AMC-SS: Analysis and Computation of Multi-Scale Stochastic Chemical Kinetic Systems with Application to Genetic Regulatory Networks

AMC-SS：多尺度随机化学动力学系统的分析和计算及其在遗传调控网络中的应用

• 批准号: 0609315
• 负责人: Di Liu
• 金额: $ 10.12万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-06-15 至 2010-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0609315&HistoricalAwards=false
• 关键词: AMC; SS; Analysis; Computation; Multi

Proteins play an essential role in the development and functioning of organisms. The synthesis of cellular proteins is a multi-step process inside living cells. The genetic information stored in DNA directs the production of proteins through a bio-chemical process called gene expression. When a specific gene is expressed, its DNA is first transcribed into a single stranded sequence of mRNA. The mRNA sequence is then translated into a sequence of amino acids as the protein is formed. These steps form the three levels of gene expression: transcription, translation, and post-translational modification. Genetic Regulatory Networks (GRNs), consisting of genes, proteins, small molecules within cells in relatively low concentrations, and their interactions, function to regulate gene expression process for the production of proteins in response to certain physical, chemical, and biological stimuli. GRNs can only be effectively modeled as stochastic systems with random molecular fluctuations instead of deterministic systems. Very often GRNs are multi-scale in terms of multiple steady states, reaction rates, and molecular concentrations, making standard simulation algorithms inefficient. Simplifying and reducing complex chemical and biological models enables easier conceptualization and interpretation and efficient simulations of inherently stochastic systems. The main objective of the proposed research project is to provide simplified dynamics and to design efficient numerical schemes for complex stochastic chemical kinetic systems exhibiting multiple steady states and multiple time and concentration scales. Applications will be emphasized on Genetic Regulatory Networks, for which only stochastic modeling incorporating random molecular fluctuations has proved to be successful. On the mathematical side, using asymptotic analysis and probability theory, the transition rates and transition pathways of chemical kinetic systems with multiple steady states will be investigated, and the effective dynamics for stochastic chemical kinetic systems with multiple well-separated time and concentration scales will be studied. On the numerical side, computational methods will be developed to simulate the reduced dynamics obtained from the mathematical work. Computer-based optimization methods will be adopted to find the transition rates and pathways of multi-stable systems. Convergence and error estimates for the proposed numerical schemes will be proved mathematically. Issues like efficiency, robustness, adaptivity, and parallelism of the computing schemes will also be studied. The proposed research will advance the frontiers of Applied Mathematics through significant generalizations and developments of the modeling, analytical, and computational techniques for stochastic and multi-scale systems. It will help to understand functional issues of chemically reacting networks at the system level, which is becoming the new focus of genomic research. The ideas from the stochastic and multi-scale analysis can be applied to a spectrum of biological, chemical, physical, and other scientific problems involving multi-scale modeling and can broaden the scope of research topics in the related fields. The research projects will also promote interdisciplinary interactions between applied mathematicians, chemists, and biologists.

蛋白质在生物体的发育和功能中起着至关重要的作用。细胞蛋白质的合成在活细胞内是一个多步骤的过程。储存在DNA中的遗传信息通过一种称为基因表达的生化过程来指导蛋白质的生产。当一个特定的基因被表达时，它的DNA首先被转录成单链的mRNA序列。当蛋白质形成时，信使核糖核酸序列被翻译成氨基酸序列。这些步骤形成了基因表达的三个水平：转录、翻译和翻译后修饰。遗传调控网络(GRN)由相对较低浓度的基因、蛋白质、细胞内小分子及其相互作用组成，在一定的物理、化学和生物刺激下调节基因表达过程以产生蛋白质。GRN只能有效地模拟为具有随机分子涨落的随机系统，而不是确定性系统。通常，GRN在多个稳态、反应速率和分子浓度方面是多尺度的，这使得标准的模拟算法效率低下。简化和简化复杂的化学和生物模型可以更容易地概念化和解释，并对固有的随机系统进行有效的模拟。该研究项目的主要目的是为具有多个稳态和多个时间和浓度尺度的复杂随机化学动力学系统提供简化的动力学和设计有效的数值格式。应用重点将放在遗传调控网络上，只有纳入随机分子波动的随机建模才被证明是成功的。在数学方面，将利用渐近分析和概率论研究具有多个稳态的化学动力学系统的转变速率和转变路径，以及具有多个良好分离的时间和浓度尺度的随机化学动力学系统的有效动力学。在数值方面，将开发计算方法来模拟从数学工作中获得的约化动力学。将采用基于计算机的优化方法来寻找多稳态系统的转换率和路径。所提出的数值格式的收敛和误差估计将从数学上得到证明。还将研究计算方案的效率、健壮性、适应性和并行性等问题。这项拟议的研究将通过对随机和多尺度系统的建模、分析和计算技术的重大概括和发展，推动应用数学的前沿。这将有助于在系统水平上理解化学反应网络的功能问题，这正成为基因组研究的新焦点。来自随机和多尺度分析的思想可以应用于涉及多尺度建模的一系列生物、化学、物理和其他科学问题，并可以拓宽相关领域的研究课题的范围。这些研究项目还将促进应用数学家、化学家和生物学家之间的跨学科互动。