Sidje R B, Vo H D
Department of Mathematics, The University of Alabama, Tuscaloosa, AL 35487, USA.
Math Biosci. 2015 Nov;269:10-6. doi: 10.1016/j.mbs.2015.08.010. Epub 2015 Aug 28.
The mathematical framework of the chemical master equation (CME) uses a Markov chain to model the biochemical reactions that are taking place within a biological cell. Computing the transient probability distribution of this Markov chain allows us to track the composition of molecules inside the cell over time, with important practical applications in a number of areas such as molecular biology or medicine. However the CME is typically difficult to solve, since the state space involved can be very large or even countably infinite. We present a novel way of using the stochastic simulation algorithm (SSA) to reduce the size of the finite state projection (FSP) method. Numerical experiments that demonstrate the effectiveness of the reduction are included.
化学主方程（CME）的数学框架使用马尔可夫链来对生物细胞内发生的生化反应进行建模。计算这个马尔可夫链的瞬态概率分布，使我们能够追踪细胞内分子组成随时间的变化，在分子生物学或医学等许多领域具有重要的实际应用。然而，CME通常很难求解，因为所涉及的状态空间可能非常大，甚至是可数无限的。我们提出了一种使用随机模拟算法（SSA）来减小有限状态投影（FSP）方法规模的新方法。文中包含了证明这种缩减有效性的数值实验。
