Numerical solution of the chemical master equation in cell biology

细胞生物学化学主方程的数值解

• 批准号: 1320849
• 负责人: Roger Sidje
• 金额: $ 19.37万
• 依托单位: University of Alabama Tuscaloosa
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-08-01 至 2017-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1320849&HistoricalAwards=false
• 关键词: Numerical; solution; chemical; master; equation

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.

求解化学主方程所需的计算量往往会爆炸式增长，因为系统的潜在状态数量很高，这一事实促使人们需要开发复杂的计算技术来解决这种所谓的“维度诅咒”。这个项目试图通过组合技术来解决这个问题，如模型简化技术、简化问题的有效嵌入技术以及集成模式中不精确或松弛的函数评估。当使用数学建模来表示调节细胞内新陈代谢的生化反应时，出现了化学主方程。细胞过程模型使实验者可以避免在活细胞中进行昂贵的反复试验。这种建模带来了一个具有挑战性的问题，因为一些关键调控分子的数量如此之少，以至于与它们相关的细胞过程似乎是随机的或随机的，细胞可能会通过无数条路径发生变化，即使在速度最快的超级计算机上也很难追踪。因此，使用数学建模来准确地模拟关键分子并应用计算方法来有效地编码模拟的能力在分子生物学和医学领域具有重要的应用，因为需要准确地实时地模拟细胞内的生化反应。