The chemical master equation and the Gillespie algorithm are widely used to model the reaction kinetics inside living cells. It is thereby assumed that cell growth and division can be modelled through effective dilution reactions and extrinsic noise sources. We here re-examine these paradigms through developing an analytical agent-based framework of growing and dividing cells accompanied by an exact simulation algorithm, which allows us to quantify the dynamics of virtually any intracellular reaction network affected by stochastic cell size control and division noise. We find that the solution of the chemical master equation—including static extrinsic noise—exactly agrees with the agent-based formulation when the network under study exhibits stochastic concentration homeostasis, a novel condition that generalizes concentration homeostasis in deterministic systems to higher order moments and distributions. We illustrate stochastic concentration homeostasis for a range of common gene expression networks. When this condition is not met, we demonstrate by extending the linear noise approximation to agent-based models that the dependence of gene expression noise on cell size can qualitatively deviate from the chemical master equation. Surprisingly, the total noise of the agent-based approach can still be well approximated by extrinsic noise models.

化学主方程和 Gillespie 算法被广泛用于模拟活细胞内的反应动力学。因此假设细胞生长和分裂可以通过有效的稀释反应和外部噪声源来建模。我们在这里通过开发基于分析代理的生长和分裂细胞框架以及精确的模拟算法来重新检查这些范例，这使我们能够量化几乎任何受随机细胞大小控制和分裂噪声影响的细胞内反应网络的动力学。我们发现，当研究中的网络表现出随机浓度稳态时，化学主方程的解（包括静态外在噪声）与基于代理的公式完全一致，一种将确定性系统中的浓度稳态推广到高阶矩和分布的新条件。我们说明了一系列常见基因表达网络的随机浓度稳态。当这个条件不满足时，我们通过将线性噪声近似扩展到基于代理的模型来证明基因表达噪声对细胞大小的依赖性可以定性地偏离化学主方程。令人惊讶的是，基于代理的方法的总噪声仍然可以通过外部噪声模型很好地近似。