how patterned connections can be set up by self-organization d.j. willshaw c. von der malsburg

How Patterned Connections Can Be Set Up by Self-Organization

D.J. Willshaw

C. Von Der Malsburg

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)

Outline

• 2 early hypothesis for map formation– Gradient models– Correlated activity models

• Willshaw and von der Malsburg’s model

• Retinal waves

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

Chemospecificity Hypothesis

• Retinal axons returned to original, maladaptive tectal targets

Gradient Models

• topographic branching results from repulsive ligand gradients

• Growth cones have different densities of ligand receptors

• Multiple ligands create complex branching

Example Ligands

• Ephrin-A family

• boundaries vary

Monschau et al. (1997).

Q: How do maps become fine-tuned?

Q: How do maps become fine-tuned?A: Correlated neural activity

all-to-all connectivity selective connectivity

Input layer neighbors output layer neighbors

tectum

retina

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.

General Structure

•Short range excitatory connections

•Long range inhibitory connections

•Competitive, Hebbian synapses

•Spontaneous activity within input layer

tectum

retina

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 cellsN = # post cells

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

Mapping results

• Mean coordinates of weighted pre-cells projecting to each post-cell.

• Maps shift to accommodate new cells.

Correlated Firing: Retinal Waves

Feller et al, (1996)

• 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

Properties of Retinal Waves

• Occur spontaneously

• Appear randomly

• Spread to a limited region: local excitation; global inhibition

Movie Time!

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.