A neuron with dendrites is believed to be the fundamental computational unit in the brain. To understand information processing in the brain, mathematical modeling of single-neuron dynamics has proven to be an effective approach. Among all the neuron models, multi-compartment (PDEs) models and single-compartment (ODE) models are two popular frameworks that describe a neuron at different levels. In general, multi-compartment models incorporating dendritic features are biologically detailed but mathematically intractable and computationally inefficient, while single-compartment models only characterizing the cell body are mathematically tractable and computationally efficient but biologically oversimplified. A neuron model with both simple mathematical structure and rich biological detail is thus still lacking. In this talk, by using asymptotic analysis, I will derive a class of single-compartment neuron models, consisting of one ordinary differential equation, from the corresponding multi-compartment models consisting of hundreds of partial differential equations, and further verify the derived model in realistic neuron simulations and biological experiments. In contrast to the existing single-compartment models, our derived model is capable of performing detailed dendritic computations such as feature selectivity and sound localization, and can greatly reduce the computational cost in large-scale neuronal network simulations without the loss of dendritic functions.
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