This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
This project will develop mathematical models to study the influence of subcellular architecture on the dynamics of gene expression and regulation in eukaryotes. Detailed three-dimensional stochastic reaction-diffusion models that incorporate the exclusion of nuclear volume by chromatin and the sliding of transcription factors along DNA will be constructed. Systems of spatially-continuous Smoluchowski diffusion-limited reaction equations (SDLR) and lattice-based reaction-diffusion master equations (RDME) are the two primary stochastic reaction-diffusion models that have been used to study systems in which both the stochasticity in the chemical reaction process and the spatial diffusion of molecules is important. We will develop extensions to the RDME and SDLR systems of equations to account for the influence of chromatin on the motion of proteins and messenger ribonucleoproteins (mRNPs) within the nucleus of cells. A multiscale approach will be developed in which an initial model that explicitly represents chromatin fibers over length scales significantly smaller than the size of the nucleus will be constructed. This model will then be coarse grained, and combined with existing experimental imaging data to estimate parameters in effective whole-nucleus scale RDME and SDLR models. These new coarse grained models will be used to study the influence of global nuclear substructure on the time needed for gene regulatory proteins, upon entering the nucleus, to find specific DNA binding sites. Methods will also be developed for improving the accuracy of the RDME in approximating the SDLR model, and for exactly simulating the stochastic processes described by the SDLR model in the complex geometries that are present in cells. A rigorous analytical and numerical study of the predictions that the two models make for general multi-particle systems and for specific biological systems with realistic geometries will be undertaken.
To better comprehend how organisms function, respond to environmental stimuli, and to aid in treating disease, it is necessary to understand, predict, and control the behavior of individual cells. Each cell contains numerous complex dynamical processes involving proteins undergoing biochemical reactions that play a major role in cell to cell communication, cell growth and division, heart and nervous system development and function, and the development and progression of cancer. Understanding the ways that these processes activate and inactivate genes inside individual cells is fundamental to determining how these processes influence cell function. In this work we will develop explicit mathematical models of how proteins within a cell find the specific genes that they activate or inactivate. These models will allow the quantitative study of how the interior physical structure of cells influences this process. New mathematical equations will be developed to model the movement of proteins within cells containing realistic cellular substructures. New computational methods will be developed to efficiently solve these mathematical equations in order to better predict and control the dynamical processes that influence cell behavior.
