Topographic projection grown from genes

Question. Can a projection that preserves neighbourhoods (a topographic map) be specified by a handful of guidance genes, and does it hold for every developmental seed?

Model. A fixed 6 × 6 sensor sheet projects onto a map of 200 cells whose number and positions come from the genome. Each sensor axon aims at an affine function of its own position (positional chemoaffinity; Sperry 1963) and connects to map cells near that target with a Gaussian probability.

../_images/topographic_map_growth.gif

The circuit appearing step by step (see the frame titles for what each frame adds).

../_images/topographic_precision.png

Sensor position against the mean position of its targets in the map, for the grown network.

Run it.

python examples/topographic_map.py --cpu

stimulus at corner (0, 0): 4 map neurons fire, spike-weighted mean u of the map 0.09
stimulus at corner (1, 1): 7 map neurons fire, spike-weighted mean u of the map 0.74

In this simulation, opposite corners of the sheet drive opposite sides of the map.

Going further.

  • Make sigma, B and c genes (guidance_genes("sensor", "map")) and evolve them for topographic precision across development seeds (Tutorial 4 — Genes and evolution).

  • Add the topographic target rule or a refinement stage with correlated activity (retinal-wave-like) to sharpen the map (Willshaw & von der Malsburg 1976).

PLACEHOLDER

A quantitative study: precision vs sigma and number of map cells, across 100 development seeds, with and without activity-dependent refinement.