The nervous system is made up of a large number of interacting elements. To understand how such a complex system functions requires the construction and analysis of computational models at many different levels. This book provides a step-by-step account of how to model the neuron and neural circuitry to understand the nervous system at all levels, from ion channels to networks. Starting with a simple model of the neuron as an electrical circuit, gradually more details are added to include the effects of neuronal morphology, synapses, ion channels and intracellular signalling. The principle of abstraction is explained through chapters on simplifying models, and how simplified models can be used in networks. This theme is continued in a final chapter on modelling the development of the nervous system. Requiring an elementary background in neuroscience and some high school mathematics, this textbook is an ideal basis for a course on computational neuroscience.
The subthalamic nucleus (STN) and external globus pallidus (GP) form a recurrent excitatory-inhibitory interaction within the basal ganglia. Through a computational model of these interactions we show that, under the influence of appropriate external input, the two nuclei can be switched between states of high and low activity or can generate oscillations consisting of bursts of high-frequency activity repeated at a low rate. It is further demonstrated from the model that the generation of the repetitive bursting behaviour is favoured by increased inhibition of the GP, which is a condition indicated in Parkinson's disease. Paradoxically, increased striatal inhibition of the GP is predicted to cause an increase rather than a decrease in its mean firing rate. These behaviours, arising from a biologically inspired computational model of the STN-GP interaction, have important consequences for basal ganglia function and dysfunction.
A computational model of the rat subthalamic nucleus projection neuron is constructed using electrophysiological and morphological data and a restricted set of channel specifications. The model cell exhibits a wide range of electrophysiological behaviors characteristic of rat subthalamic neurons. It reveals that a key set of three channels play a primary role in distinguishing behaviors: a high-voltage-activated calcium channel (Cav 1.2.-1.3), a low-voltage-activated calcium channel (Cav 3.-), and a small current calcium-activated potassium channel (KCa 2.1-2.3). Short and long posthyperpolarization rebound responses, low-frequency rhythmic bursting (< 1 Hz), higher-frequency rhythmic bursting (4-7 Hz), and slow action and depolarizing potentials are behaviors all mediated by the interaction of these channels. This interaction can generate a robust calcium-dependent extended depolarization in the dendrites (a depolarizing plateau). The diversity observed in the rat subthalamic physiology (such as short or long rebounds, or the presence of low-frequency rhythmic busting) can arise from alterations in both the density and distributions of these channel types and, consequently, their ability to generate this depolarizing plateau. A number of important predictions arise from the model. For example, blocking or disrupting the low-voltage-activated Cav 3.- calcium current should mute the emergence of rebound responses and rhythmic bursting. Conversely, increasing this channel current via large hyperpolarizing potentials in combination with partial blockade of the high-voltage-activated calcium channels should lead to the more experimentally elusive in vitro high-frequency bursting.
A composite model of the subthalamic nucleus is developed from physiological and anatomical considerations. First, study of a geometric model of the anatomical arrangements of projection neurons within the nucleus indicates that they form a massively connected network. Second, given the excitatory nature of these neurons, their threshold and peak firing rates, a simple model of neuron responses reveals that large regions of this highly interconnected nucleus can respond to excitatory input in the form of a wide-spread uniform pulse. Such widespread pulses of activity may act as a braking signal that resets the major basal ganglia output nuclei.
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