Lunz Davin, Batt Gregory, Ruess Jakob, Bonnans J Frédéric
Inria Saclay - Île de France, Palaiseau, France.
École Polytechnique, CMAP, Palaiseau, France.
PLoS Comput Biol. 2021 Jul 28;17(7):e1009214. doi: 10.1371/journal.pcbi.1009214. eCollection 2021 Jul.
The chemical master equation and its continuum approximations are indispensable tools in the modeling of chemical reaction networks. These are routinely used to capture complex nonlinear phenomena such as multimodality as well as transient events such as first-passage times, that accurately characterise a plethora of biological and chemical processes. However, some mechanisms, such as heterogeneous cellular growth or phenotypic selection at the population level, cannot be represented by the master equation and thus have been tackled separately. In this work, we propose a unifying framework that augments the chemical master equation to capture such auxiliary dynamics, and we develop and analyse a numerical solver that accurately simulates the system dynamics. We showcase these contributions by casting a diverse array of examples from the literature within this framework and applying the solver to both match and extend previous studies. Analytical calculations performed for each example validate our numerical results and benchmark the solver implementation.
化学主方程及其连续近似是化学反应网络建模中不可或缺的工具。它们通常用于捕捉复杂的非线性现象，如多峰性，以及瞬态事件，如首次通过时间，这些现象准确地表征了大量的生物和化学过程。然而，一些机制，如异质细胞生长或群体水平的表型选择，无法用主方程表示，因此需要单独处理。在这项工作中，我们提出了一个统一的框架，该框架扩展了化学主方程以捕捉此类辅助动力学，并且我们开发并分析了一个能精确模拟系统动力学的数值求解器。我们通过在这个框架内展示文献中的各种示例，并应用该求解器来匹配和扩展先前的研究，以展示这些贡献。对每个示例进行的解析计算验证了我们的数值结果，并对求解器的实现进行了基准测试。
