Ch 5. The Patterning of Neural Connections 5.5 ~ 5.6 Adaptive Cooperative Systems, Martin Beckerman, 1997. Summarized by Kwonill, Kim Biointelligence Laboratory,

Ch 5. The Patterning of Neural Connec-tions

5.5 ~ 5.6

Adaptive Cooperative Systems, Martin Beckerman, 1997.

Summarized by Kwonill, Kim

Biointelligence Laboratory, Seoul National Universityhttp://bi.snu.ac.kr/

2(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Contents

Prolog : LGN & Ocular Dominance Column at Visual Cortex 5.5 The Multiple Constraint Model

¨ 5.5.1 Position-Independent Affinity¨ 5.5.2 Fiber-Fiber Repulsion¨ 5.5.3 Nearest-Neighbor Correlated Activity¨ 5.5.4 Position-Dependent Affinity¨ 5.5.5 Multiple Stable States in the Retinotectal Projection

5.6 Morphogenesis of the Lateral Geniculate Nucleus¨ 5.6.1 Interaction Potentials¨ 5.6.2 Induction of the Laminar Transition¨ 5.6.3 Trapping of the Transition by the Blind Spot

Prolog : LGN & Ocular Dominance Column at Visual Cortex


Visual Pathway to Primary Visual Cor-tex for Mammals(http://scienceblogs.com/purepedantry/2007/10/ocular_dominance_columns_and_t.php)

Connection between Retina and LGN (http://dels.nas.edu/ilar_n/ilarjournal/46_4/html/v4604Kaas.shtml)

Retinotopic maps in V1(http://www.journalofvision.org/3/10/1/article.aspx)

Inputs to LGN(Bear et al. Neuroscience: Exploring the brain. (Lippincott Williams & Wilkins: 2006).)

http://bi.snu.ac.kr/

Prolog : LGN & Ocular Dominance Col-umn at Visual Cortex


Inducing Ocular Dominance Columns by the Transplantation of a third eye (http://www.nature.com/nrn/journal/v3/n1/box/nrn703_BX1.html)

Ocular Dominance Column (https://bbs.stardestroyer.net/view-topic.php?f=5&t=124049&start=0)


Question

What can we infer from these models?



Multiple Constraint Model

Steinberg’s differential adhesion hypothesis¨ Minimize the adhesive-free energy

Self sorting of cells Morphology or Hierarchy

Multiple constraint model of Fraser & Perkel¨ Influences of

Chemotropic factor Electrical activity Cell surface molecules

¨ Adhesive-free energy Fiber-fiber & fiber-tectum interaction


E


Arbor Discs & Tectal Disc

Arbor terminal and tectum are modeled as discs¨ Diameter of a arbor disc =

10% of diameter of a tectal disc


Tectum

Arbor Terminal

Arbor Terminal

Arbor Terminal


Position-Independent Affinity

The contribution to the total free energy of the position-independent affinity of the ith fiber

¨ c0: coupling strength (positive)¨ : fractional overlap of the ith fiber disc with the optic tectum

¨ Ignore boundary effects Square potential well


0 0i iE c (5.1)

i


Fiber-Fiber Repulsion

Short-range fiber-fiber repulsion due to interactions of the ith fiber with the others

¨ c1: positive coupling constant (< c0 )¨ : percent overlap between fibers i and j¨ : the distance between the retinal ganglion

cells responsible for fibers i and j¨ , : constants


(5.2)

ijr

1a 2a


Nearest-Neighbor Correlated Activity

Electrical-activity-dependent interaction¨ Neighboring retinal ganglion cells

Neighboring tectal cells¨ Weak



Position-Dependent Affinity

A set of position dependent affinities between growth cones and their tectal targets

Fiber-fiber term

Fiber-tectum term


2 2 3AP DV

i ij ij ij ijj j

E c r c r (5.3)

2 2 2( ) ( )DV APij ij ijr r r (5.4)

3 4 5(1 ) (1 )AP DVi i i iE c t c t (5.5)


Total Free Energy

¨ Position-Independent Affinity¨ Fiber-Fiber Repulsion

+ Nearest-Neighbor Correlated Activity¨ Fiber-fiber Position-Dependent Affinity¨ Fiber-tectum Position-Dependent Affinity


0 1 2 3( )tot i i i ii

E E E E E (5.6)


Multiple Stable States in the Retinotectal Projection Simulated Annealing Without the retinal input & the tectal

environment modification¨ Fully satisfying energy constraints¨ Normal projection

With tectal environment modifica-tion¨ Partially satisfying energy constraints¨ Topography (uniform)



Multiple Stable States in the Retinotectal Projection Ablation

With the retinal inputs¨ Ocular Dominance



Morphogenesis of the LGN

Visual field of the retina of the rhesus monkey represented by layers 6, 4, 2 of the LGN¨ Dot: blind spot

Laminar structure of LGN Blind spot



Interaction Potentials

Total free energy

1st term: retinotopy-generating term 2nd term: Correlational energy 3rd term: Vertical positioning energy


( , ) ( )corri i i i i i iE E e x E E y (5.7)


Correlational Energy Terms

Correlational energy for a type of interaction for a given terminal i

¨ dij: distance between terminals i and j¨ Wa: the set of all terminals participating in interaction a¨ Ba: the overall strength of the interaction energy of type a¨ : gradient ¨ ki: project number (?)


( )a

a ai ij

j W

E G d

(5.8)2

( ) exp( )( )ija a

ij ai

dG d B

s k

(5.9)

( ) 0.0015 0.4i ik k (5.10)

( )ik


Correlational Energy Terms



Vertical positioning energy

¨ yi: the vertical position of the ith terminal

¨ a = 1.5¨ Kg : sequence of progressively

more negative constants for the six terminal types.


2( )i i i g iE y ay K y (5.10)


Induction of the Laminar Transition



Trapping of the Transition by the Blind Spot Blind spot modeling

¨ Ghost magnocellular (layer 1) and prvocellular, ON po-larity (layer 6) terminals in a small portion of the con-tralateral eye

By simulated annealing



Summary

The Multiple Constraint Model Morphogenesis of the Lateral Geniculate Nucleus



QnA

What can we infer from these models?



Documents

Ch 5. The Patterning of Neural Connections 5.5 ~ 5.6 Adaptive Cooperative Systems, Martin Beckerman, 1997. Summarized by Kwonill, Kim Biointelligence Laboratory,