Modeling Neural Activity

This paper provides an overview of different types of models for studying activity of nerve cells and their networks with a special emphasis on neural oscillations. One part describes the neuronal models based on the Hodgkin and Huxley formalism first described in the 1950s. It is discussed how further simplifications of this formalism enable mathematical analysis of the process of neural excitability. The focus of the paper’s second component is on network activity. Understanding network function is one of the important frontiers remaining in neuroscience. At present, experimental techniques can only provide global recordings or samples of the activity of the huge networks that form the nervous system. Models in neuroscience can therefore play a critical role by providing a framework for integration of necessarily incomplete datasets, thereby providing insight into the mechanisms of neural function. Network models can either explicitly contain individual network nodes that model the neurons, or they can be based on representations of compound population activity. The latter approach was pioneered by Wilson and Cowan in the 1970s. Finally I provide an overview and discuss how network models are employed in the study of neuronal network pathology such as epilepsy. 1. Introduction A fundamental and famous model in neuroscience was described by Hodgkin and Huxley in 1952 [1]. They generated a formalism for the dynamics of the membrane potential of the giant axon of squid describing measurements of sodium, potassium, and leakage currents. Their model can be represented by an equivalent electronic circuit of the axon’s membrane in which a capacitor models the membrane’s phospholipids and several voltage-dependent resistors represent its ion channels. Much later, after computer technology became readily available, their formalism has been widely employed and also includes other types of channels. In addition, it is used to create detailed cell models in which the cell is divided into a set of coupled compartments each represented by a separate membrane model. In many studies these computational models are embedded in networks (e.g., [2–7]). In this approach, the individual nodes of the network and their connections are simulated with the purpose of finding the properties associated with emergent network activities such as generation of synchronized bursts and oscillations. The enormous advantage of these models is that they are close to the experimental domain; that is, they may include recorded ion conductance values, morphology of observed cell types, and