Multiscale Modeling of Subcellular Structure and its Effects on Gene Expression and Regulation

该奖项是根据2009年《美国复苏和再投资法案》(公法111-5)提供资金的。这个项目将开发数学模型来研究亚细胞结构对真核生物中基因表达和调控动态的影响。详细的三维随机反应扩散模型，包括染色质对核体积的排除和转录因子沿DNA的滑动。空间连续的Smoluchowski扩散限制反应方程组(SDLR)和基于格子的反应扩散主方程(RDME)是研究化学反应过程中的随机性和分子的空间扩散都很重要的两种主要的随机反应扩散模型。我们将对RDME和SDLR方程系统进行扩展，以考虑染色质对细胞核内蛋白质和信使核糖核蛋白(MRNP)运动的影响。将开发一种多尺度方法，其中将构建一个明确表示染色质纤维长度的初始模型，该长度尺度明显小于核的大小。这个模型将被粗粒化，并结合现有的实验成像数据来估计有效的全核尺度RDME和SDLR模型中的参数。这些新的粗粒模型将被用来研究全球核亚结构对基因调控蛋白进入细胞核后寻找特定DNA结合位点所需时间的影响。还将开发方法，以提高RDME在近似SDLR模型方面的精度，并在单元中存在的复杂几何中准确地模拟SDLR模型所描述的随机过程。将对这两个模型对一般多粒子系统和具有真实几何形状的特定生物系统的预测进行严格的分析和数值研究。为了更好地理解生物体如何发挥作用，对环境刺激的反应，以及帮助治疗疾病，了解、预测和控制单个细胞的行为是必要的。每个细胞都包含许多复杂的动态过程，涉及经历生化反应的蛋白质，这些生化反应在细胞之间的交流、细胞的生长和分裂、心脏和神经系统的发育和功能以及癌症的发展和进展中发挥着重要作用。了解这些过程如何激活和失活单个细胞内的基因，是确定这些过程如何影响细胞功能的基础。在这项工作中，我们将建立明确的数学模型，说明细胞内的蛋白质如何找到它们激活或失活的特定基因。这些模型将允许对细胞内部物理结构如何影响这一过程进行定量研究。将开发新的数学方程来模拟含有真实细胞子结构的细胞内蛋白质的运动。为了更好地预测和控制影响细胞行为的动态过程，将开发新的计算方法来有效地求解这些数学方程。

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.