Decoding neuronal firing and modelling neural networks.

Biological neural networks are large systems of complex elements interacting through a complex array of connections. Individual neurons express a large number of active conductances (Connors et al., 1982; Adams & Gavin, 1986; Llinás, 1988; McCormick, 1990; Hille, 1992) and exhibit a wide variety of dynamic behaviors on time scales ranging from milliseconds to many minutes (Llinás, 1988; Harris-Warrick & Marder, 1991; Churchland & Sejnowski, 1992; Turrigiano et al., 1994). Neurons in cortical circuits are typically coupled to thousands of other neurons (Stevens, 1989) and very little is known about the strengths of these synapses (although see Rosenmund et al., 1993; Hessler et al., 1993; Smetters & Nelson, 1993). The complex firing patterns of large neuronal populations are difficult to describe let alone understand. There is little point in accurately modeling each membrane potential in a large neural circuit unless we have an effective method for interpreting (or even visualizing) the enormous numerical output of such a model. Thus, major issues in modeling biological circuits are: i) How do we describe and interpret the activity of a large population of neurons and how do we model neural circuits when ii) individual neurons are such complex elements and iii) our knowledge of the synaptic connections is so incomplete. This review covers some of the approaches and techniques that have been developed to try to deal with these problems. Although they cannot be considered solved, progress has been made and, by combining a number of different techniques, we can put together a fairly comprehensive description of at least some aspects of how neural systems function. In this review, I will concentrate on mathematical and computational methods with applications provided primarily to illustrate the methods. The reader can consult the references for applications to specific neural systems. Four general techniques have proven particularly valuable for analyzing complex neural systems and dealing with the problems mention above: