# Mostly Biomathematics Lunchtime Seminar

#### Modeling Single Neuron Dynamics and Dendritic Computation

**Speaker:**
Songting Li, New York University, Courant Institute of Mathematical Sciences

**Location:**
Warren Weaver Hall 1314

**Date:**
Tuesday, November 28, 2017, 12:30 p.m.

**Synopsis:**

A neuron is believed to be the fundamental computational unit in the brain. To theoretically investigate brain computation, various types of single-neuron models have been developed. Among them, multi-compartment models incorporating dendritic features are biologically detailed but mathematically intractable, while single-compartment models describing the cell body are mathematically tractable but biologically oversimplified. A single-neuron model possessing both simple mathematical structures and rich biological details is lacking in general. In this talk, using asymptotic analysis, I will derive a single-compartment neuron model simply described by an ordinary differential equation from a multi-compartment model described by a set of partial differential equations. The derived model captures the effect of dendritic integration, which has been further verified in realistic neuron simulations and electrophysiological experiments. In contrast to traditional single-compartment models, our derived model is capable of performing many dendritic computations including directional selectivity and coincidence detection, and it greatly improves the computational efficiency in large-scale neuronal network simulations without the loss of neuronal dendritic functions.