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

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Presentation on theme: "Ch 5. The Patterning of Neural Connections 5.5 ~ 5.6 Adaptive Cooperative Systems, Martin Beckerman, 1997. Summarized by Kwonill, Kim Biointelligence Laboratory,"— Presentation transcript:

1 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/

2 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

3 Prolog : LGN & Ocular Dominance Column at Visual Cortex 3(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Visual Pathway to Primary Visual Cortex for Mammals (http://scienceblogs.com/purepedantry/ 2007/10/ocular_dominance_columns_a nd_t.php) Connection between Retina and LGN (http://dels.nas.edu/ilar_n/ilarjour nal/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).)

4 Prolog : LGN & Ocular Dominance Column at Visual Cortex 4(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/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/viewtopic.php?f=5&t=124049&start =0)

5 Question What can we infer from these models? 5(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

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

7 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/http://bi.snu.ac.kr/ Tectum Arbor Terminal

8 Position-Independent Affinity The contribution to the total free energy of the position- independent affinity of the ith fiber  c 0 : 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/http://bi.snu.ac.kr/ (5.1)

9 Fiber-Fiber Repulsion Short-range fiber-fiber repulsion due to interactions of the ith fiber with the others  c 1 : positive coupling constant (< c 0 )  : 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/http://bi.snu.ac.kr/ (5.2)

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

11 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/http://bi.snu.ac.kr/ (5.3) (5.4) (5.5)

12 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/http://bi.snu.ac.kr/ (5.6)

13 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 modification  Partially satisfying energy constraints  Topography (uniform) 13(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

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

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

16 Interaction Potentials Total free energy 1 st term: retinotopy-generating term 2 nd term: Correlational energy 3 rd term: Vertical positioning energy 16(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ (5.7)

17 Correlational Energy Terms Correlational energy for a type of interaction for a given terminal i  d ij : distance between terminals i and j  W a : the set of all terminals participating in interaction a  B a : the overall strength of the interaction energy of type a  : gradient  k i : project number (?) 17(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ (5.8)(5.9) (5.10)

18 Correlational Energy Terms 18(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

19 Vertical positioning energy  y i : the vertical position of the ith terminal  a = 1.5  K g : sequence of progressively more negative constants for the six terminal types. 19(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ (5.10)

20 Induction of the Laminar Transition 20(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

21 Trapping of the Transition by the Blind Spot Blind spot modeling  Ghost magnocellular (layer 1) and prvocellular, ON polarity (layer 6) terminals in a small portion of the contralateral eye By simulated annealing 21(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

22 Summary The Multiple Constraint Model Morphogenesis of the Lateral Geniculate Nucleus 22(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

23 QnA What can we infer from these models? 23(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

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