Ch 5. The Patterning of Neural Connections 5.5 ~ 5.6 Adaptive Cooperative Systems, Martin Beckerman, 1997. Summarized by Kwonill, Kim Biointelligence Laboratory, Seoul National University http://bi.snu.ac.kr/
Jan 17, 2018
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
3(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
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).)
Prolog : LGN & Ocular Dominance Col-umn at Visual Cortex
4(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
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?
5(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
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
6(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
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
7(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
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
8(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
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
9(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
(5.2)
ijr
1a 2a
Nearest-Neighbor Correlated Activity
Electrical-activity-dependent interaction¨ Neighboring retinal ganglion cells
Neighboring tectal cells¨ Weak
10(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Position-Dependent Affinity
A set of position dependent affinities between growth cones and their tectal targets
Fiber-fiber term
Fiber-tectum term
11(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
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
12(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
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)
13(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Multiple Stable States in the Retinotectal Projection Ablation
With the retinal inputs¨ Ocular Dominance
14(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
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
15(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Interaction Potentials
Total free energy
1st term: retinotopy-generating term 2nd term: Correlational energy 3rd term: Vertical positioning energy
16(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
( , ) ( )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 (?)
17(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
( )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
18(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
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.
19(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
2( )i i i g iE y ay K y (5.10)
Induction of the Laminar Transition
20(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
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
21(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Summary
The Multiple Constraint Model Morphogenesis of the Lateral Geniculate Nucleus
22(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/
QnA
What can we infer from these models?
23(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/