How Patterned Connections Can Be Set Up by Self-Organization
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Transcript of How Patterned Connections Can Be Set Up by Self-Organization
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How Patterned Connections Can Be Set Up by Self-Organization
D.J. Willshaw
C. Von Der Malsburg
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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)
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Outline
• 2 early hypothesis for map formation– Gradient models– Correlated activity models
• Willshaw and von der Malsburg’s model
• Retinal waves
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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
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Chemospecificity Hypothesis
• Retinal axons returned to original, maladaptive tectal targets
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Gradient Models
• topographic branching results from repulsive ligand gradients
• Growth cones have different densities of ligand receptors
• Multiple ligands create complex branching
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Example Ligands
• Ephrin-A family
• boundaries vary
Monschau et al. (1997).
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Q: How do maps become fine-tuned?
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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
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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.
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General Structure
•Short range excitatory connections
•Long range inhibitory connections
•Competitive, Hebbian synapses
•Spontaneous activity within input layer
tectum
retina
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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
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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
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Mapping results
• Mean coordinates of weighted pre-cells projecting to each post-cell.
• Maps shift to accommodate new cells.
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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
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Properties of Retinal Waves
• Occur spontaneously
• Appear randomly
• Spread to a limited region: local excitation; global inhibition
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Movie Time!
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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.