Computational Neuroscience

From Wikipedia,

Computational Neuroscience is an interdisciplinary science that links the diverse fields of neuroscience, cognitive science, electrical engineering, computer science, physics and applied mathematics together. It serves as the primary theoretical method for investigating the function and mechanism of the nervous system. Computational neuroscience traces its historical roots to the work of people such as Andrew Huxley, Alan Hodgkin, and David Marr. Hodgkin and Huxley developed the voltage clamp and created the first mathematical model of the action potential. David Marr's work focused on the interactions between neurons, suggesting computational approaches to the study of how functional groups of neurons within the hippocampus and neocortex interact, store, process, and transmit information. Computational modeling of biophysically realistic neurons and dendrites began with the work of Wilfrid Rall, with the first multicompartmental model using cable theory.

Computational neuroscience is distinct from psychological connectionism and theories of learning from disciplines such as machine learning, neural networks and statistical learning theory in that it emphasizes descriptions of functional and biologically realistic neurons and their physiology and dynamics. These models capture the essential features of the biological system at multiple spatial-temporal scales, from membrane currents, protein and chemical coupling to network oscillations and learning and memory. These computational models are used to test hypotheses that can be directly verified by current or future biological experiments.

Currently, the field is undergoing a rapid expansion. There are many software packages, such as NEURON, that allow rapid and systematic in silico modeling of realistic neurons. Blue Brain, a collaboration between IBM and École Polytechnique Fédérale de Lausanne, aims to construct a biophysically detailed simulation of a cortical column on the Blue Gene supercomputer.

Single Neuron Modeling

Even single neurons have complex biophysical characteristics. Hodgkin and Huxley's original model only employed two voltage-sensitive currents, the fast-acting sodium and the inward-rectifying potassium. Though successful in predicting the timing and qualitative features of the action potential, it nevertheless failed to predict a number of important features such as adaptation and shunting. We now believe that there are a wide variety of voltage-sensitive currents, and the implications of the differing dynamics, modulations and sensitivity of these currents is an important topic of computational neuroscience (for reference, see Johnston and Wu, 1994).

The computational functions of complex dendrites are also under intense investigation. There is a large body of literature regarding how different currents interact with geometric properties of neurons (for reference, see Koch, 1998).

Development, Axonal Patterning and Guidance

How do axons and dendrites form during development? How do axons know where to target and how to reach these targets? How do neurons migrate to the proper position in the central and peripheral systems? How do synapses form? We know from molecular biology that distinct parts of the nervous system release distinct chemical cues, from growth factors to hormones that modulate and influence the growth and development of functional connections between neurons.

Theoretical investigations into the formation and patterning of synaptic connection and morphology is still nascent. One hypothesis that has recently garnered some attention is the minimal wiring hypothesis, which postulates that the formation of axons and dendrites effectively minimizes resource allocation while maintains maximal information storage. (for a review, see Chklovskii, 2004)

Sensory processing

Models of sensory processing understood within a theoretical framework is credited to Horace Barlow. Somewhat similar to the minimal wiring hypothesis described in the preceding section, Barlow understood the processing of the early sensory systems to be a form of efficient coding, where the neurons encoded information which minimized the number of spikes. Experimental and computational work have since supported this hypothesis in one form or another.

Current research in sensory processing is divided among biophysical modelling of different subsystems and more theoretical modelling function of perception. Current models of perception have suggested that the brain performs some form of Bayesian inference and integration of different sensory information in generating our perception of the physical world.

Memory and synaptic plasticity

Earlier models of memory are primarily based on the postulates of Hebbian learning. Biologically relevant models such as Hopfield net have been developed to address the properties of associative, rather than content-addressable style of memory that occur in biological systems. These attempts are primarily focusing on the formation of medium-term and long-term memory, localizing in the hippocampus. Models of working memory, relying on theories of network oscillations and persistent activity, have been built to capture some features of the prefrontal cortex in context-related memory. (For review, see Durstewitz et al, 2000)

One of the major problems in biological memory is how it is maintained and changed through multiple time scales. Unstable synapses are easy to train but also prone to stochastic disruption. Stable synapses forget less easily, but they are also harder to consolidate. One recent computational hypothesis involves cascades of plasticity (Fusi et al, 2004) that allow synapses to function at multiple time scales. Stereochemically detailed models of the acetylcholine receptor-based synapse with Monte Carlo method, working at the time scale of microseconds, have been built (Coggan et al, 2005). It is likely that computational tools will contribute greatly to our understanding of how synapses function and change in relation to external stimulus in the coming decades.

Behaviors of Networks

Biological neurons are connected to each other in a complex, recurrent fashion. These connections are, unlike most artificial neural networks, sparse and most likely, specific. It is not known how information is transmitted through such sparsely connected networks. It is also unknown what the computational functions, if any, of these specific connectivity pattern are.

The interactions of neurons in a small network can be often reduced to simple models such as the Ising model. The statistical mechanics of such simple systems are well-characterized theoretically. There have been some recent evidence that suggests that dynamics of arbitrary neuronal networks can be reduced to pairwise interactions (Schneidman et al, 2006; Shlens et al, 2006.) It's unknown, however, whether such descriptive dynamics impart any important computational function. With the emergence of two-photon microscopy and calcium imaging, we now have powerful experimental methods with which to test the new theories regarding neuronal networks.

Cognition, Discrimination and Learning

Computational modeling of higher cognitive functions has only begun recently. Experimental data comes primarily from single unit recording in primates. The frontal lobe and parietal lobe function as integrators of information from multiple sensory modalities. There are some tentative ideas regarding how simple mutually inhibitory functional circuits in these areas may carry out biologically relevant computation (Machens et al, 2005).

The brain seems to be able to discriminate and adapt particularly well in certain contexts. For instance, human beings seem to have an enormous capacity for memorizing and recognizing faces. One of the key goals of computational neuroscience is to dissect how biological systems carry out these complex computations efficiently and potentially replicate these processes in building intelligent machines.


The ultimate goal of neuroscience is to be able to explain the every day experience of conscious life. Francis Crick and Christof Koch made some attempts in formulating a consistent framework for future work in neural correlates of consciousness (NCC), though much of the work in this field remains speculative. (for a review, see Koch and Crick, 2003)

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