In theoretical biophysics, Professor Clark and his students are engaged in a program of research in computational neuroscience in collaboration with faculty in the Washington University School of Medicine.
The central hypothesis being explored by the computational neuroscience group as they seek a fundamental understanding of brain function is that ensembles of neurons, through their collective activities, encode and process probability density functions (PDFs) of analog variables pertaining to the organism's environment or internal states.
The formulation is explicitly based on the Bayesian approach to probability theory advanced by Wayman Crow Professor Emeritus Edwin Jaynes (1922-1998). An extension of Bayesian belief nets--together with the mathematics of signal processing, neural coding, and overcomplete functional representation--provides a general framework for the design of large-scale cortical circuits in which top-down models influence bottom-up processing of external stimuli. These ideas, along with more traditional modeling approaches such as dynamical systems theory, are being applied to problems in vision, sensory-motor processing, synaptic competition, and learning.
Professor Clark and his co-workers have also been developing and applying advanced methods for classification and function approximation involving artificial neural networks that can learn by example. These methods are employed to create global statistical models of the properties of complex physical systems, including atomic nuclei and crystalline materials of technological interest. The same techniques may be applied to medical diagnosis and analysis of medical images.
Professor Carlsson's work, in computational cell biology, is aimed at developing a microscopic understanding of the polymerization-depolymerization processes which allow cells to move and divide. Such processes involve the formation of supramolecular structures, such as branched networks, or parallel bundles, built from filaments of the protein actin. These structures appear and disappear rapidly in cells, and are crucial for generating mechanical force. The growth of the supramolecular structures is being modeled by a combination of Brownian dynamics and stochastic growth simulation, and analytic theory. The main aims of the modeling are to understand the extraordinary responsiveness of the supramolecular actin structures to external stimuli, to explain how the interior of a cell acts as an excitable medium, and to predict the phase diagram of the supramolecular structures in terms of the parameters that characterize their growth, cross-linking, and depolymerization. This work is being carried out in collaboration with Professor John Cooper's group at the Washington University School of Medicine.