Sep 24, 2020
Mathematical modeling of spatial neuron dynamics: from dendritic integration to conductance measurement
Douglas Zhou 周栋焯
School of Mathematical Sciences & Institute of Natural Sciences, Shanghai Jiao Tong University
Abstract：
Neurons compute by integrating spatiotemporal excitatory (E) and inhibitory (I) synaptic inputs received from the dendrites. The investigation of dendritic integration is crucial for understanding neuronal information processing. Yet quantitative rules of dendritic integration and their mathematical modeling remain to be fully elucidated. Here neuronal dendritic integration is investigated by using theoretical and computational approaches. Based on the passive cable theory, a high dimensional PDE-based cable neuron model with spatially branched dendritic structure is introduced to describe the neuronal subthreshold membrane potential dynamics, and the analytical solutions in response to conductance-based synaptic inputs are derived. Using the analytical solutions, a bilinear dendritic integration rule is identified, and it characterizes the change of somatic membrane potential when receiving multiple spatiotemporal synaptic inputs from the dendrites. In addition, the PDE-based cable neuron model is reduced to an ODE-based point neuron model with the feature of bilinear dendritic integration inherited, thus providing an efficient computational framework of neuronal simulation incorporating certain important dendritic functions. Furthermore, to solve the inverse problem related to dendritic integration, methods are developed to recover both the effective and local synaptic conductances from the somatic membrane potential or the synaptic current arriving at the soma induced by synaptic inputs from the dendrites. Our methods overcome the challenge of the space clamp effect and present a reliable assessment of the role of synaptic activity in neuronal computation. The above results to the situation of active dendrites are further extended by numerical verification in realistic neuron simulations. Our work provides a comprehensive and systematic theoretical and computational framework for the study of spatial neuron dynamics.
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