Chen Minghan, Li Fei, Wang Shuo, Cao Young
Department of Computer Science, Virginia Tech, Blacksburg, 24061, VA, USA.
BMC Syst Biol. 2017 Mar 14;11(Suppl 3):21. doi: 10.1186/s12918-017-0401-9.
Stochastic simulation of reaction-diffusion systems presents great challenges for spatiotemporal biological modeling and simulation. One widely used framework for stochastic simulation of reaction-diffusion systems is reaction diffusion master equation (RDME). Previous studies have discovered that for the RDME, when discretization size approaches zero, reaction time for bimolecular reactions in high dimensional domains tends to infinity.
In this paper, we demonstrate that in the 1D domain, highly nonlinear reaction dynamics given by Hill function may also have dramatic change when discretization size is smaller than a critical value. Moreover, we discuss methods to avoid this problem: smoothing over space, fixed length smoothing over space and a hybrid method.
Our analysis reveals that the switch-like Hill dynamics reduces to a linear function of discretization size when the discretization size is small enough. The three proposed methods could correctly (under certain precision) simulate Hill function dynamics in the microscopic RDME system.
反应扩散系统的随机模拟给时空生物建模与模拟带来了巨大挑战。反应扩散主方程（RDME）是反应扩散系统随机模拟中广泛使用的一个框架。先前的研究发现，对于RDME，当离散化尺寸趋近于零时，高维域中双分子反应的反应时间趋于无穷大。
在本文中，我们证明在一维域中，当离散化尺寸小于临界值时，由希尔函数给出的高度非线性反应动力学也可能发生显著变化。此外，我们讨论了避免此问题的方法：空间平滑、空间固定长度平滑和混合方法。
我们的分析表明，当离散化尺寸足够小时，类似开关的希尔动力学简化为离散化尺寸的线性函数。所提出的三种方法可以（在一定精度下）正确模拟微观RDME系统中的希尔函数动力学。
