Numerical solution of the chemical master equation in cell biology

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The number of computations needed to solve the chemical master equation tends to explode because of the high number of potential states of the system and this fact motivates the need to develop sophisticated computational techniques to address this so-called "curse of dimensionality." This project seeks to address the problem using a combination of techniques such as model reduction techniques, efficient embedded techniques for the reduced problem, and inexact or relaxed function evaluations in the integration schemes.The chemical master equation arises when mathematical modeling is used to represent the biochemical reactions that regulate the metabolism within the cells. Models of cellular processes allow experimentalists to avoid costly trial-and-error laboratory experiments in live cells . This sort of modeling poses a challenging problem because some key regulatory molecules are so small in number that the cellular processes associated with them seem random or stochastic and cells can change through a myriad of pathways that are difficult to track even on the fastest supercomputers. Thus the ability to use mathematical modeling to accurately mimic key molecules and to apply computational methods to efficiently code the simulations have important applications for fields of molecular biology and medicine because there is a significant need to accurately simulate biochemical reactions inside a cell in real time.