CAREER: Stochastic Dynamical Models in Microbiology

Rensselaer Polytechnic Institute, Troy NY

Investigators

Abstract

The research aspect of this CAREER project concerns the application of stochastic modeling and asymptotic techniques toward two problems in microbiology which can be cast within the framework of stochastic motion in random environments. First, a stochastic model will be developed to represent how water molecules interact with the surface of a protein. Water plays a crucial role in the functioning of proteins, and must be accounted for in molecular dynamics simulations which attempt to predict the dynamics of a protein molecule. The detailed inclusion of water molecules in such simulations is however very costly and limits the practical scope of these simulations. The stochastic model for the water-protein interaction to be developed in the research is intended to provide a more efficient representation of the effects of water and thereby accelerate protein dynamics calculations. It will consist of a lattice model parameterization of the chemistry and geometry of the protein surface and a generalized diffusion process for the water molecules moving in a potential induced by the surface lattice model. A second component of the proposed research is an extension of the analytical and computational methodology for modeling molecular motors to include more physical realism. Asymptotic and stochastic techniques will be employed to characterize molecular motors operating in multiple dimensions and/or with multiple degrees of freedom, and to incorporate random modulations in the force potentials. The Immersed Boundary computational method, recently extended to include thermal fluctuations, will be used to simulate molecular motor processes in a way which incorporates in a natural way osmotic effects and the dynamics of the fluid medium. More broadly, this CAREER project comprises a research program and course developments at the undergraduate and graduate levels which will apply the principal investigator's prior experience in turbulence modeling to new problems in microbiology, and provide more systematic opportunities to communicate knowledge and problem-solving approaches to undergraduate and graduate students. The research objective pertaining to the interaction between protein and water molecules has the potential for providing a significant speedup in simulations of protein dynamics by reducing the cost of modeling the effects of the water. Accelerated protein dynamic simulations would expedite both our basic understanding of protein dynamics and the technological development of drugs and devices designed to interact with proteins. Analytical and computational research on molecular motors will aim to improve the physical understanding of how biological cells move and transport material within themselves. The broader impacts of the project include the interdisciplinary training of graduate students in mathematical and computational modeling in microbiology, the introduction of new graduate courses on stochastic modeling, the renovation of an undergraduate course on probability theory to incorporate modern research efforts and issues as contexts for the learning of mathematical techniques, material to be posted on the World Wide Web to disseminate these pedagogical applications, and broader opportunities for undergraduate students to gain experience in mathematical modeling.