How Patterned Connections Can Be Set Up by Self-Organization

1. How Patterned Connections Can Be Set Up by Self-Organization D.J. Willshaw C. Von Der Malsburg

2. Early Visual Pathway • Retinal ganglion cells project to LGN of the Thalamus and optic tectum in midbrain • Optic tectum is the primary visual area in lower vertebrates (e.g. frogs, fish)

3. Outline • 2 early hypothesis for map formation • Gradient models • Correlated activity models • Willshaw and von der Malsburg’s model • Retinal waves

4. How are maps initially formed? 2 possibilities: • Axons project randomly. Only appropriate connections with congruent activity survive. Paul Weiss OR • Chemospecificity Hypothesis. Axons are guided to targets via chemical markers. Roger Sperry

5. Chemospecificity Hypothesis • Retinal axons returned to original, maladaptive tectal targets

6. Gradient Models • topographic branching results from repulsive ligand gradients • Growth cones have different densities of ligand receptors • Multiple ligands create complex branching

7. Example Ligands • Ephrin-A family • boundaries vary Monschau et al. (1997).

8. Q: How do maps become fine-tuned?

9. Q: How do maps become fine-tuned?A: Correlated neural activity tectum retina all-to-all connectivity  selective connectivity Input layer neighbors  output layer neighbors

10. Willshaw & von der Malsburg 1976 • Sperry-type models assume axons seek targets independently using neuron specific labels • W & vdM’s model uses the lateral connections within input and output layers • Goal of model is to encode the geometrical proximity of input cells using their correlated neural activity.

11. General Structure retina tectum • Short range excitatory connections • Long range inhibitory connections • Competitive, Hebbian synapses • Spontaneous activity within input layer

12. Equations Hj* = activity in post-syn cell j Ai* = state of pre-cell i; 1 if active at time t, 0 otherwise sij = connection weight i  j ekj = excitatory connection of post- cell k  post-cell j ikj = inhibitory connection of post- cell k  post-cell j Weight update: Normalization: M = # pre cells N = # post cells

13. Orientation of the map • orientation of map can be fixed using polarity markers • bias weights of a small pre-syn region in the desired orienation with a small post-syn region

14. Mapping results • Mean coordinates of weighted pre-cells projecting to each post-cell. • Maps shift to accommodate new cells.

15. Correlated Firing: Retinal Waves • Segregation of retinal inputs in LGN is complete before birth • TTX on optic chiasm disrupts segregation, suggests activity dependence • Spontaneous waves of synchronous RGC firing might organize mapping Feller et al, (1996)

16. Properties of Retinal Waves • Occur spontaneously • Appear randomly • Spread to a limited region: local excitation; global inhibition

17. Movie Time!

18. Summary • Retino-tectal maps are initially formed using chemical gradients. • Correlated activity is used to fine tune connections. • Exploiting lateral connections allows for more efficient genetic coding versus Sperry type models. • Retinal waves share many properties of Willshaw and von der Malsburg’s model.