ABSTRACT

Biological forms of computation present some of the most promising?yet challenging?examples of adaptive mechanisms that we would like to understand well enough to engineer ourselves. However, models for biological processes are becoming increasingly detailed and unwieldy in an effort to reproduce ever-more detailed experimental observations. This research involves the development of mathematical theory, algorithms, and software for efficiently constraining models to data and to analyze their properties mathematically. A sufficiently detailed understanding through mathematical analysis permits the generalization of operating principles that provide biological insights and a basis for engineering similar mechanisms. In particular, the investigators apply these methods to infer adaptive and self-governing properties from detailed dynamical models of excitable neural and cardiac tissue.

Although detailed models of physical systems may involve many variables and parameters, mathematical analysis often demonstrates effective lower dimensionality in their operating principles. A decomposition of a complex model to approximate lower-dimensional sub-regimes facilitates analysis by standard techniques from dynamical systems and optimization theory. In contrast to a priori reductions to ?toy? models, software tools monitor and control the sources of error in the approximations, in particular the assumptions underlying the decomposition are validated against global constraints to ensure consistency with the behavior of the full physical system. To study abstract properties of the system such as adaptiveness, decompositions can be made in terms of measurements of qualitative features in the dynamics. These features may be simple or complex according to the needs of the problem. Their formalized definition in software structures enables existing techniques for model optimization and inference to be applied more intelligently, particularly in the context of model behavior that may resemble experimental data only in qualitative terms.

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