A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions
A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions
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DOI：
10.1063/1.4902239
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发表时间：
2014-12-07
影响因子：
4.4
通讯作者：
El-Samad, Hana
中科院分区：
文献类型：
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作者：
Chevalier, Michael W.;El-Samad, Hana
噪声和随机性是生物学的基础，源于生物化学反应的本质，其中分子的热运动转化为反应顺序和时间的随机性。这种随机性甚至在克隆群体中也导致细胞间的变异。随机生化网络传统上被建模为连续时间离散状态马尔可夫过程，其概率密度函数根据化学主方程（CME）演化。在膜上扩散反应系统中，假设反应倾向恒定的马尔可夫形式并不直接适用。这是因为扩散反应发生的瞬时倾向取决于所涉及分子的产生时间。在这项工作中，我们为这类系统建立了一个化学主方程。虽然这种新的CME在计算上是难以处理的，但我们进行了合理的降维以形成一个近似方程，其矩也被导出并显示为产生有效，准确的结果。这个新的框架形成了一种比马尔科夫CME更通用的方法，并扩展了可以有效建模的可能的随机生化系统的领域。(C) 2014 AIP出版有限责任公司
Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-stateMarkov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation times of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled. (C) 2014 AIP Publishing LLC.