Analysis of the dendritic integration of excitatory and inhibitory inputs using cable models

We address the question of how a neuron integrates excitatory (E) and inhibitory (I) synaptic inputs from different dendritic sites. For an idealized neuron model with an unbranched dendritic cable, we construct its Green's function and carry out an asymptotic analysis to obtain its solutions. Using these asymptotic solutions, in the presence of E and I inputs, we can successfully reveal the underlying mechanisms of a dendritic integration rule, which was discovered in a recent experiment. Our analysis can be extended to the multi-branch case to characterize the E-I dendritic integration on any branches. The novel characterization is confirmed by the numerical simulation of a biologically realistic neuron.