CAREER: Modeling, Analysis and Computation of Stochastic Intracellular Reactions

提出的研究的主要目的是为复杂的细胞内随机化学反应网络提供简化的动力学和设计有效的数值方法。将开发数值方案来模拟具有多个时间和浓度尺度的系统，并解决具有亚稳态的系统的转变路径和转变速率。将提供这些方案的误差分析以及对过渡率的更精确估计。通过与密歇根州立大学（MSU）的生物学家合作，应用将集中于开发和分析胰岛素反应网络的定量模型。教育计划包括研究生的博士论文培训，为应用数学和计算数学的学生开发研究生水平的课程，将相关主题引入本科课程，并组织一次关于同一主题的研讨会。本研究将对理解细胞内反应网络在系统水平上的功能问题至关重要，这将成为基因组研究的新焦点。多尺度系统的数值研究将为随机系统的模拟方案提供新的见解。发展多尺度化学反应系统的精确和有效的数值方法涉及随机分析的新分析方法。对亚稳化学反应系统中波动驱动跃迁的研究将为先进的概率论和优化技术找到新的应用。本研究提出的多尺度和随机方法将在生物科学和纳米技术中得到广泛应用。PI将为活细胞内的化学反应建立数学模型并设计高效的基于计算机的模拟算法，这些化学反应通常涉及多种类型的反应通道和反应物种，以及随机波动。所提出的研究是简化和减少复杂的模型，这将导致有洞察力的系统概念化。这项研究将与生物学家合作进行，理论结果将根据实验室实验产生的真实数据进行校准。定向应用，即胰岛素反应网络的建模，对促进公众健康具有重要的潜力。2型糖尿病和糖耐量受损是美国发病率和死亡率的主要原因。在胰岛素抵抗的情况下，肌肉、脂肪和肝脏等组织对胰岛素的反应减弱或抵抗。这种疾病还与其他常见的健康问题有关，如肥胖、高脂血症、高血压等。由PI开发的模型和算法将有助于改进主要的反应和反应物，这些反应和反应物在进食和禁食期间维持个体正常的血浆含氧量范围。该研究成果将有助于了解胰岛素紊乱的机制和2型糖尿病的病因。

The main objective of the proposed research is toprovide simplified dynamics and design efficient numerical methods forcomplex intracellular stochastic chemical reacting networks. Numericalschemes will be developed to simulate systems exhibiting multiple timeand concentration scales, and to solve transition paths and transitionrates for systems with metastability. Error analysis of the schemes aswell as sharper estimates on the transition rates will beprovided. Applications will be focused on developing and analyzing aquantitative model for the Insulin response network, throughcollaboration with biologists at Michigan State University (MSU). Theeducation plan includes training of graduate students that will leadto Ph.D. theses, developing a graduate level course for students inapplied and computational mathematics, introducing the related topicsto undergraduate curriculum, and organizing a workshop on the same topic.The proposed research will be crucial to the understanding offunctional issues of intracellular reacting networks at the systemlevel, which is becoming the new focus of genomic research. Numerical studies of the multi-scale systems will lead to new insights into the simulationschemes for stochastic systems. The development of accurate andefficient numerical methods for multi-scale chemical reaction systemsinvolves novel analytical approaches from stochastic analysis. The studyof the fluctuation driven transitions in metastable chemical reactionsystems will find new applications for advanced probability theory andoptimization techniques. The multi-scale and stochastic methodsdeveloped by the proposed research will find a wide range ofapplications in biological sciences and nano-technologies.The PI is going to build mathematical models and design efficientcomputer based simulation algorithms for chemical reactions insideliving cells, which ususally involve many types of reacting channelsand reacting species, as well as random fluctuations. The proposedresearch is to simplify and reduce complex models, which will lead toinsightful conceptualization of the system. The research will beconducted in collaboration with biologists and the theoretical resultswith be calibrated with real data generated by experiments inlabs. The targeted application, namely the modeling of Insulinresponse network, has a significant potential for the promotion ofpublic health. Type 2 diabetes and impaired glucose tolerance are topcauses of morbidity and mortality in the United States. In the case ofinsulin resistance, tissues such as muscle, fat and liver become lessresponsive or resistant to insulin. The disorder is also linked toother common health problems, such as obesity, hyperlipidaemia,hypertension etc. The models and algorithms developed by the PI willhelp to dandify the major reactions and reactants that are maintainingthe normal range of plasma glaucous in individuals throughout periodsof feeding and fasting. The research output will help to understandthe mechanism of the Insulin disorders and the cause of type2 diabetes.