Towards inferring circuits from calcium imaging Joshua
Vogelstein Yuriy Mishchenko JHU/CU March 24, 2009 Joshua Vogelstein
Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging
March 24, 2009 1 / 34
The Most important slide of the talk Acknowledgments Eric D.
Young Liam Paninski Adam M. Packer Joshua Vogelstein Yuriy
Mishchenko (JHU/CU)Inferring circuits from calcium imaging March
24, 2009 2 / 34
Outline Introduction 1 Single Neuron 2 Generative Model
Inverting the model Results Population of Neurons 3 Generative
Model Algorithm for inferring connectivity Results Discussion 4
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from
calcium imaging March 24, 2009 3 / 34
Introduction Outline Introduction 1 Single Neuron 2 Generative
Model Inverting the model Results Population of Neurons 3
Generative Model Algorithm for inferring connectivity Results
Discussion 4 Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring
circuits from calcium imaging March 24, 2009 4 / 34
Introduction What is our goal? Inferring a microcircuit Joshua
Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium
imaging March 24, 2009 5 / 34
Introduction Everybody wants it List of Publications [Smetters
et al., 1999, Ikegaya et al., 2004, Aaron and Yuste, 2006,
Nikolenko et al., 2007] [Shepherd et al., 2005, Shepherd and
Svoboda, 2005, Stepanyants and Chklovskii, 2005] [Yoshimura et al.,
2005, Kerr et al., 2007] Pubmed: > 100 articles using the word
microcircuit Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring
circuits from calcium imaging March 24, 2009 6 / 34
Introduction Why is this a hard problem? Many reasons. . . Too
many spike trains (2T ) to search through them all 1 Noise is
non-Gaussian 2 Observation are non-linear 3 Parameters are unknown
4 ... 5 Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring
circuits from calcium imaging March 24, 2009 7 / 34
Introduction What are we going to do? Our strategy Write down a
generative model, explaining the causal relationship between spikes
and movies Develop an algorithm to invert that model, to obtain
spike trains and microcircuits from the movies Test our approach on
real data Answer neurobiological questions that were previously
intractable Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring
circuits from calcium imaging March 24, 2009 8 / 34
Introduction What are we going to do? Our strategy Write down a
generative model, explaining the causal relationship between spikes
and movies Develop an algorithm to invert that model, to obtain
spike trains and microcircuits from the movies Test our approach on
real data Answer neurobiological questions that were previously
intractable Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring
circuits from calcium imaging March 24, 2009 9 / 34
Single Neuron Outline Introduction 1 Single Neuron 2 Generative
Model Inverting the model Results Population of Neurons 3
Generative Model Algorithm for inferring connectivity Results
Discussion 4 Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring
circuits from calcium imaging March 24, 2009 10 / 34
Single Neuron Generative Model Outline Introduction 1 Single
Neuron 2 Generative Model Inverting the model Results Population of
Neurons 3 Generative Model Algorithm for inferring connectivity
Results Discussion 4 Joshua Vogelstein Yuriy Mishchenko
(JHU/CU)Inferring circuits from calcium imaging March 24, 2009 11 /
34
Single Neuron Generative Model Generative Model for a single
neuron Equations n(t) Poisson() C (t) C (t 1) = C (t 1) + Cb + An(t
1) + c C (t) F (x, t) Poisson (x) + C (t) + kd I (x, t) = F (x, t)
+ + I Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits
from calcium imaging March 24, 2009 12 / 34
Single Neuron Generative Model Generative Model for a single
neuron Simulation Joshua Vogelstein Yuriy Mishchenko
(JHU/CU)Inferring circuits from calcium imaging March 24, 2009 13 /
34
Single Neuron Generative Model Generative Model for a single
neuron Simulation Spatially Filtered Fluorescence Calcium Spike
Train 3 6 9 Time (sec) Joshua Vogelstein Yuriy Mishchenko
(JHU/CU)Inferring circuits from calcium imaging March 24, 2009 14 /
34
Single Neuron Inverting the model Outline Introduction 1 Single
Neuron 2 Generative Model Inverting the model Results Population of
Neurons 3 Generative Model Algorithm for inferring connectivity
Results Discussion 4 Joshua Vogelstein Yuriy Mishchenko
(JHU/CU)Inferring circuits from calcium imaging March 24, 2009 15 /
34
Single Neuron Inverting the model Inverting the model How do we
do it? Our model is a hidden markov model (HMM) We adapt tools for
HMMs to our model This yields both an estimate of the spike train
and the parameters Joshua Vogelstein Yuriy Mishchenko
(JHU/CU)Inferring circuits from calcium imaging March 24, 2009 16 /
34
Single Neuron Inverting the model Inverting the model How do we
do it? We use anexpectation-maximization (EM) algorithm to iterate
between Computing the expected spike train Maximizing the
parameters, given our guess of the spike train We approximate the E
step in 3 ways: tridiagonal non-negative deconvolution sequential
monte carlo (or particle lter) (SMC or PF) markov chain monte carlo
relaxation of PF We use gradient ascent to perform the M step
(which is concave) Joshua Vogelstein Yuriy Mishchenko
(JHU/CU)Inferring circuits from calcium imaging March 24, 2009 17 /
34
Single Neuron Inverting the model Approximating the E step
Using the tridiagonal non-negative deconvolution How we do it Try
to maximize P(n|F ) Constrain it to be non-negative Approximate
integer spikes with spikes of any (non-negative) size Why is it
good Super fast Gives us an optimal spatial lter Joshua Vogelstein
Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging
March 24, 2009 18 / 34
Single Neuron Inverting the model Approximating the E step
Using sequential monte carlo How we do it Try to maximize P(nt |F )
at each time step At each time, we sample a spike or no spike, and
see which performs better We do this many times, and compute the
average Why is it good Incorporates saturating function Better SNR
than non-negative method Can incorporate refractoriness and
stimulus dependence Joshua Vogelstein Yuriy Mishchenko
(JHU/CU)Inferring circuits from calcium imaging March 24, 2009 19 /
34
Single Neuron Results Outline Introduction 1 Single Neuron 2
Generative Model Inverting the model Results Population of Neurons
3 Generative Model Algorithm for inferring connectivity Results
Discussion 4 Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring
circuits from calcium imaging March 24, 2009 20 / 34
Single Neuron Results Results Four cells simulated according to
our generative model Joshua Vogelstein Yuriy Mishchenko
(JHU/CU)Inferring circuits from calcium imaging March 24, 2009 21 /
34
Single Neuron Results Matlab Demo Joshua Vogelstein Yuriy
Mishchenko (JHU/CU)Inferring circuits from calcium imaging March
24, 2009 22 / 34
Single Neuron Results Results Sequential monte carlo results
Cell 1 Cell 2 Cell 3 Cell 4 1.5 3 4.5 6 7.5 9 10.5 12 13.5 15 Time
(sec) Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits
from calcium imaging March 24, 2009 24 / 34
Population of Neurons Outline Introduction 1 Single Neuron 2
Generative Model Inverting the model Results Population of Neurons
3 Generative Model Algorithm for inferring connectivity Results
Discussion 4 Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring
circuits from calcium imaging March 24, 2009 25 / 34
Population of Neurons Generative Model Outline Introduction 1
Single Neuron 2 Generative Model Inverting the model Results
Population of Neurons 3 Generative Model Algorithm for inferring
connectivity Results Discussion 4 Joshua Vogelstein Yuriy
Mishchenko (JHU/CU)Inferring circuits from calcium imaging March
24, 2009 26 / 34
Population of Neurons Generative Model Joshua Vogelstein Yuriy
Mishchenko (JHU/CU)Inferring circuits from calcium imaging March
24, 2009 27 / 34
Population of Neurons Algorithm for inferring connectivity
Outline Introduction 1 Single Neuron 2 Generative Model Inverting
the model Results Population of Neurons 3 Generative Model
Algorithm for inferring connectivity Results Discussion 4 Joshua
Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium
imaging March 24, 2009 28 / 34
Population of Neurons Algorithm for inferring connectivity
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from
calcium imaging March 24, 2009 29 / 34
Population of Neurons Results Outline Introduction 1 Single
Neuron 2 Generative Model Inverting the model Results Population of
Neurons 3 Generative Model Algorithm for inferring connectivity
Results Discussion 4 Joshua Vogelstein Yuriy Mishchenko
(JHU/CU)Inferring circuits from calcium imaging March 24, 2009 30 /
34
Population of Neurons Results Joshua Vogelstein Yuriy
Mishchenko (JHU/CU)Inferring circuits from calcium imaging March
24, 2009 31 / 34
Discussion Outline Introduction 1 Single Neuron 2 Generative
Model Inverting the model Results Population of Neurons 3
Generative Model Algorithm for inferring connectivity Results
Discussion 4 Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring
circuits from calcium imaging March 24, 2009 32 / 34
Discussion Discussion Conclusions We have developed optimal
inference algorithms for inferring spike trains from calcium movies
The code is easy to use and runs very quickly Next steps Conrm
simulated results with in vitro data Generalized theory to account
for novel scenarios (like genetic sensors) Include optimal
stimulation protocol to reduce variance of connectivity error
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from
calcium imaging March 24, 2009 33 / 34
Discussion Ideal data sets Calibration data 1 Movies with high
frame rates ( 67 Hz), many neurons (> 50), many spikes/neuron
(> 100), with ground truth from a few neurons Include
stimulation of neurons 2 Excitatory/inhibitory labeling of neurons
using uorescent markers 3 Joshua Vogelstein Yuriy Mishchenko
(JHU/CU)Inferring circuits from calcium imaging March 24, 2009 34 /
34
Discussion Ideal data sets Calibration data 1 Movies with high
frame rates ( 67 Hz), many neurons (> 50), many spikes/neuron
(> 100), with ground truth from a few neurons Include
stimulation of neurons 2 Excitatory/inhibitory labeling of neurons
using uorescent markers 3 Answering circuit questions Impact of
thalamic stimulation on subsets of observable neurons 1 Statistical
properties of the network (eg, how common are reciprocal 2
connections) Insert your experimental question here. . . 3 Joshua
Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium
imaging March 24, 2009 34 / 34
Discussion Aaron, G. and Yuste, R. (2006). Reverse optical
probing (roping) of neocortical circuits. Synapse, 60(6):437440.
Ikegaya, Y., Aaron, G., Cossart, R., Aronov, D., Lampl, I.,
Ferster, D., and Yuste, R. (2004). Synre chains and cortical songs:
temporal modules of cortical activity. Science, 304(5670):559564.
Kerr, J., de Kock, C., Greenberg, D., Bruno, R., Sakmann, B., and
Helmchen, F. (2007). Spatial organization of neuronal population
responses in layer 2/3 of rat barrel cortex. Journal of
Neuroscience, 27(48):13316. Nikolenko, V., Poskanzer, K., and
Yuste, R. (2007). Two-photon photostimulation and imaging of neural
circuits. Nature Methods, 4:943950. Joshua Vogelstein Yuriy
Mishchenko (JHU/CU)Inferring circuits from calcium imaging March
24, 2009 34 / 34
Discussion Shepherd, G., Stepanyants, A., Bureau, I.,
Chklovskii, D., and Svoboda, K. (2005). Geometric and functional
organization of cortical circuits. Nature neuroscience, 8:782790.
Shepherd, G. and Svoboda, K. (2005). Laminar and columnar
organization of ascending excitatory projections to layer 2/3
pyramidal neurons in rat barrel cortex. Journal of Neuroscience,
25(24):56705679. Smetters, D., Majewska, A., and Yuste, R. (1999).
Detecting action potentials in neuronal populations with calcium
imaging. Methods, 18(2):215221. Stepanyants, A. and Chklovskii, D.
(2005). Neurogeometry and potential synaptic connectivity. TRENDS
in Neurosciences, 28(7):387394. Yoshimura, Y., Dantzker, J., and
Callaway, E. (2005). Joshua Vogelstein Yuriy Mishchenko
(JHU/CU)Inferring circuits from calcium imaging March 24, 2009 34 /
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Discussion Excitatory cortical neurons form ne-scale functional
networks. Nature, 433:868873. Joshua Vogelstein Yuriy Mishchenko
(JHU/CU)Inferring circuits from calcium imaging March 24, 2009 34 /
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