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）资助的。本计画将发展数学模型，以研究真核生物中亚细胞结构对基因表现与调控动态的影响。 详细的三维随机反应扩散模型，包括核体积的排斥染色质和转录因子沿沿着DNA的滑动将被构建。空间连续的Smoluchowski扩散限制反应方程组（SDLR）和基于格点的反应扩散主方程组（RDME）是研究化学反应过程中的随机性和分子空间扩散都很重要的系统的两种主要的随机反应扩散模型。我们将扩展RDME和SDLR方程系统，以解释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。一个多尺度的方法将开发一个初始模型，明确表示染色质纤维的长度尺度显着小于细胞核的大小将被构建。然后将该模型进行粗粒化，并与现有的实验成像数据相结合，以估计有效的全核尺度RDME和SDLR模型中的参数。这些新的粗粒度模型将被用来研究全球核子结构的基因调控蛋白，在进入细胞核，找到特定的DNA结合位点所需的时间的影响。方法也将被开发用于提高精度的RDME近似的SDLR模型，并精确地模拟的随机过程所描述的SDLR模型在复杂的几何形状，存在于细胞。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将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功能，对环境刺激做出反应，并帮助治疗疾病，有必要理解，预测和控制单个细胞的行为。每个细胞都包含许多复杂的动力学过程，这些过程涉及经历生化反应的蛋白质，这些蛋白质在细胞间通讯、细胞生长和分裂、心脏和神经系统发育和功能以及癌症的发展和进展中发挥重要作用。了解这些过程激活和激活单个细胞内基因的方式对于确定这些过程如何影响细胞功能至关重要。在这项工作中，我们将开发明确的数学模型，说明细胞内的蛋白质如何找到它们激活或激活的特定基因。这些模型将允许定量研究细胞的内部物理结构如何影响这一过程。 将开发新的数学方程来模拟蛋白质在含有真实细胞亚结构的细胞内的运动。将开发新的计算方法来有效地求解这些数学方程，以便更好地预测和控制影响细胞行为的动力学过程。

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.