Redwood Neuroscience
Title: “Network Models with "Realistic"Synaptic Connections”
Harold
Lecar and Michael Wu
Department
of Neurobiology
Biophysics
Graduate Group
Abstract:
We discuss two neural network
problems for which we have attempted to incorporate physiologically and neuroanatomically reasonable synaptic connections.
(a) Mutual information in dilute, asymmetric networks (Greenfield & Lecar, Phys. rev. E 63 , 041905,
2001). Networks of binary neurons with asymmetric synaptic connections
can be shown to undergo an order-chaos phase transition
as network parameters, such as connectivity and degree of asymmetry, are
varied. We show that mutual information, which has been used as a measure of
computational activity, is maximized at the onset of chaos. Generic
random Boolean networks with arbitrary threshold conditions tend to exhibit the
phase transition at rather low degrees of connectivity, which would contradict
the generally quiet state of the cortex. When the network model is
modified to incorporate realistic postsynaptic integration, the critical
connectivity is pushed up to realistic values.
(b) From local learning rules in the visual cortex to systems of nonlinear Volterra-Hammerstein integrodifferential
equations. Using current knowledge of synaptic plasticity and including
the lateral connectivity of cortical networks, we are able to derive a system of nonlinear integrodifferential
equations which governs the development of receptive field domains in the
visual cortex.. The system is solved numerically using a forward Euler
method, and exhibits (albeit suboptimally) symmetry
breaking and redistribution of lateral weights. The system has flexible
features which allow us to incorporate realistic physiological details without
much additional computational load. Specifically we wil
discuss ways to incorporate synaptic efficacy and multi-time-scale synaptic
plasticity in order to test consequences of current experimental work.