The main objective of the proposed research is to provide simplified dynamics and design efficient numerical methods for complex intracellular stochastic chemical reacting networks. Numerical schemes will be developed to simulate systems exhibiting multiple time and concentration scales, and to solve transition paths and transition rates for systems with metastability. Error analysis of the schemes as well as sharper estimates on the transition rates will be provided. Applications will be focused on developing and analyzing a quantitative model for the Insulin response network, through collaboration with biologists at Michigan State University (MSU). The education plan includes training of graduate students that will lead to Ph.D. theses, developing a graduate level course for students in applied and computational mathematics, introducing the related topics to undergraduate curriculum, and organizing a workshop on the same topic. The proposed research will be crucial to the understanding of functional issues of intracellular reacting networks at the system level, which is becoming the new focus of genomic research. Numerical studies of the multi-scale systems will lead to new insights into the simulation schemes for stochastic systems. The development of accurate and efficient numerical methods for multi-scale chemical reaction systems involves novel analytical approaches from stochastic analysis. The study of the fluctuation driven transitions in metastable chemical reaction systems will find new applications for advanced probability theory and optimization techniques. The multi-scale and stochastic methods developed by the proposed research will find a wide range of applications in biological sciences and nano-technologies.
The PI is going to build mathematical models and design efficient computer based simulation algorithms for chemical reactions inside living cells, which ususally involve many types of reacting channels and reacting species, as well as random fluctuations. The proposed research is to simplify and reduce complex models, which will lead to insightful conceptualization of the system. The research will be conducted in collaboration with biologists and the theoretical results with be calibrated with real data generated by experiments in labs. The targeted application, namely the modeling of Insulin response network, has a significant potential for the promotion of public health. Type 2 diabetes and impaired glucose tolerance are top causes of morbidity and mortality in the United States. In the case of insulin resistance, tissues such as muscle, fat and liver become less responsive or resistant to insulin. The disorder is also linked to other common health problems, such as obesity, hyperlipidaemia, hypertension etc. The models and algorithms developed by the PI will help to dandify the major reactions and reactants that are maintaining the normal range of plasma glaucous in individuals throughout periods of feeding and fasting. The research output will help to understand the mechanism of the Insulin disorders and the cause of type2 diabetes.
