Hebbian learning is jointly controlled by electrotonic and input structure

Previous studies have examined how synaptic weights in simple processing elements self-organize under a Hebbian learning rule. Here we treat the problem of a neuron with realistic electrotonic structure, discuss the relevance of our findings to synaptic modifications in hippocampal pyramidal cells, and illustrate them with simulations of an anatomically accurate hippocampal neuron model. We show that the synaptic weight vector M converges toward the principal eigenvector of the matrix [〈xj(xk*ν˜kj)〉], where xj and xk represent presynaptic activity, ν˜kj(t) is the membrane potential at location j recorded t seconds after a unit impulse of charge is injected at location k, and * is the convolution operator. Thus the synaptic strengths are regulated by the spatiotemporal pattern of presynaptic activity filtered by the electrotonic structure of the neuron.