title: Bilinearity in spatiotemporal integration of synaptic inputs.
abstract: Neurons process information via integration of synaptic inputs from dendrites. Many experimental results demonstrate dendritic integration could be highly nonlinear, yet few theoretical analyses have been performed to obtain a precise quantitative characterization analytically. Based on asymptotic analysis of a two-compartment passive cable model, given a pair of time-dependent synaptic conductance inputs, we derive a bilinear spatiotemporal dendritic integration rule. The summed somatic potential can be well approximated by the linear summation of the two postsynaptic potentials elicited separately, plus a third additional bilinear term proportional to their product with a proportionality coefficient [Formula: see text]. The rule is valid for a pair of synaptic inputs of all types, including excitation-inhibition, excitation-excitation, and inhibition-inhibition. In addition, the rule is valid during the whole dendritic integration process for a pair of synaptic inputs with arbitrary input time differences and input locations. The coefficient [Formula: see text] is demonstrated to be nearly independent of the input strengths but is dependent on input times and input locations. This rule is then verified through simulation of a realistic pyramidal neuron model and in electrophysiological experiments of rat hippocampal CA1 neurons. The rule is further generalized to describe the spatiotemporal dendritic integration of multiple excitatory and inhibitory synaptic inputs. The integration of multiple inputs can be decomposed into the sum of all possible pairwise integration, where each paired integration obeys the bilinear rule. This decomposition leads to a graph representation of dendritic integration, which can be viewed as functionally sparse.
authors.affiliation: Department of Mathematics, MOE-LSC and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China.
authors.forename: Songting
authors.initials: S
authors.lastname: Li
authors.affiliation: State Key Laboratory of Cognitive Neuroscience and Learning and IDG/McGovern Institute for Brain Research, Beijing Normal University, Beijing, China.
authors.forename: Nan
authors.initials: N
authors.lastname: Liu
authors.affiliation: State Key Laboratory of Cognitive Neuroscience and Learning and IDG/McGovern Institute for Brain Research, Beijing Normal University, Beijing, China.
authors.forename: Xiao-Hui
authors.initials: XH
authors.lastname: Zhang
authors.affiliation: Department of Mathematics, MOE-LSC and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China.
authors.forename: Douglas
authors.initials: D
authors.lastname: Zhou
authors.affiliation: Department of Mathematics, MOE-LSC and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China; Courant Institute of Mathematical Sciences and Center for Neural Science, New York University, New York, New York, United States of America; NYUAD Institute, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates.
authors.forename: David
authors.initials: D
authors.lastname: Cai
mesh_terms: D000818:Animals; D056547:CA1 Region, Hippocampal / Q000166:cytology; D003198:Computer Simulation; D003712:Dendrites / Q000502:physiology; D008959:Models, Neurological; D051381:Rats; D013569:Synapses / Q000502:physiology*