Collaborative Research: FRG:Stochastic models for intracellular reaction networks

随着细菌、酵母和人类的大量基因组计划的完成，人们越来越有兴趣了解基因组中编码的分子如何相互作用来定义细胞的各种功能网络。完整的分子反应网络往往涉及许多不同的分子物种，因此提出了复杂的分析问题。为了预测和仿真的目的，必须同时降低问题的模型和计算复杂性，同时仍然捕获网络的所有基本特征和潜在行为。该项目将系统地开发化学反应网络的随机模型，从经典的马尔可夫链模型开始，并开发考虑到涉及RNA和DNA分子的反应的逐步发展的新模型。需要解决的具体问题包括基于系统中广泛的时间和其他定量尺度的定标限制，通过定标极限近似和其他方法进行的模型缩减，反应结构对系统施加的组合限制的含义，随机模型参数的灵敏度分析，以及基于经常通过间接和/或聚集测量获得的数据的模型验证的统计方法。在细胞水平上，化学动力学很可能由存在于每个细胞水平上的仅几个拷贝的调控分子的作用所主导。因此，这些组分的分子涨落可能决定反应网络的动力学。这些分子波动似乎有显著的后果；观察到一个细胞中分子物种的发育速度、形态和浓度的巨大差异往往导致表型结果的随机化和非遗传种群的异质性。由于这些波动可能会对细胞的生理产生深远的影响，如果要很好地理解系统，细胞内反应网络的随机模型和仔细的统计分析似乎是必不可少的。该项目还将为研究生和博士后研究人员提供肥沃的培训场地。对训练有素的数学科学家的需求很高，他们具有必要的兴趣和专业知识，有助于解决细胞和分子生物学中出现的问题。

With the completion of numerous genome projects for bacteria, yeast, and humans, there is an increasing interest in understanding how molecules encoded within the genomes interact to define various functional networks of the cell. Network of integrated molecular reactions tend to involve many different molecular species, thus posing complex analytical problems. For prediction and simulation purposes it is essential to reduce both the model and computational complexity of the problem, while still capturing all the essential characteristics and potential behavior of the network. This project will systematically develop stochastic models for chemical reaction networks, beginning with classical Markov chain models and developing new models that take into account the stepwise development of reactions involving RNA and DNA molecules. Specific issues to be addressed include scaling limits based on the wide range of time and other quantitative scales in the system, model reduction through scaling limit approximations and other approaches, the implications of the combinatorial restrictions the reaction structure places on the system, sensitivity analysis for the parameters of the stochastic models, and statistical methods for model validation based on data that is frequently obtained through indirect and/or aggregated measurements.At the level of the cell, the chemical dynamics may well be dominated by the action of regulatory molecules that are present at levels of only a few copies per cell. Therefore, the molecular fluctuations of these components may determine the dynamics of the reaction network. These molecular fluctuations appear to have significant consequences; the observed large variation in rates of development, morphology and concentration of molecular species in a cell often lead to a randomization of phenotypic outcomes and non-genetic population heterogeneity. Since these fluctuations may have profound effects on the physiology of the cell, stochastic models for the intra-cellular reaction networks and careful statistical analysis appear to be essential if the system is to be well understood. The project will also provide a fertile training ground for graduate students and postdoctoral researchers. There is a high demand for well-trained mathematical scientists with the interest and expertise necessary to contribute to the solution of problems arising in cell and molecular biology.