COMPARTMENTAL-MODEL RESPONSE FUNCTION FOR DENDRITIC TREES

The membrane-potential response function of a dendritic tree is constructed using a compartmental model. It is shown that if certain conditions are imposed on the compartments at branching nodes and terminals of an arbitrary tree, then the response function has a simple matrix solution that may be evaluated explicitly. Moreover, it reduces to the corresponding path-integral expression of cable theory in the continuum limit. The response function in the presence of synaptic inputs with shunting is also constructed. The compartmental approach presented here provides a particularly simple method for exploring the effects of complex geometries on spatio-temporal pattern processing in neurons.