Dobrzynski Maciej, Rodríguez Jordi Vidal, Kaandorp Jaap A, Blom Joke G
CWI (Center for Mathematics and Computer Science), Kruislaan 413 and Section Computational Science, Faculty of Science, University of Amsterdam, Kruislaan 403, Amsterdam, The Netherlands.
Bioinformatics. 2007 Aug 1;23(15):1969-77. doi: 10.1093/bioinformatics/btm278. Epub 2007 May 30.
We compare stochastic computational methods accounting for space and discrete nature of reactants in biochemical systems. Implementations based on Brownian dynamics (BD) and the reaction-diffusion master equation are applied to a simplified gene expression model and to a signal transduction pathway in Escherichia coli.
In the regime where the number of molecules is small and reactions are diffusion-limited predicted fluctuations in the product number vary between the methods, while the average is the same. Computational approaches at the level of the reaction-diffusion master equation compute the same fluctuations as the reference result obtained from the particle-based method if the size of the sub-volumes is comparable to the diameter of reactants. Using numerical simulations of reversible binding of a pair of molecules we argue that the disagreement in predicted fluctuations is due to different modeling of inter-arrival times between reaction events. Simulations for a more complex biological study show that the different approaches lead to different results due to modeling issues. Finally, we present the physical assumptions behind the mesoscopic models for the reaction-diffusion systems.
Input files for the simulations and the source code of GMP can be found under the following address: http://www.cwi.nl/projects/sic/bioinformatics2007/
我们比较了考虑生化系统中反应物的空间和离散性质的随机计算方法。基于布朗动力学（BD）和反应扩散主方程的实现方法被应用于一个简化的基因表达模型和大肠杆菌中的一个信号转导途径。
在分子数量较少且反应受扩散限制的情况下，不同方法预测的产物数量波动有所不同，但平均值相同。如果子体积的大小与反应物的直径相当，反应扩散主方程层面的计算方法所计算出的波动与基于粒子的方法得到的参考结果相同。通过对一对分子可逆结合的数值模拟，我们认为预测波动的差异是由于反应事件之间到达时间的不同建模方式导致的。对一个更复杂的生物学研究的模拟表明，由于建模问题，不同的方法会导致不同的结果。最后，我们阐述了反应扩散系统介观模型背后的物理假设。
模拟的输入文件和GMP的源代码可在以下地址找到：http://www.cwi.nl/projects/sic/bioinformatics2007/
