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

2(C) 2009, SNU Biointelligence Lab, Contents Prolog : LGN & Ocular Dominance Column at Visual Cortex 5.5 The Multiple Constraint Model  Position-Independent Affinity  Fiber-Fiber Repulsion  Nearest-Neighbor Correlated Activity  Position-Dependent Affinity  Multiple Stable States in the Retinotectal Projection 5.6 Morphogenesis of the Lateral Geniculate Nucleus  Interaction Potentials  Induction of the Laminar Transition  Trapping of the Transition by the Blind Spot

Prolog : LGN & Ocular Dominance Column at Visual Cortex 3(C) 2009, SNU Biointelligence Lab, Visual Pathway to Primary Visual Cortex for Mammals ( 2007/10/ocular_dominance_columns_a nd_t.php) Connection between Retina and LGN ( nal/46_4/html/v4604Kaas.shtml) Retinotopic maps in V1 ( Inputs to LGN (Bear et al. Neuroscience: Exploring the brain. (Lippincott Williams & Wilkins: 2006).)

Prolog : LGN & Ocular Dominance Column at Visual Cortex 4(C) 2009, SNU Biointelligence Lab, Inducing Ocular Dominance Columns by the Transplantation of a third eye ( Ocular Dominance Column ( =0)

Question What can we infer from these models? 5(C) 2009, SNU Biointelligence Lab,

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, 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, Tectum Arbor Terminal

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, (5.1)

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, (5.2)

Nearest-Neighbor Correlated Activity Electrical-activity-dependent interaction  Neighboring retinal ganglion cells  Neighboring tectal cells  Weak 10(C) 2009, SNU Biointelligence Lab,

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, (5.3) (5.4) (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, (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 modification  Partially satisfying energy constraints  Topography (uniform) 13(C) 2009, SNU Biointelligence Lab,

Multiple Stable States in the Retinotectal Projection Ablation With the retinal inputs  Ocular Dominance 14(C) 2009, SNU Biointelligence Lab,

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,

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, (5.7)

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, (5.8)(5.9) (5.10)

Correlational Energy Terms 18(C) 2009, SNU Biointelligence Lab,

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, (5.10)

Induction of the Laminar Transition 20(C) 2009, SNU Biointelligence Lab,

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,

Summary The Multiple Constraint Model Morphogenesis of the Lateral Geniculate Nucleus 22(C) 2009, SNU Biointelligence Lab,

QnA What can we infer from these models? 23(C) 2009, SNU Biointelligence Lab,