Communications in Mathematical Sciences

Volume 13 (2015)

Number 2

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

Pages: 565 – 575

(Fast Communication)

DOI: http://dx.doi.org/10.4310/CMS.2015.v13.n2.a16

Authors

Songting Li (Department of Mathematics, MOE-LSC and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China)

Douglas Zhou (Department of Mathematics, MOE-LSC and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China)

David Cai (Department of Mathematics, MOE-LSC and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China; Courant Institute and Center for Neural Sciences, New York Univ., U.S.A.; and NYUAD Institute, NYU Abu Dhabi, United Arab Emirates)

Abstract

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 $\textit{E-I}$ dendritic integration on any branches. The novel characterization is confirmed by the numerical simulation of a biologically realistic neuron.

Keywords

cable model, Green’s function, asymptotic solution, dendritic integration

2010 Mathematics Subject Classification

35C20, 92C20

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