Stochastic Inverse Problems in Biophysics

研究人员开发了解析和数值重建技术，以恢复理论生物物理学中的重要数量。所考虑的系统全部包含随机效应，并且要考虑的量测是首次通过时间的分布。在发展物理和统计力学模型时，他使用第一通道的时间分布函数来构造物理模型中的参数或函数。特别令人感兴趣的是从键断裂时代重建大分子势。分析了测量误差对重建量稳定性的影响，以及测量误差的范围。研究人员开发了理论和计算的数学工具，允许在波动的随机系统中从测量数据中定量重建未知量。这类问题称为随机逆问题。两个例子是分子键如何断裂，以及化学反应是如何进行的。通常，对于键断裂问题，假设已知详细的分子相互作用，由此从理论上预测键的行为(例如，它断裂的可能性有多大)。同样，在化学反应中，假定特定的反应速率和化学网络。然后用这些“给定的”参数求解速率方程，以求出，比方说，在反应开始后，作为时间函数的化学物种的浓度。在反问题的表述中，我们不知道分子间力或化学反应的速率。相反，我们测量键在断裂之前的寿命，并从这些数据推断微观分子相互作用。在化学反应中，我们试图用测量的浓度来推断化学反应速率。这些反问题和相关的反问题在许多学科中具有广泛的适用性，并可能优化和简化药物设计和药物输送等工业过程。此外，这些技术可以为探索细胞内基本的遗传调控过程提供有价值的理论工具。

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.