Stochastic Inverse Problems in Biophysics

University Of California-Los Angeles, Los Angeles CA

Investigators

Abstract

The investigator develops analytical and numerical reconstruction techniques to recover quantities important in theoretical biophysics. The systems considered all include stochastic effects, and the measurements to be considered are distributions of first passage times. Developing physical, statistical mechanical models, he uses the first passage time distribution function to construct parameters or functions in the physical model. Of particular interest is the reconstruction of macromolecular potentials from bond-breaking times. An analysis of bounds and how measurement errors affect the stability of reconstructed quantities is undertaken. The investigator develops mathematical tools, theoretical and computational, that allow quantitative reconstruction of unknown quantities from measured data in fluctuating, random systems. This class of problems is called stochastic inverse problems. Two examples are how molecular bonds break, and how chemical reactions progress. Typically, for the bond-breaking problem, the detailed molecular interactions are assumed known, from which the behavior of the bond (e.g. how likely it is to break) is theoretically predicted. Similarly, in chemical reactions, specific reaction rates and chemical networks are assumed. One then solves the rate equations with these "given" parameters to find, say, the concentration of a chemical species as a function of time after the start of a reaction. In the formulation of the inverse problem, we do not know the intermolecular forces, or the rates of chemical reactions. Rather, we measure the lifetime of a bond before it breaks, and from these data, infer the microscopic molecular interactions. In chemical reactions, we attempt to use the measured concentrations to deduce the chemical reaction rates. These and related inverse problems have wide applicability in numerous disciplines, and can potentially optimize and simplify industrial processes such as drug design and drug delivery. Moreover, the techniques can provide valuable theoretical tools with which to probe fundamental genetic regulation processes inside cells.