Simulation of GABA function in the basal ganglia: computational models of GABAergic mechanisms in basal ganglia function

Abstract

This chapter outlines current interpretation of computational aspects of GABAergic circuits of the striatum. Recent hypotheses and controversial matters are reviewed. Quantitative aspects of striatal synaptology relevant to computational models are considered, with estimates of the connectivity of the spiny projection neurons and fast-spiking interneurons. Against this background, insights into the computational properties of inhibitory circuits based on analysis and simulation of simple models are discussed. The paper concludes with suggestions for further theoretical and experimental studies.

Introduction

This chapter considers the computational operations of GABAergic circuits in the basal ganglia with a particular focus on the striatum. Although recognised as playing a key role in movement, behaviour, and learning, the function of the striatum remains enigmatic. This is a problem for ‘top-down’ modelling efforts, which must start with assumptions about the computational operation the structure is performing.

We advocate the use of ‘bottom-up’ modelling — using models based on the actual anatomy and physiology — to constrain our assumptions. The neural network of the striatum provides a special opportunity to analyse the computational operations of a brain structure. Much of the information required to quantify the GABAergic circuits of the striatum has become available recently, and formal computational models are beginning to emerge. These models have stimulated sharp debates and experimental tests, which are already leading to their refinement.

Computational models are needed to define the operations of the striatum and to understand its contribution to information processing in the basal ganglia. We use the term ‘operations’ in a mathematical sense, defined as the transformations applied to inputs to produce output. These operations are determined by the properties of the neural network that makes up the striatum. They cannot be deduced from the effects of lesions on behaviour.

Optimistically, there may be a common and mathematically definable input–output operation performed by the striatum, and reiterated throughout its extent. Even so, striatal subregions may have specific functions on account of their different input sources and output targets. Alternatively, striatal subregions may show regional specialisation of function due to regional differences in the input–output operations. To date, however, few regional differences in cellular properties or connectivity have been defined, with most data suggesting similarities in these features (Kawaguchi et al., 1989; Taverna et al., 2004). On the other hand, regional differences in the input sources and output targets are well established (Alexander et al., 1986; Hoover and Strick, 1993). Thus, it is reasonable to pursue the hypothesis of a common input–output operation.

If a common input–output operation could be defined, such a definition would extend current theories of basal ganglia function based on the effects of clinical–pathological correlations. For example, current ‘box and arrow’ models of the basal ganglia stop short of defining the computational operations performed in individual structures. Such models serve as valuable heuristic devices in the development of theories of basal ganglia function, but require specification of the input–output transformations represented by the boxes and connecting arrows. While such specification has been accepted as a laudable aim, previous computational models have been strongly challenged by experimental findings, and are regarded as in need of substantial revision.

Anatomical descriptions of the spiny projection neurons of the striatum suggest a particular type of circuitry, namely a network of projection neurons interconnected by local axon collaterals (Wilson and Groves, 1980). Based on the GABAergic nature of these neurons and their synaptic contacts with other spiny neurons, several authors have proposed that the spiny projection neurons form a lateral or feedback inhibitory network (Groves, 1983; Rolls and Williams, 1986; Wickens et al., 1991). In this idea of a lateral inhibition network, each output neuron makes inhibitory synaptic contact with its neighbours, as shown in Fig. 1A. Because of obvious physical limitations, lateral inhibition is usually thought of in terms of a local domain of inhibition, extending over the dimensions of the axonal and dendritic arborisations of neighbouring cells. Such local domains need not be physically compartmentalised, but may arise as a dynamic property of local inhibitory interactions across a homogeneous field (Wilson, 2000).

Recently, our concept of the striatal circuit has been modified in the light of new findings. The anatomical connectivity among spiny projection neurons has been recognised to be quite sparse, so that not every neuron contacts every other, even within spatially limited domains (Oorschot et al., 2002; Wickens, 2002; Wickens and Oorschot, 2000). As a result connections between pairs of neurons are not in general reciprocal or symmetrical (Kotter and Wickens, 1995; Wickens et al., 1995; Kotter and Wickens, 1998; Plenz and Kitai, 1999). Furthermore, the cortical input has also been shown to be sparsely distributed, with adjacent neurons receiving few inputs in common (Kincaid et al., 1998). This modified circuit is shown in Fig. 1B. This represents the revised model of the striatal spiny cell network.

In addition to changes in our concept of the local interactions among the spiny projection neurons, it has also become evident that the feedforward interneurons of the striatum, although relatively few in number, have a disproportionately large influence. These are represented in Fig. 1C. The number of synaptic contacts that a feedforward interneuron makes is many times that of the local synaptic contacts of a single projection neuron. However, the feedforward interneurons are outnumbered almost 100 to 1 by the spiny projection neurons. Even if they made 10 times as many connections per cell, the feedforward interneurons would account for only 10% of the total GABAergic input. On the other hand they are thought to make the majority of their synaptic connections on the soma of the spiny projection neurons, and to be relatively more excitable, so it is likely they have as much influence over the striatal network as the spiny projection neuron collaterals.

We are now at the stage where the first generation of computational models is being replaced by models that take into account our updated concepts of the striatal circuit. The more recent findings have shown that many of the assumptions made in the earlier models overestimated the strength of feedback inhibition in the striatum, and hence these models require revision. On the other hand, there have so far been few models presented which incorporate the new data into the network structure of the striatum. New computer simulation models are needed in order to understand how the measurements obtained from paired recordings translate into effects on the overall network dynamics in which many neurons are active.