Elsevier

Neural Networks

Volume 23, Issue 4, May 2010, Pages 517-527
Neural Networks

2010 Special Issue
Synaptic rewiring for topographic mapping and receptive field development

https://doi.org/10.1016/j.neunet.2010.01.005Get rights and content

Abstract

A model of topographic map refinement is presented which combines both weight plasticity and the formation and elimination of synapses, as well as both activity-dependent and activity-independent processes. The question of whether an activity-dependent process can refine a mapping created by an activity-independent process is addressed statistically. A new method of evaluating the quality of topographic projections is presented which allows independent consideration of the development of the centres and spatial variances of receptive fields for a projection. Synapse formation and elimination embed in the network topology changes in the weight distributions of synapses due to the activity-dependent learning rule used (spike-timing-dependent plasticity). In this model, the spatial variance of receptive fields can be reduced by an activity-dependent mechanism with or without spatially correlated inputs, but the accuracy of receptive field centres will not necessarily improve when synapses are formed based on distributions with on-average perfect topography.

Introduction

The development of topographic mappings in the connections between brain areas is a subject that continues to occupy neuroscientists. There have been a number of theoretical investigations on the development of maps through networks with fixed connectivity and changes to synaptic weights (Goodhill, 1993, Miller et al., 1989, Song and Abbott, 2001, Willshaw, 2006, Willshaw and von der Malsburg, 1976). Other models have considered the formation and elimination of synapses with fixed weight (Elliott & Shadbolt, 1999). There have been few attempts to include both of these forms of plasticity in a model, i.e. both synaptic weight change and synaptic formation and elimination. Theories of topographic map formation can be divided by the extent to which activity-dependent processes, based on Hebbian reinforcement of the correlated activity of neighbouring cells, are deemed responsible for the formation of topography. Some assume that activity-independent processes, based on chemoaffinity (Sperry, 1963) provide an approximate mapping, which is then refined (Ruthazer & Cline, 2004). Others (Willshaw, 2006) show how activity-independent processes may fully determine the basic topography. This paper presents a model of topographic map development, which combines both weight plasticity and the formation and elimination of synapses, as well as both activity-dependent and activity-independent processes. In Section 2, synaptic plasticity and models of topographic map development are briefly reviewed, in order to place the model in context. Section 3 then presents the model, developing it from a general to a more specific form. Section 4 describes the parameterisation of the model for the purpose of simulation, as well as describing a novel approach to analysing map quality. Simulation results are then presented in Section 5, and some interesting consequences of the model are explored. This work is part of a project to implement synaptic rewiring in neuromorphic VLSI (Bamford, Murray, & Willshaw, in press), however the results presented here are purely computational.

Section snippets

Synaptic plasticity

The term “synaptic plasticity” encompasses the formation and elimination of synapses and changes in their physiological strength. The growth of axons to form synapses between neurons of different brain areas is a prerequisite for the development of topographic maps. Synaptic connections can also be eliminated; a process which has been well studied, for example at the neuromuscular junction. In neonatal mammals, each muscle fibre is innervated by axons from several different motor neurons and

Overview

In this section a model of map formation is presented. The model is intended to be general to the extent that it could apply equally to retinotectal, retinocollicular or retinogeniculate projections, and possibly others. In brief, this model proposes the following:

  • 1.

    Activity-independent processes fully specify a topographic mapping between a source and target area and guide axons from the source area towards their “ideal” location in the target area, i.e. the location dictated by the topographic

Experimental parameters

In this section, the process by which the model was parameterised is explained. Parameters for the following simulations are given in Table 1.

Simulations were run with a C++ function, with initial conditions created and data analysis carried out with Matlab. Simulations used a time step of 0.1 ms and rewiring simulations typically settled within 5 min of simulated time. Full-scale simulations were computationally intensive, necessitating the use of relatively small numbers of neurons and

Results and discussion

Three main experiments were carried out: case 1 had both rewiring and input correlations, as described in Section 3; case 2 had input correlations but no rewiring; case 3 had rewiring but no input correlations (i.e. all input neurons had rate fmean). The results are given in Table 2.

For comparisons, mean σaff and mean AD were each calculated for the feed-forward connections of the following networks: (a) the initial state (with all weights initially maximised) — these results are suffixed “init

Conclusions

A model of topographic development has been presented which includes both weight and wiring plasticity. There are three key assumptions: (a) synapses preferentially form in locations to which their axons are guided, (b) weights of dendritic synapses of a neuron are modified according to a competitive Hebbian learning rule, and (c) weaker synapses are more likely to be eliminated. In order to instantiate the model, more assumptions have been made, the main one being that the weight-change

Acknowledgements

This work was funded by EPSRC. We are grateful to Guy Billings for providing the basis of the simulator code, and to Adrian Haith and Chris Williams, as well as others at the Institute of Adaptive and Neural Computation, for mathematical insights.

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