CAREER: Modeling, Analysis and Computation of Stochastic Intracellular Reactions

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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.