Stochastic Inverse Problems in Biophysics

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The investigator develops analytical and numericalreconstruction techniques to recover quantities important intheoretical biophysics. The systems considered all includestochastic effects, and the measurements to be considered aredistributions of first passage times. Developing physical,statistical mechanical models, he uses the first passage timedistribution function to construct parameters or functions in thephysical model. Of particular interest is the reconstruction ofmacromolecular potentials from bond-breaking times. An analysisof bounds and how measurement errors affect the stability ofreconstructed quantities is undertaken. The investigator develops mathematical tools, theoreticaland computational, that allow quantitative reconstruction ofunknown quantities from measured data in fluctuating, randomsystems. This class of problems is called stochastic inverseproblems. Two examples are how molecular bonds break, and howchemical reactions progress. Typically, for the bond-breakingproblem, the detailed molecular interactions are assumed known,from which the behavior of the bond (e.g. how likely it is tobreak) is theoretically predicted. Similarly, in chemicalreactions, specific reaction rates and chemical networks areassumed. One then solves the rate equations with these "given"parameters to find, say, the concentration of a chemical speciesas a function of time after the start of a reaction. In theformulation of the inverse problem, we do not know theintermolecular forces, or the rates of chemical reactions.Rather, we measure the lifetime of a bond before it breaks, andfrom these data, infer the microscopic molecular interactions. In chemical reactions, we attempt to use the measuredconcentrations to deduce the chemical reaction rates. These andrelated inverse problems have wide applicability in numerousdisciplines, and can potentially optimize and simplify industrialprocesses such as drug design and drug delivery. Moreover, thetechniques can provide valuable theoretical tools with which toprobe fundamental genetic regulation processes inside cells.