to match their input. However, in so doing they, inevitably, will not

be able to match the range of a di↵erent set of inputs. With coordinated dynamic

encoding the retina splits the problem between two distinct classes of cells that un-

dergo di↵erent forms of plasticity: the previously known contrast adaptation, and the

newly discovered contrast sensitization.

The notion that adaptive systems have di�culty during transitions of their inputs

is not a new one. We have all experienced the failure of light adaptation when we

leave a dark room for one with more light. Our visual system initially saturates in

the light, until it can adapt to the new environment. However, as we have seen with

coordinated dynamic encoding, there is no reason that every transition of inputs must

lead to such absolute failures in encoding.

In a now classic paper, Fairhall and colleagues highlighted the ambiguity inherent

to adaptation (Fairhall et al., 2001). They focused on the H1 neuron in the blowfly,

which encodes the velocity of visual inputs. The H1 neuron adapts to the variance

of the distribution of the velocities, a quantity comparable to contrast. In so doing

115

116 CHAPTER 6. CONCLUSIONS

it was expected that the H1 neuron should lose the ability to encode the variance of

the velocity since it was scaling that quantity out of its response function (Brenner

et al., 2000). However, they showed that the variance could be decoded from the spike

timing, instead of the firing rate (Lundstrom and Fairhall, 2006), an instance where

di↵erent features within a single neuron combine to encode more than a single feature

could.

The seeds of coordinated dynamic encoding exist in other areas of the nervous

system. In the auditory cortex of marmosets at least two di↵erent types of adaptation

exist (Watkins and Barbour, 2008). One group of cells always adapted to maintain

sensitivity around the most common intensities of the stimulus distribution. Another

group of neurons did the same except if the most common intensities were too high,

at which point these neurons raised their sensitivity to maintain the ability to encode

lower intensities. Had the second form of adaptation not existed those lower intensities

would have been poorly encoded and potentially even lost (Watkins and Barbour,

2008).

In the somatosensory cortex of rats, neurons adapt less than would be expected

based on simple models of synaptic depression (Ganmor et al., 2010). This study

looked at the potential outcome of using coordinated dynamic encoding, whereby

using distinct types of adaptation in the sensory periphery can enable a more sta-

ble response to a dynamic stimulus in the cortex. In fact, the same group recently

reported, in abstract form, that di↵erent subcortical structures use di↵erent types

of adaptation (B. Mohar, I. Lampl, Soc. Neurosci Abstr, 704.17, 2011), potentially

combining to form the more stable representation in the cortical neurons.

Within early sensory systems it is easier to relate the input to the output, making it

an ideal place to study dynamic encoding. However, adaptation and plasticity are not

exclusive to early sensory systems. Even higher processing centers have been shown to

use distinct forms of plasticity in encoding their inputs (Miller and Desimone, 1994).

Using a task that requires working memory for monkeys to select a matching item,

neurons in the inferotemporal cortex show two responses to the second presentation

of the item. Some neurons have a diminished response, while others show an enhanced

6.1. GENERALIZATION OF WORK 117

response. Although the functional relevance of such parallel processing remains un-

clear, even the inferotemporal cortex distributes its encoding between distinct forms

of plasticity.

In addition to the coordination between cell types with di↵erent plasticity, I have

also measured the adaptive field of retinal cell types. Surprisingly, I found that a

single cell type changes its form of plasticity from adaptation to sensitization based

upon the stimulus. These center-surround adaptive fields enable coordinated dynamic

encoding at the level of a single population of cells.

In the somatosensory cortex of the rat the e↵ective spatial adaptive field of neurons

was measured (Katz et al., 2006). Here the spatial component came from stimulating

di↵erent whiskers, which fed into di↵erent barrels. These neurons had a local adaptive

field, in that adapting to the stimulation of one whisker does not e↵ect the response

to stimulation of another whisker.

The adaptive field has also recently been measured in the auditory cortex of ferrets

(Rabinowitz et al., 2011). In audition, frequency comprises the spatial aspect of the

neuron’s responsiveness, and adaptation at a neuron’s best frequency was a↵ected

by stimulation at other frequencies. As was the case in somatosensory cortex, and

the previous measurement of slow changes of the adaptive field in the retina (Brown

and Masland, 2001), these measurements were made to understand the mechanisms

of adaptation. The functional significance of these other adaptive field remain unex-

plored.

Although the phenomenon of sensitization is new in the retina, it resembles plastic-

ity in other brain regions. In the somatosensory thalamus facilitating responses have

been reported, whereby a cell’s response will be sensitized by a previously strong

stimulation (Ganmor et al., 2010). This facilitation was also recently reported, in

abstract form, to exist in the barrel cortex as well (K. Cohen-Kashi, M. Jubran, I.

Lampl, Soc. Neurosci Abstr, 385.10, 2011). Interestingly, this group has suggested

that the facilitation is due to depressed inhibitory inputs, in a very similar fashion to

what is seen in the retina.

Because of the view that sensitization can function as a form of information stor-

age, it is not too surprising that people have tried to connect similar types of responses


to memory storage in the hippocampus (Larimer and Strowbridge, 2010), and other

brain regions (Miller and Desimone, 1994). Additionally, it has been proposed the-

oretically, that information storage can come about by combining facilitating and

depressing excitatory inputs (Mongillo et al., 2008). Such a model is functionally

indistinguishable from the underlying mechanism of sensitization where depressing

inhibition plays the role of facilitating excitation.

Finally, sensitization also contains features similar to exogenous attention. When a

strong stimulus is flashed in a region of space, a subject will become more sensitive in

that region of space (Bisley and Goldberg, 2003; Carrasco et al., 2004; Ingle, 1975). I

have shown that sensitization can be evoked with a very brief strong stimulus. Perhaps

similar forms of plasticity underlie various aspects of attention as well.

6.2 Future directions

A major question that my work raised, but that I have not been able to address is

if and how the adapted and sensitized signals are combined. I have shown that the

retina splits the encoding of its input between two populations of cells. One takes

responsibility for the weak signals, while the other focuses on the strong signals.

It could be very interesting and informative to understand what the visual system

does with these two streams of information. The most appealing and straightforward

outcome would be that these two populations are recombined in the thalamus or

primary visual cortex. However, that is in no way necessary. The important thing is

that the animal has access to the two streams of information. It could be possible

that the animal uses the stronger signals for certain behaviors, while it uses the

weaker signals for di↵erent behaviors. That leaves the possibility open that these two

information streams go to very di↵erent brain regions, and then the information is

only recombined at the level of the behavior of the animal.

To address this question, the salamander would probably not be the ideal organ-

ism. Fortunately, I have shown sensitization to exist in mice as well. All of the new

mouse lines that have genetically labeled ganglion cells (Huberman et al., 2008, 2009;

Kim et al., 2008) could prove quite useful. In essence all that would be required is the

6.2. FUTURE DIRECTIONS 119

identification of the genetically labeled lines as either sensitizing or adapting because

the projection patterns of the labeled cell types is readily accessible, if not already

known.

Once the ganglion cells within a genetically labeled mouse line are identified as

sensitizing then another implication of my work can be tested. We have proposed

multiple di↵erent, yet linked, functions for sensitization. If the labeled ganglion cells

can be knocked out of the retinal circuit, what behavioral deficits will the mice exhibit?

Will they have deficiencies in tracking camouflaged objects? Will they be deficient in

exogenous attention? Such studies would be extremely interesting and informative.

Our understanding of the role of inhibition in neural computations is advancing

rapidly (Baccus, 2007; Isaacson and Scanziani, 2011; Moore et al., 2010). I have

elucidated a role for inhibitory dynamics in retinal contrast plasticity. However, it is

also clear that inhibition helps to set the steady state response of ganglion cells during

contrast plasticity as well. Why is the steady state response so tightly regulated? What

aspects of the visual input are better encoded due to the role of inhibition?

A way forward for these questions can come about by getting a richer understand-

ing of what ganglion cells encode even while they undergo contrast plasticity. I have

begun this process in the measurement of the temporal adaptive field. That measure-

ment has a direct parallel to the spike-triggered average of standard linear-nonlinear

modeling. Because of that correspondence, one could also measure a nonlinearity that

follows the temporal adaptive field. Such a nonlinearity would indicate the contrasts

which could be decoded from a cell’s response. Additionally, it could allow for better

characterization of a cell’s response, to see how that response changes with drugs

that block various forms of inhibition, or during current injection into amacrine cells.

Either manipulation could begin to give clues as to how inhibition shapes the retinal

response.

Finally, the methodology used to show that inhibitory transmission depresses over

the course of sensitization is quite general. It could be used to determine a role for

other dynamic processes in the retina, such as one proposed for inhibition in pattern

adaptation (Hosoya et al., 2005). But it need not be limited to the retina. Optogenetics

(Yizhar et al., 2011) and microstimulation (Clark et al., 2011) can also be used as


the mode of perturbation of the system. As long as there was some other secondary

readout, these perturbations can be used to great e↵ects in deciphering the underlying

mechanisms of various neural computations.

Appendix A

Publications

A.1 Journal Articles

1. Kastner DB, Baccus SA. Coordinated dynamic encoding in the retina using

opposing forms of plasticity. Nature Neuroscience, 14(10):1317-1322.

This work appears as Chapter 2. I collected the data, designed and performed

all analyses with SAB, and wrote the manuscript with SAB.

2. Kastner DB, Baccus SA (accepted). Spatial segregation of adaptation and pre-

dictive sensitization in retinal ganglion cells. Neuron.

This work appears as Chapter 3. I collected the data, designed and performed

all analyses with SAB, and wrote the manuscript with SAB.

A.2 Refereed conference articles and abstracts

1. Kastner DB, Baccus SA (2009, poster/spotlight). Distinct adaptive modes for

weak and strong signals in a retinal populations Frontiers in Neuroscience. Con-

ference Abstract: Computational and Systems Neuroscience (COSYNE), Salt

Lake City, UT.

This work became Kastner et al. (2011).

121

122 APPENDIX A. PUBLICATIONS

2. Kastner DB, Baccus SA (2010, poster). The adaptive field and predictive object

representation in the retina Conference Abstract: Gordon Conference on Sensory

Coding and the Natural Environment, Bates College, Me.

This work became Kastner et al. (accepted).

3. Kastner DB, Baccus SA (2011, talk). The adaptive field and predictive object

representation in the retina. Nature Preceding. Conference Abstract: Computa-

tional and Systems Neuroscience (COSYNE)

Part of this work is contained in Chapter 5.

4. Kastner DB, Baccus SA, Sharpee TO (2012, poster). Optimal placement of

dynamic range by coordinated populations of retinal ganglion cells. Conference

Abstract: Computational and Systems Neuroscience (COSYNE), Salt Lake City,

UT.

Part of this work is contained in Chapter 4.

References

Abbott, L. F., Dayan, P., Jan. 1999. The e↵ect of correlated variability on the accuracy

of a population code. Neural Computation 11 (1), 91–101.

Ames, A., Li, Y., Heher, E. C., Kimble, C. R., Mar. 1992. Energy metabolism of

rabbit retina as related to function: high cost of Na+ transport. The Journal of

Neuroscience 12 (3), 840–853.

Asari, H., Meister, M., Oct. 2012. Divergence of visual channels in the inner retina.

Nature Neuroscience 15 (11), 1581–1589.

Atick, J., Jan. 1992. Could information theory provide an ecological theory of sensory

processing? Network 3 (2), 213–251.

Attwell, D., Laughlin, S. B., Oct. 2001. An energy budget for signaling in the grey

matter of the brain. Journal of Cerebral Blood Flow and Metabolism 21 (10),

1133–1145.

Baccus, S. A., Jan. 2007. Timing and computation in inner retinal circuitry. Annual

Review of Physiology 69, 271–290.

Baccus, S. A., Meister, M., Dec. 2002. Fast and Slow Contrast Adaptation in Retinal

Circuitry. Neuron 36 (5), 909–919.

Baccus, S. A., Olveczky, B. P., Manu, M., Meister, M., Jul. 2008. A retinal circuit

that computes object motion. The Journal of Neuroscience 28 (27), 6807–6817.

Balasubramanian, V., Berry, M. J., Nov. 2002. A test of metabolically e�cient coding

in the retina. Network 13 (4), 531–552.

123

124 REFERENCES

Barlow, H. B., Jan. 1953. Summation and inhibition in the frog’s retina. Journal of

Physiology 119 (1), 69–88.

Barlow, H. B., Fitzhugh, R., Ku✏er, S. W., Aug. 1957. Change of organization in the

receptive fields of the cat’s retina during dark adaptation. Journal of Physiology

137 (3), 338–354.

Baylor, D. A., Nunn, B. J., Schnapf, J. L., Dec. 1984. The photocurrent, noise and

spectral sensitivity of rods of the monkey Macaca fascicularis. The Journal of Phys-

iology 357, 575–607.

Beaudoin, D. L., Borghuis, B. G., Demb, J. B., Mar. 2007. Cellular basis for contrast

gain control over the receptive field center of mammalian retinal ganglion cells. The

Journal of Neuroscience 27 (10), 2636–2645.

Berry, M. J., Brivanlou, I. H., Jordan, T. A., Meister, M., Mar. 1999. Anticipation of

moving stimuli by the retina. Nature 398 (6725), 334–338.

Bisley, J. W., Goldberg, M. E., Jan. 2003. Neuronal activity in the lateral intraparietal

area and spatial attention. Science 299 (5603), 81–86.

Blakemore, C., Campbell, F. W., Jul. 1969. On the existence of neurones in the human

visual system selectively sensitive to the orientation and size of retinal images. The

Journal of Physiology 203 (1), 237–260.

Bolinger, D., Gollisch, T., Jan. 2012. Closed-loop measurements of iso-response stimuli

reveal dynamic nonlinear stimulus integration in the retina. Neuron 73 (2), 333–346.

Bonin, V., Mante, V., Carandini, M., Nov. 2005. The suppressive field of neurons in

lateral geniculate nucleus. The Journal of Neuroscience 25 (47), 10844–10856.

Bower, T., 1967. Development of Object-Permanence—Some Studies of Existence

Constancy. Perception & Psychophysics 2 (9), 411–418.

Brainard, D. H., 1997. The Psychophysics Toolbox. Spatial Vision 10 (4), 433–436.

REFERENCES 125

Brenner, N., Bialek, W., de Ruyter van Steveninck, R., Jun. 2000. Adaptive rescaling

maximizes information transmission. Neuron 26 (3), 695–702.

Brown, S. P., Masland, R. H., Jan. 2001. Spatial scale and cellular substrate of contrast

adaptation by retinal ganglion cells. Nature Neuroscience 4 (1), 44–51.

Butts, D. A., May 2003. How much information is associated with a particular stim-

ulus? Network 14 (2), 177–187.

Camp, A. J., Tailby, C., Solomon, S. G., Apr. 2009. Adaptable mechanisms that

regulate the contrast response of neurons in the primate lateral geniculate nucleus.

The Journal of Neuroscience 29 (15), 5009–5021.

Carandini, M., Ferster, D., May 1997. A tonic hyperpolarization underlying contrast

adaptation in cat visual cortex. Science 276 (5314), 949–952.

Carrasco, M., Ling, S., Read, S., Feb. 2004. Attention alters appearance. Nature

Neuroscience 7 (3), 308–313.

Chance, F. S. F., Abbott, L. F. L., Reyes, A. D. A., Aug. 2002. Gain modulation

from background synaptic input. Neuron 35 (4), 10–10.

Chander, D., Chichilnisky, E. J., Dec. 2001. Adaptation to temporal contrast in pri-

mate and salamander retina. The Journal of Neuroscience 21 (24), 9904–9916.

Chichilnisky, E. J., May 2001. A simple white noise analysis of neuronal light re-

sponses. Network 12 (2), 199–213.

Chichilnisky, E. J., Kalmar, R. S., Apr. 2002. Functional asymmetries in ON and OFF

ganglion cells of primate retina. The Journal of Neuroscience 22 (7), 2737–2747.

Clark, K. L., Armstrong, K. M., Moore, T., Apr. 2011. Probing neural circuitry and

function with electrical microstimulation. Proceedings Biological sciences / The

Royal Society 278 (1709), 1121–1130.

126 REFERENCES

Cook, P. B., Lukasiewicz, P. D., McReynolds, J. S., Mar. 1998. Action potentials

are required for the lateral transmission of glycinergic transient inhibition in the

amphibian retina. The Journal of Neuroscience 18 (6), 2301–2308.

Cuthill, I. C., Stevens, M., Sheppard, J., Maddocks, T., Parraga, C. A., Troscianko,

T. S., Mar. 2005. Disruptive coloration and background pattern matching. Nature

434 (7029), 72–74.

Dayan, P., Abbott, L. F., 2009. Theoretical neuroscience: computational and mathe-

matical modeling of neural systems. computational and mathematical modeling of

neural systems. MIT Press.

de Vries, S. E. J., Baccus, S. A., Meister, M., Jun. 2011. The projective field of a

retinal amacrine cell. The Journal of Neuroscience 31 (23), 8595–8604.

DeWeese, M., Zador, A. M., Jan. 1998. Asymmetric dynamics in optimal variance

adaptation. Neural Computation 10 (5), 1179–1202.

Dowling, J. E., 1987. The retina: an approachable part of the brain. Belknap Press.

Dunn, F. A., Lankheet, M. J., Rieke, F., Oct. 2007. Light adaptation in cone vision

involves switching between receptor and post-receptor sites. Nature 449 (7162),

603–606.

Enroth-Cugell, C., Robson, J. G., Dec. 1966. The contrast sensitivity of retinal gan-

glion cells of the cat. The Journal of Physiology 187 (3), 517–552.

Euler, T., Detwiler, P. B., Denk, W., Aug. 2002. Directionally selective calcium signals

in dendrites of starburst amacrine cells. Nature 418 (6900), 845–852.

Fairhall, A. L., Lewen, G. D., Bialek, W., de Ruyter van Steveninck, R., Aug. 2001.

E�ciency and ambiguity in an adaptive neural code. Nature 412 (6849), 787–792.

Field, D. J., Dec. 1987. Relations between the statistics of natural images and the

response properties of cortical cells. Journal of the Optical Society of America A,

Optics and Image Science 4 (12), 2379–2394.

REFERENCES 127

Field, G. D., Rieke, F., May 2002. Nonlinear signal transfer from mouse rods to bipolar

cells and implications for visual sensitivity. Neuron 34 (5), 773–785.

Flores-Herr, N., Protti, D. A., Wassle, H., Jul. 2001. Synaptic currents generating

the inhibitory surround of ganglion cells in the mammalian retina. The Journal of

Neuroscience 21 (13), 4852–4863.

Frazor, R. A., Geisler, W. S., May 2006. Local luminance and contrast in natural

images. Vision Research 46 (10), 1585–1598.

Ganmor, E., Katz, Y., Lampl, I., Apr. 2010. Intensity-dependent adaptation of cortical

and thalamic neurons is controlled by brainstem circuits of the sensory pathway.

Neuron 66 (2), 273–286.

Garvert, M. M., Gollisch, T., Mar. 2013. Local and global contrast adaptation in

retinal ganglion cells. Neuron 77 (5), 915–928.

Ge↵en, M. N., de Vries, S. E. J., Meister, M., Mar. 2007. Retinal ganglion cells can

rapidly change polarity from O↵ to On. PLoS Biology 5 (3), e65.

Geisler, W. S., 2008. Visual perception and the statistical properties of natural scenes.

Annual Review of Psychology 59, 167–192.

Geisler, W. S., Perry, J. S., Jan. 2009. Contour statistics in natural images: grouping

across occlusions. Visual Neuroscience 26 (1), 109–121.

Gollisch, T., Meister, M., Feb. 2008. Rapid neural coding in the retina with relative

spike latencies. Science 319 (5866), 1108–1111.

Gollisch, T., Meister, M., Jan. 2010. Eye smarter than scientists believed: neural

computations in circuits of the retina. Neuron 65 (2), 150–164.

Graziano, M. S., Hu, X. T., Gross, C. G., Jan. 1997. Coding the locations of objects

in the dark. Science 277 (5323), 239–241.

Hecht, S., Shlaer, S., Pirenne, M. H., Jul. 1942. Energy, quanta, and vision. The

Journal of General Physiology 25 (6), 819–840.

128 REFERENCES

Heidelberger, R. R., Matthews, G. G., Feb. 1992. Calcium influx and calcium current

in single synaptic terminals of goldfish retinal bipolar neurons. Journal of Physiol-

ogy 447, 235–256.

Hosoya, T., Baccus, S. A., Meister, M., Jul. 2005. Dynamic predictive coding by the

retina. Nature 436 (7047), 71–77.

Huberman, A. D., Manu, M., Koch, S. M., Susman, M. W., Lutz, A. B., Ullian, E. M.,

Baccus, S. A., Barres, B. A., Aug. 2008. Architecture and activity-mediated refine-

ment of axonal projections from a mosaic of genetically identified retinal ganglion

cells. Neuron 59 (3), 425–438.

Huberman, A. D., Wei, W., Elstrott, J., Sta↵ord, B. K., Feller, M. B., Barres, B. A.,

May 2009. Genetic identification of an On-O↵ direction-selective retinal ganglion

cell subtype reveals a layer-specific subcortical map of posterior motion. Neuron

62 (3), 327–334.

Ichinose, T., Lukasiewicz, P. D., Jun. 2005. Inner and outer retinal pathways both

contribute to surround inhibition of salamander ganglion cells. The Journal of Phys-

iology 565 (Pt 2), 517–535.

Ingle, D., Jun. 1975. Focal attention in the frog: behavioral and physiological corre-

lates. Science 188 (4192), 1033–1035.

Isaacson, J. S., Scanziani, M., Oct. 2011. How inhibition shapes cortical activity.

Neuron 72 (2), 231–243.

Jarsky, T., Cembrowski, M., Logan, S. M., Kath, W. L., Riecke, H., Demb, J. B.,

Singer, J. H., Jul. 2011. A synaptic mechanism for retinal adaptation to luminance

and contrast. The Journal of Neuroscience 31 (30), 11003–11015.

Kastner, D. B., Baccus, S. A., 2011. Coordinated dynamic encoding in the retina

using opposing forms of plasticity. Nature Neuroscience 14 (10), 1317–1322.

Katz, Y., Heiss, J. E., Lampl, I., Dec. 2006. Cross-whisker adaptation of neurons in

the rat barrel cortex. The Journal of Neuroscience 26 (51), 13363–13372.

REFERENCES 129

Kersten, D., Mamassian, P., Yuille, A., Jan. 2004. Object perception as Bayesian

inference. Annual Review of Psychology 55, 271–304.

Kim, I.-J., Zhang, Y., Yamagata, M., Meister, M., Sanes, J. R., Mar. 2008. Molec-

ular identification of a retinal cell type that responds to upward motion. Nature

452 (7186), 478–482.

Kim, K. J., Rieke, F., Jan. 2001. Temporal contrast adaptation in the input and

output signals of salamander retinal ganglion cells. The Journal of Neuroscience

21 (1), 287–299.

Kim, K. J., Rieke, F., Feb. 2003. Slow Na+ inactivation and variance adaptation in

salamander retinal ganglion cells. The Journal of Neuroscience 23 (4), 1506–1516.

Kobayashi, S., Pinto de Carvalho, O., Schultz, W., Jan. 2010. Adaptation of reward

sensitivity in orbitofrontal neurons. The Journal of Neuroscience 30 (2), 534–544.

Kohn, A., Movshon, J. A., Aug. 2003. Neuronal adaptation to visual motion in area

MT of the macaque. Neuron 39 (4), 681–691.

Kording, K. P., Wolpert, D. M., Jul. 2006. Bayesian decision theory in sensorimotor

control. Trends in Cognitive Sciences 10 (7), 8–8.

Kotrschal, A., Rogell, B., Bundsen, A., Svensson, B., Zajitschek, S., Brannstrom, I.,

Immler, S., Maklakov, A. A., Kolm, N., Dec. 2012. Artificial Selection on Relative

Brain Size in the Guppy Reveals Costs and Benefits of Evolving a Larger Brain.

Current Biology 23 (2), 168–171.

Ku✏er, S. W., Jan. 1953. Discharge patterns and functional organization of mam-

malian retina. Journal of Neurophysiology 16 (1), 37–68.

Larimer, P., Strowbridge, B. W., Feb. 2010. Representing information in cell assem-

blies: persistent activity mediated by semilunar granule cells. Nature Neuroscience

13 (2), 213–222.

130 REFERENCES

Laughlin, S. B., Jan. 1981. A simple coding procedure enhances a neuron’s information

capacity. Zeitschrift fur Naturforschung Section C: Biosciences 36 (9-10), 910–912.

Laughlin, S. B., de Ruyter van Steveninck, R. R. R., Anderson, J. C. J., May 1998.

The metabolic cost of neural information. Nature Neuroscience 1 (1), 36–41.

Lehky, S. R., Sejnowski, T. J., Jun. 1988. Network model of shape-from-shading:

neural function arises from both receptive and projective fields. Nature 333 (6172),

452–454.

Li, G., Vigh, J., von Gersdor↵, H., Jul. 2007. Short-term depression at the reciprocal

synapses between a retinal bipolar cell terminal and amacrine cells. The Journal of

Neuroscience 27 (28), 7377–7385.

Logothetis, N. K., Sheinberg, D. L., 1996. Visual object recognition. Annual Review

of Neuroscience 19, 577–621.

Lukasiewicz, P. D. P., Maple, B. R. B., Werblin, F. S. F., Mar. 1994. A novel GABA

receptor on bipolar cell terminals in the tiger salamander retina. The Journal of

Neuroscience 14 (3 Pt 1), 1202–1212.

Lundstrom, B. N., Fairhall, A. L., Aug. 2006. Decoding stimulus variance from a dis-

tributional neural code of interspike intervals. The Journal of Neuroscience 26 (35),

9030–9037.

Maguire, G., Maple, B., Lukasiewicz, P. D., Werblin, F. S., Dec. 1989. Gamma-

aminobutyrate type B receptor modulation of L-type calcium channel current at

bipolar cell terminals in the retina of the tiger salamander. Proceedings of the Na-

tional Academy of Sciences of the United States of America 86 (24), 10144–10147.

Manookin, M. B., Demb, J. B., May 2006. Presynaptic mechanism for slow contrast

adaptation in mammalian retinal ganglion cells. Neuron 50 (3), 453–464.

Manu, M., Baccus, S. A., Nov. 2011. Disinhibitory gating of retinal output by trans-

mission from an amacrine cell. Proceedings of the National Academy of Sciences of

the United States of America 108 (45), 18447–18452.

REFERENCES 131

Maravall, M., Petersen, R. S., Fairhall, A. L., Arabzadeh, E., Diamond, M. E., Feb.

2007. Shifts in coding properties and maintenance of information transmission dur-

ing adaptation in barrel cortex. PLoS Biology 5 (2), e19.

Martinez-Conde, S., Macknik, S. L., Jan. 2008. Fixational eye movements across verte-

brates: comparative dynamics, physiology, and perception. Journal of Vision 8 (14),

28.1–16.

Masland, R. H., Sep. 2001. The fundamental plan of the retina. Nature Neuroscience

4 (9), 877–886.

McMahon, M. J., Packer, O. S., Dacey, D. M., Apr. 2004. The classical receptive

field surround of primate parasol ganglion cells is mediated primarily by a non-

GABAergic pathway. The Journal of Neuroscience 24 (15), 3736–3745.

Meister, M., Pine, J., Baylor, D. A., Jan. 1994. Multi-neuronal signals from the retina:

acquisition and analysis. Journal of Neuroscience Methods 51 (1), 95–106.

Mennerick, S., Matthews, G., Dec. 1996. Ultrafast exocytosis elicited by calcium cur-

rent in synaptic terminals of retinal bipolar neurons. Neuron 17 (6), 1241–1249.

Miller, E. K., Desimone, R., Jan. 1994. Parallel neuronal mechanisms for short-term

memory. Science 263 (5146), 520–522.

Mongillo, G., Barak, O., Tsodyks, M., Mar. 2008. Synaptic theory of working memory.

Science 319 (5869), 1543–1546.

Moore, C. I., Carlen, M., Knoblich, U., Cardin, J. A., Jul. 2010. Neocortical interneu-

rons: from diversity, strength. Cell 142 (2), 189–193.

Munch, T. A., da Silveira, R. A., Siegert, S., Viney, T. J., Awatramani, G. B., Roska,

B., Oct. 2009. Approach sensitivity in the retina processed by a multifunctional

neural circuit. Nature Neuroscience 12 (10), 1308–1316.

Nagel, K. I., Doupe, A. J., Sep. 2006. Temporal processing and adaptation in the

songbird auditory forebrain. Neuron 51 (6), 845–859.

132 REFERENCES

Nikitin, A. P., Stocks, N. G., Morse, R. P., McDonnell, M. D., 2009. Neural population

coding is optimized by discrete tuning curves. Physical Review Letters 103 (13),

138101.

Olveczky, B. P., Baccus, S. A., Meister, M., May 2003. Segregation of object and

background motion in the retina. Nature 423 (6938), 401–408.

Olveczky, B. P., Baccus, S. A., Meister, M., Nov. 2007. Retinal adaptation to object

motion. Neuron 56 (4), 689–700.

Ozuysal, Y., Baccus, S. A., Mar. 2012. Linking the computational structure of variance

adaptation to biophysical mechanisms. Neuron 73 (5), 1002–1015.

Pelli, D. G., 1997. The VideoToolbox software for visual psychophysics: transforming

numbers into movies. Spatial Vision 10 (4), 437–442.

Pinsker, H. M., Hening, W. A., Carew, T. J., Kandel, E. R., Dec. 1973. Long-term

sensitization of a defensive withdrawal reflex in Aplysia. Science 182 (116), 1039–

1042.

Pitkow, X. X., Meister, M. M., Apr. 2012. Decorrelation and e�cient coding by retinal

ganglion cells. Nature Neuroscience 15 (4), 628–635.

Puchalla, J. L., Schneidman, E., Harris, R. A., Berry, M. J., May 2005. Redundancy

in the population code of the retina. Neuron 46 (3), 493–504.

Rabinowitz, N. C., Willmore, B. D. B., Schnupp, J. W. H., King, A. J., Jun. 2011.

Contrast gain control in auditory cortex. Neuron 70 (6), 1178–1191.

Ratli↵, C. P., Borghuis, B. G., Kao, Y.-H., Sterling, P., Balasubramanian, V., Oct.

2010. Retina is structured to process an excess of darkness in natural scenes. Pro-

ceedings of the National Academy of Sciences of the United States of America

107 (40), 17368–17373.

Reinagel, P., Reid, R. C., Jul. 2000. Temporal coding of visual information in the

thalamus. The Journal of Neuroscience 20 (14), 5392–5400.

REFERENCES 133

Rieke, F., Dec. 2001. Temporal contrast adaptation in salamander bipolar cells. The

Journal of Neuroscience 21 (23), 9445–9454.

Rieke, F., Rudd, M. E., Dec. 2009. The challenges natural images pose for visual

adaptation. Neuron 64 (5), 605–616.

Ringach, D. L., Malone, B. J., Jul. 2007. The operating point of the cortex: neurons

as large deviation detectors. The Journal of Neuroscience 27 (29), 7673–7683.

Roska, B., Werblin, F. S., Jun. 2003. Rapid global shifts in natural scenes block

spiking in specific ganglion cell types. Nature Neuroscience 6 (6), 600–608.

Rucci, M., Jan. 2008. Fixational eye movements, natural image statistics, and fine

spatial vision. Network: Computation in Neural Systems 19 (4), 253–285.

Rucci, M., Iovin, R., Poletti, M., Santini, F., Jun. 2007. Miniature eye movements

enhance fine spatial detail. Nature 447 (7146), 851–854.

Ruderman, D. L., Bialek, W., Aug. 1994. Statistics of natural images: scaling in the

woods. Physical Review Letters 73 (6), 814–817.

Russell, T. L., Werblin, F. S., May 2010. Retinal synaptic pathways underlying the

response of the rabbit local edge detector. Journal of Neurophysiology 103 (5),

2757–2769.

Sagdullaev, B. T., Eggers, E. D., Purgert, R., Lukasiewicz, P. D., Oct. 2011. Nonlin-

ear interactions between excitatory and inhibitory retinal synapses control visual

output. The Journal of Neuroscience 31 (42), 15102–15112.

Schwartz, G., Rieke, F., Sep. 2011. Perspectives on: information and coding in mam-

malian sensory physiology: nonlinear spatial encoding by retinal ganglion cells:

when 1 + 1 6= 2. The Journal of General Physiology 138 (3), 283–290.

Schwartz, G., Taylor, S., Fisher, C., Harris, R. A., Berry, M. J., Sep. 2007a. Synchro-

nized firing among retinal ganglion cells signals motion reversal. Neuron 55 (6),

958–969.

134 REFERENCES

Schwartz, O., Hsu, A., Dayan, P., Jul. 2007b. Space and time in visual context. Nature

Reviews Neuroscience 8 (7), 522–535.

Segev, R., Goodhouse, J., Puchalla, J. L., Berry, M. J., Oct. 2004. Recording spikes

from a large fraction of the ganglion cells in a retinal patch. Nature Neuroscience

7 (10), 1154–1161.

Segev, R., Puchalla, J. L., Berry, M. J., Apr. 2006. Functional organization of ganglion

cells in the salamander retina. Journal of Neurophysiology 95 (4), 2277–2292.

Sharpee, T. O., Sugihara, H., Kurgansky, A. V., Rebrik, S. P., Stryker, M. P., Miller,

K. D., Feb. 2006. Adaptive filtering enhances information transmission in visual

cortex. Nature 439 (7079), 936–942.

Shinskey, J. L., Munakata, Y., Jun. 2003. Are infants in the dark about hidden ob-

jects? Developmental Science 6 (3), 273–282.

Simoncelli, E. P., Olshausen, B. A., Jan. 2001. Natural image statistics and neural

representation. Annual Review of Neuroscience 24, 1193–1216.

Smirnakis, S. M., Berry, M. J., Warland, D. K., Bialek, W., Meister, M., Mar.

1997. Adaptation of retinal processing to image contrast and spatial scale. Nature

386 (6620), 69–73.

Snippe, H. P., van Hateren, J. H., Jul. 2003. Recovery from contrast adaptation

matches ideal-observer predictions. Journal of the Optical Society of America A,

Optics, Image Science, and Vision 20 (7), 1321–1330.

Solomon, S. G., Peirce, J. W., Dhruv, N. T., Lennie, P., Apr. 2004. Profound contrast

adaptation early in the visual pathway. Neuron 42 (1), 155–162.

Solomon, S. G., White, A. J. R., Martin, P. R., Jan. 2002. Extraclassical receptive field

properties of parvocellular, magnocellular, and koniocellular cells in the primate

lateral geniculate nucleus. The Journal of Neuroscience 22 (1), 338–349.

REFERENCES 135

Srinivasan, M., Laughlin, S. B., Dubs, A., Jan. 1982. Predictive coding: a fresh view

of inhibition in the retina. Proceedings of the Royal Society of London. Series B,

Biological Sciences 216 (1205), 427–459.

Stevens, M., Cuthill, I. C., Sep. 2006. Disruptive coloration, crypsis and edge detection

in early visual processing. Proceedings Biological sciences / The Royal Society

273 (1598), 2141–2147.

Stocker, A., Simoncelli, E. P., 2006. Sensory adaptation within a Bayesian framework

for perception. Advances in Neural Information Processing Systems 18, 1289.

Strong, S. P., Koberle, R., de Ruyter van Steveninck, R. R., Bialek, W., 1998. Entropy

and information in neural spike trains. Physical Review Letters 80 (1), 197–200.

Thoreson, W. B., Mangel, S. C., Sep. 2012. Lateral interactions in the outer retina.

Progress in Retinal & Eye Research 31 (5), 407–441.

Tkacik, G., Callan, C. G., Bialek, W., Aug. 2008. Information flow and optimization

in transcriptional regulation. Proceedings of the National Academy of Sciences of

the United States of America 105 (34), 12265–12270.

Tkacik, G., Walczak, A., Bialek, W., Sep. 2009. Optimizing information flow in small

genetic networks. Physical Review E 80 (3), 031920–031920.

Tobler, P. N., Fiorillo, C. D., Schultz, W., Mar. 2005. Adaptive coding of reward value

by dopamine neurons. Science 307 (5715), 1642–1645.

van Hateren, J. H., Dec. 1997. Processing of natural time series of intensities by the

visual system of the blowfly. Vision Research 37 (23), 3407–3416.

van Hateren, J. H., Ruderman, D. L., Dec. 1998. Independent component analysis of

natural image sequences yields spatio-temporal filters similar to simple cells in pri-

mary visual cortex. Proceedings Biological sciences / The Royal Society 265 (1412),

2315–2320.

136 REFERENCES

Victor, J. D., Shapley, R. M., Dec. 1979. The nonlinear pathway of Y ganglion cells

in the cat retina. The Journal of General Physiology 74 (6), 671–689.

Wark, B., Fairhall, A. L., Rieke, F., Mar. 2009. Timescales of inference in visual

adaptation. Neuron 61 (5), 750–761.

Watkins, P. V., Barbour, D. L., Sep. 2008. Specialized neuronal adaptation for pre-

serving input sensitivity. Nature Neuroscience 11 (11), 1259–1261.

Werblin, F. S., Mar. 1972. Lateral interactions at inner plexiform layer of vertebrate

retina: antagonistic responses to change. Science 175 (4025), 1008–1010.

Wessel, R., Koch, C., Gabbiani, F., Jun. 1996. Coding of time-varying electric field

amplitude modulations in a wave-type electric fish. Journal of Neurophysiology

75 (6), 2280–2293.

Wissig, S. C., Kohn, A. A., Jun. 2012. The influence of surround suppression on

adaptation e↵ects in primary visual cortex. Journal of Neurophysiology 107 (12),

3370–3384.

Yarbus, A., 1967. Eye movements and vision. Plenum Press, New York.

Yizhar, O., Fenno, L. E., Davidson, T. J., Mogri, M., Deisseroth, K., Jul. 2011. Op-

togenetics in neural systems. Neuron 71 (1), 9–34.

Yuille, A., Kersten, D., Jul. 2006. Vision as Bayesian inference: analysis by synthesis?

Trends in Cognitive Sciences 10 (7), 8–8.

Zaghloul, K., Boahen, K., Demb, J. B., 2003. Di↵erent circuits for ON and OFF retinal

ganglion cells cause di↵erent contrast sensitivities. The Journal of Neuroscience

23 (7), 2645–2654.

Zhang, Y., Kim, I., Sanes, J. R., Meister, M., Sep. 2012. The most numerous ganglion

cell type of the mouse retina is a selective feature detector. Proceedings of the

National Academy of Sciences of the United States of America 109 (36), E2391–

E2398.

Documents

CONTRAST SENSITIZATION: FUNCTION, THEORY, AND …