Neural modeling

Abstract

The brain is extraordinarily complex, containing 1011 neurons linked with 1014 connections. We can improve our understanding of individual neurons and neuronal networks by describing their behavior in mathematical and computational models. This chapter provides an introduction to neural modeling, laying the foundation for several basic models and surveying key topics. After some discussion on the motivations of modelers and the uses of neural models, we explore the properties of electrically excitable membranes. We describe in some detail the Hodgkin-Huxley model, the first neural model to describe biophysically the behavior of biological membranes. We explore how this model can be extended to describe a variety of excitable membrane behaviors, including axonal propagation, dendritic processing, and synaptic communication. This chapter also covers mathematical models that replicate basic neural behaviors through more abstract mechanisms. We briefly explore efforts to extend single-neuron models to the network level and provide several examples of insights gained through this process. Finally, we list common resources, including modeling environments and repositories, that provide the guidance and parameter sets necessary to begin building neural models.