An Introduction to the Principles of Neuronal Modelling

Neuronal modelling is the process by which a biological neuron is represented by a mathematical structure that incorporates its biophysical and geometrical characteristics. This structure is referred to as the mathematical model or the model of the neuron. The behavior of this representation may serve a number of purposes: for example, it may be used as the basis for estimating the biophysical parameters of real neurons or it may be used to define the computational and information processing properties of a neuron. Neuronal modelling requires not only an understanding of mathematical and computational techniques, but also an understanding of the what the process of modelling entails. A general treatment of models, however, would necessarily lead to the examination of a number of philosophical questions. Here we simply discuss some aspects of modelling that in our experience have proved to be useful in the construction and application of models. These topics are not usually considered in the neurophysiological modelling literature, but an understanding of the basic assumptions of modelling, and the presumed relation between model and reality is essential for constructive work in computational neuroscience.