CAREER: Modeling, Analysis and Computation of Stochastic Intracellular Reactions

该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。将开发数值格式来模拟具有多个时间和浓度尺度的系统，并求解具有亚稳态的系统的转变路径和转变速率。将提供对这些方案的误差分析以及对过渡率的更准确的估计。应用程序将通过与密歇根州立大学(MSU)的生物学家合作，重点开发和分析胰岛素反应网络的定量模型。教育计划包括培养研究生以获得博士论文，为应用和计算数学专业的学生开发研究生水平的课程，将相关主题引入本科课程，并组织同一主题的研讨会。拟议的研究将对在系统水平上理解细胞内反应网络的功能问题至关重要，这正成为基因组研究的新焦点。对多尺度系统的数值研究将使人们对随机系统的仿真方案有新的认识。发展精确高效的多尺度化学反应系统数值方法涉及到从随机分析到新的分析方法。对亚稳态化学反应体系中涨落驱动跃迁的研究将为先进的概率理论和最优化技术找到新的应用。该研究开发的多尺度随机方法将在生物科学和纳米技术中得到广泛的应用，PI将建立数学模型并设计高效的基于计算机的模拟算法，以研究细胞内的化学反应，这些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。提出的研究是简化和减少复杂的模型，这将导致系统的有洞察力的概念化。这项研究将与生物学家合作进行，理论结果将用实验室实验产生的真实数据进行校准。胰岛素反应网络的建模这一有针对性的应用，对于促进公共健康具有巨大的潜力。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较差或产生抵抗力。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。PI开发的模型和算法将有助于改变在整个进食和禁食期间维持个体血浆苍白正常范围的主要反应和反应物。这项研究成果将有助于了解胰岛素紊乱的机制和2型糖尿病的原因。

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.