Green's-function reaction dynamics: A particle-based approach for simulating biochemical networks in time and space
Green's-function reaction dynamics: A particle-based approach for simulating biochemical networks in time and space
复制标题
DOI：
10.1063/1.2137716
复制
发表时间：
2005-12-15
影响因子：
4.4
通讯作者：
ten Wolde, PR
中科院分区：
文献类型：
--
作者：
van Zon, JS;ten Wolde, PR
我们已经开发了一种称为Green的功能动力学（GFRD）的新数值技术，该技术使在粒子级别和时间和空间中模拟生化网络成为可能。在此方案中，选择最长的时间步骤，以便仅考虑单个颗粒或成对的粒子。对于这些粒子，可以使用Green的功能分析求解Smoluchowski方程。 GFRD的主要思想是利用Smoluchoswki方程的精确解决方案来设置事件驱动的算法，该算法在一个步骤中结合了空间中粒子的传播与它们之间的反应。事件驱动的性质允许GFRD彼此相距遥远时，可以在时间和空间上大大跳跃。在这里，我们将技术应用于基因表达的简单模型。模拟表明，空间波动可能是生化网络中噪声的主要来源。计算还表明GFRD高效。在生物学上相关的条件下，GFRD的数量级最高五个数量级，比常规粒子基于时空的生化网络更快。 GFRD不仅限于生化网络。它也可以应用于大量其他反应扩散问题。
We have developed a new numerical technique, called Green's-function reaction dynamics (GFRD), that makes it possible to simulate biochemical networks at the particle level and in both time and space. In this scheme, a maximum time step is chosen such that only single particles or pairs of particles have to be considered. For these particles, the Smoluchowski equation can be solved analytically using Green's functions. The main idea of GFRD is to exploit the exact solution of the Smoluchoswki equation to set up an event-driven algorithm, which combines in one step the propagation of the particles in space with the reactions between them. The event-driven nature allows GFRD to make large jumps in time and space when the particles are far apart from each other. Here, we apply the technique to a simple model of gene expression. The simulations reveal that spatial fluctuations can be a major source of noise in biochemical networks. The calculations also show that GFRD is highly efficient. Under biologically relevant conditions, GFRD is up to five orders of magnitude faster than conventional particle-based techniques for simulating biochemical networks in time and space. GFRD is not limited to biochemical networks. It can also be applied to a large number of other reaction-diffusion problems.