Spatiotemporal pattern processing in a compartmental-model neuron

A neural-network model is constructed in which the activation state V(t) of a neuron is of the general form V(t)=${\mathit{tsum}}_{\mathit{j}}$ F ${\mathrm{\chi }}_{\mathit{j}}$(t,s)${\mathit{w}}_{\mathit{j}}$ ${\mathit{a}}_{\mathit{j}}$(s)ds, where ${\mathit{w}}_{\mathit{j}}$ is the weight of the jth input line, ${\mathit{a}}_{\mathit{j}}$(s) is the input at time s, and ${\mathrm{\chi }}_{\mathit{j}}$ is a response function that incorporates details concerning the passive membrane properties of dendrites. The response function is determined using a compartmental model of the dendrites. A simple analytical expression for ${\mathrm{\chi }}_{\mathit{j}}$ is derived in the special case of an infinite uniform chain of compartments along similar lines to the analysis of diffusion on a one-dimensional lattice. This is then used to study the response of the model neuron to input patterns of specific spatial frequency across the chain. It is also shown how the inclusion of shunting effects results in the neuron’s activation state being a nonlinear function of inputs, and that this provides a possible solution to the problem of high firing rates in neural-network models. Finally, perceptronlike learning in the model neuron is discussed, and the ability of the neuron to extract temporal features of an input signal is investigated.