Stochastic Inverse Problems in Biophysics

研究者发展分析和数字重建技术，以恢复理论生物物理学中重要的数量。 所考虑的系统都包含随机效应，所考虑的测量值是首次穿越时间的分布。 发展物理的、统计的力学模型，他使用第一通道时间传递函数来构造物理模型中的参数或函数。 特别感兴趣的是重建ofmolecular潜力从键断裂时间。 分析了测量误差对重构量稳定性的影响以及测量误差对重构量稳定性的影响。 研究人员开发数学工具，理论和计算，允许定量重建ofunknown数量从测量数据波动，随机系统。 这类问题称为随机逆问题。 两个例子是分子键如何断裂，以及化学反应如何进行。 通常，对于键断裂问题，假设详细的分子相互作用是已知的，从理论上预测键的行为（例如，它断裂的可能性）。 类似地，在化学反应中，假定了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，以找到化学物质的浓度作为反应开始后时间的函数。 在反问题的表述中，我们并不知道分子间的作用力，也不知道化学反应的速率，而是测量一个键断裂前的寿命，并从这些数据中推断微观分子间的相互作用。在化学反应中，我们试图利用测量的浓度来推断化学反应速率。 这些和相关的逆问题在许多学科中具有广泛的适用性，并且可以潜在地优化和简化工业过程，例如药物设计和药物递送。 此外，这些技术可以提供有价值的理论工具，以探测细胞内的基本遗传调控过程。

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.