General Introduction
Powerful physical theories and mathematical tools are available for understanding "information processing" systems generally construed. However, applying these tools effectively to neurobiological systems raises a host of new and challenging problems. We have developed a framework that takes seriously the unique computational characteristics of neurons and neural systems while adopting the well-established tools of information theory and signal processing. We believe that this synergistic approach provides a path to discovering how these very complex systems operate at multiple levels of scale. The methodology that results from our framework has proved a uniquely powerful one for constructing simulations of sensory, motor, and cognitive systems.
Our aim is to provide both engineers and neuroscientists with the theoretical background and mathematical tools necessary for generating precise quantitative models of complex, realistic, spiking networks. We have developed the framework by trying to gain a practical understanding of signal encoding, signal transmission, and signal decoding in realistic neurons.
Our approach is widely applicable at the systems level, while remaining committed to realistic single cell models. In particular, we have extended previous work by Rieke et al. (1997) on single cell representation, and Georgopoulos (1986) on population coding, by combining them into a single framework. Thus, we can explore how large populations of neurons can be used to distributedly encode scalars, vectors, and functions.
In addition, we have developed a general means of embedding dynamics into such networks, by relying on the well-established tools of control theory for constructing models of neurobiological systems. For example, we have described how to build models of the kinds of attractor networks found in real biological systems (including point attractors, line attractors, and cyclic attractors). As well, we have developed a novel model of lamprey locomotion, and the vestibular system.
Notably, our framework does not depend on any particular model of spike generation at the cellular level. Thus, the complexity of the model (and the resulting computing time) can be chosen by the designer to a significant degree. In addition, the modeler can construct models of large systems using mixed degrees of detail. This allows researchers to model a few neurons in the system in exquisite detail while modeling the remainder of the system at lower levels of detail. This enables a modeler to explore the influence of ion channels on large scale system performance in a computationally efficient manner. This is very important for researchers interested in running models of large neural systems with limited computational resources.
On this website, we provide examples of the application of our approach to neural systems commonly studied in neuroscience. As well, we have provided Matlab® code that can be used to apply the framework to construct new models. For more information on the framework please see the research, framework, and publication pages. The most indepth information regarding our approach can be found in our recent book.
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