Department of Cell and Molecular Biology, Uppsala University, 75124 Uppsala, Sweden.
Proc Natl Acad Sci U S A. 2010 Nov 16;107(46):19820-5. doi: 10.1073/pnas.1006565107. Epub 2010 Nov 1.
Quantitative analysis of biochemical networks often requires consideration of both spatial and stochastic aspects of chemical processes. Despite significant progress in the field, it is still computationally prohibitive to simulate systems involving many reactants or complex geometries using a microscopic framework that includes the finest length and time scales of diffusion-limited molecular interactions. For this reason, spatially or temporally discretized simulations schemes are commonly used when modeling intracellular reaction networks. The challenge in defining such coarse-grained models is to calculate the correct probabilities of reaction given the microscopic parameters and the uncertainty in the molecular positions introduced by the spatial or temporal discretization. In this paper we have solved this problem for the spatially discretized Reaction-Diffusion Master Equation; this enables a seamless and physically consistent transition from the microscopic to the macroscopic frameworks of reaction-diffusion kinetics. We exemplify the use of the methods by showing that a phosphorylation-dephosphorylation motif, commonly observed in eukaryotic signaling pathways, is predicted to display fluctuations that depend on the geometry of the system.
生化网络的定量分析通常需要考虑化学过程的空间和随机方面。尽管在该领域取得了重大进展，但使用包括扩散限制分子相互作用的最细长度和时间尺度的微观框架来模拟涉及许多反应物或复杂几何形状的系统在计算上仍然是不可行的。出于这个原因，在建模细胞内反应网络时，通常使用空间或时间离散化的模拟方案。定义这种粗粒度模型的挑战在于，给定微观参数和空间或时间离散化引入的分子位置的不确定性，计算反应的正确概率。在本文中，我们已经解决了空间离散化反应-扩散主方程的这个问题；这使得从反应-扩散动力学的微观框架到宏观框架的无缝和物理一致的转变成为可能。我们通过展示一个常见于真核信号通路中的磷酸化-去磷酸化基序，来举例说明这些方法的使用，该基序预计会显示出依赖于系统几何形状的波动。
