Numerical solution of the chemical master equation in cell biology

求解化学主方程所需的计算量往往会爆炸，因为系统的潜在状态的数量很高，这一事实促使需要开发复杂的计算技术来解决这个所谓的“维数灾难”。“这个项目试图解决这个问题，使用的技术组合，如模型简化技术，有效的嵌入技术减少的问题，和不精确或放松的功能评估的集成方案。化学主方程时，数学建模是用来表示生化反应，调节细胞内的新陈代谢。细胞过程的模型使实验者能够避免在活细胞中进行昂贵的试错实验室实验。这种建模提出了一个具有挑战性的问题，因为一些关键的调节分子数量非常少，以至于与它们相关的细胞过程似乎是随机的或随机的，细胞可以通过无数的途径发生变化，即使在最快的超级计算机上也难以跟踪。因此，使用数学建模来准确地模拟关键分子以及应用计算方法来有效地对模拟进行编码的能力对于分子生物学和医学领域具有重要的应用，这是因为非常需要在真实的时间内准确地模拟细胞内的生化反应。

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.