Principles of Computational Modelling in Neuroscience

Abstract

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.

A subsequent closed-form description of propagated signaling phenomena in the membrane of an axon

“…[5][6][7] The model (1) demonstrates how intracellular conductance, the thermodynamics of magnetization, and current modulation, function together in generating an action potential in a single, closed-form description. a subsequent formulation of an alternative model in terms of N, G, and now the membrane electric field, E m .…”

“…a subsequent formulation of an alternative model in terms of N, G, and now the membrane electric field, E m . [8][9][10][11] The model (1), that started with well-known relations from cable theory, [5][6][7]12 is consistently included in my subsequent formulation. That is to say, the axon leaky-cable conductance [5][6][7] (Ω −1 ) term G forms the basis of (1) and of my subsequent formulation ( III.…”

Neurobiological Computation and Synthetic Intelligence

“…Understanding the brain requires understanding at many different spatial scales, including those of ion channels (at a scale around 1 pm), signalling pathways (1 nm), synapses (1 μm), dendritic subunits (10 μm), neurons (100 μm), microcircuits (1 mm), neural networks (1 cm), subsystems (10 cm) and the whole nervous system (1 m) [22]. For understanding intelligence, a key question is: at what levels of the hierarchy are information processes critical to intelligence carried out?…”

“…It is also possible to model the internal processes of cells in terms of information processing and/or computation (e.g. [22]). This includes the effects of neurotransmitter reception, continuous metabolic processes, and interactions between these two.…”

“…All of the hierarchical levels of the human nervous system have been simulated in detail using digital computer technology [22]. However, both cognitive and neural simulations have had limited success to date and certainly fall far short of HLI.…”