CAREER: Stochastic Dynamical Models in Microbiology

这一职业项目的研究方面涉及到随机建模和渐近技术在微生物学中的两个问题上的应用，这两个问题可以在随机环境中的随机运动的框架内投射。首先，将开发一个随机模型来表示水分子如何与蛋白质表面相互作用。水在蛋白质的功能中起着至关重要的作用，在试图预测蛋白质分子动力学的分子动力学模拟中必须加以考虑。然而，将水分子详细地包含在这种模拟中是非常昂贵的，并且限制了这些模拟的实际范围。本研究中建立的水-蛋白质相互作用的弹性模型旨在更有效地表示水的影响，从而加快蛋白质动力学的计算。它将包括蛋白质表面化学和几何的晶格模型参数化和水分子在由表面晶格模型诱导的势中运动的广义扩散过程。拟议研究的第二个组成部分是对分子动力建模的分析和计算方法的扩展，以包括更多的物理真实感。渐近和随机技术将被用来描述分子马达在多个维度和/或多个自由度上工作的特征，并在力势中加入随机调制。浸没边界计算方法，最近扩展到包括热波动，将被用来模拟分子马达过程，它以一种自然的方式结合渗透效应和流体介质的动力学。更广泛地说，这个职业项目包括一个研究计划和课程开发，在本科生和研究生水平上，将主要研究人员在湍流建模方面的先前经验应用到微生物学的新问题上，并为本科生和研究生提供更系统的交流知识和解决问题的方法的机会。与蛋白质和水分子相互作用有关的研究目标有可能通过降低模拟水的影响的成本来显著加速蛋白质动力学的模拟。加速的蛋白质动力学模拟将有助于我们对蛋白质动力学的基本理解，以及设计用于与蛋白质相互作用的药物和设备的技术开发。对分子马达的分析和计算研究将旨在提高对生物细胞如何在其内部移动和运输材料的物理理解。该项目的更广泛影响包括对研究生进行微生物学数学和计算建模的跨学科培训，开设关于随机建模的新的研究生课程，改革关于概率理论的本科课程，将现代研究努力和问题作为学习数学技术的背景，将在万维网上发布材料以传播这些教学应用，并为本科生提供更广泛的机会获得数学建模经验。

The research aspect of this CAREER project concerns the application ofstochastic modeling and asymptotic techniques toward two problems inmicrobiology which can be cast within the framework of stochasticmotion in random environments. First, a stochastic model will bedeveloped to represent how water molecules interact with the surfaceof a protein. Water plays a crucial role in the functioning ofproteins, and must be accounted for in molecular dynamics simulationswhich attempt to predict the dynamics of a protein molecule. Thedetailed inclusion of water molecules in such simulations is howeververy costly and limits the practical scope of these simulations. Thestochastic model for the water-protein interaction to bedeveloped in the research is intended toprovide a more efficient representation of the effects of water andthereby accelerate protein dynamics calculations. It will consist ofa lattice model parameterization of the chemistry and geometry of theprotein surface and a generalized diffusion process for the watermolecules moving in a potential induced by the surface lattice model.A second component of the proposed research is an extension of theanalytical and computational methodology for modeling molecular motorsto include more physical realism. Asymptotic and stochastictechniques will be employed to characterize molecular motors operatingin multiple dimensions and/or with multiple degrees of freedom, and toincorporate random modulations in the force potentials. The ImmersedBoundary computational method, recently extended to include thermalfluctuations, will be used to simulate molecular motor processes in away which incorporates in a natural way osmotic effects and thedynamics of the fluid medium.More broadly, this CAREER project comprises a research program andcourse developments at the undergraduate and graduate levels whichwill apply the principal investigator's prior experience in turbulencemodeling to new problems in microbiology, and provide more systematicopportunities to communicate knowledge and problem-solvingapproaches to undergraduate and graduate students. The researchobjective pertaining to the interaction between protein and watermolecules has the potential for providing a significant speedup insimulations of protein dynamics by reducing the cost of modeling theeffects of the water. Accelerated protein dynamic simulations wouldexpedite both our basic understanding of protein dynamics and thetechnological development of drugs and devices designed to interactwith proteins. Analytical and computational research on molecularmotors will aim to improve the physical understanding of howbiological cells move and transport material within themselves. Thebroader impacts of the project include the interdisciplinary trainingof graduate students in mathematical and computational modeling inmicrobiology, the introduction of new graduate courses on stochasticmodeling, the renovation of an undergraduate course on probabilitytheory to incorporate modern researchefforts and issues as contexts for the learning of mathematicaltechniques, material to be posted on the World Wide Web to disseminatethese pedagogical applications, and broader opportunities forundergraduate students to gain experience in mathematical modeling.