Theory and Simulation in Neuroscience

Abstract

Abstract:Modeling work in neuroscience can be classified using two different criteria. The first one is the complexity of the model ranging from simplified conceptual models that are amenable to mathematical analysis to detailed models that require simulations in order to understand their properties. The second criterion is that of direction of workflow, which can be from microscopic to macroscopic scales (bottom-up) or from behavioral target functions to properties of components (top-down). We review the interaction of theory and simulation using examples of top-down and bottom-up studies and point to some current developments in the fields of computational and theoretical neuroscience.Mathematical and computational approaches in neuroscience have a long tradition that can be followed back to early mathematical theories of perception [1,2] and of current integration by a neuronal cell membrane [3]. Hodgkin and Huxley combined their experiments with a mathematical description, which they used for simulations on one of the early computers [4]. Hebb's ideas on assembly formation [5] have, already in 1956, inspired simulations on the largest computers available at that time [6]. Since the 1980ies the field of theoretical and computational neuroscience has grown enormously [7].Modern neuroscience methods requiring extensive training have led to a specialization of researchers so that neuroscience today is fragmented into labs working on genes and molecules; on single-cell electrophysiology; on multi-neuron recordings; on cognitive neuroscience and psychophysics, to name just a few. One of the central tasks of computational neuroscience is to bridge these different levels of description by simulation and mathematical theory. The bridge can be built in two different directions. Bottom-up models integrate what is known on a lower level (e.g., properties of ion channels) to explain phenomena observed on a higher level (e.g., generation of action potentials [4,[8][9][10]). Top-down models, on the other hand, start with known cognitive functions of the brain (e.g., working memory), and deduce from these how components (e.g., neurons or groups of neurons) should behave to achieve these functions. Influential examples of the top-down approach are theories of associative memories [11,12], reinforcement learning [13,14], and sparse coding [15,16].Bottom-up and top-down models can either be studied by mathematical theory (theoretical neuroscience) or by computer simulations (computational neuroscience). Theory has the advantage of providing a complete picture of the model behavior for all possible parameter settings, but analytical solutions are restricted to relatively simple models. The aim of theory is therefore to purify biological ideas to the bare minimum, so as to arrive at a 'toy model', which crystallizes a concept in a set of mathematical equations that can be fully understood. Simulations, in contrast, can be applied to all models, simplified as well as complex ones, but they can only sample the model behavior for a...

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