CAREER: Stochastic Dynamical Models in Microbiology

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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.