发表机构
Indian Institute of Technology Kharagpur（印度理工学院克哈格布尔分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过化学主方程分析双态随机切换下的mRNA积累模型，解析计算稳态分布、Fano因子和熵产生率，揭示动力学参数如何调控分布模态、噪声与耗散，建立广义随机积累动力学框架。
AI 中文摘要
基因表达状态之间的随机切换，与产生和降解动力学相耦合，控制着细胞中mRNA和蛋白质的积累。这些积累实体的浓度决定了基因相同细胞的表型分布。潜在的积累动力学可由双态启动子切换模型很好地描述，其统计和热力学性质通过Fano因子和熵产生率来量化。然而，这些度量如何与浓度分布及其在变化动力学参数下的偏移相关联，在很大程度上仍未探索。为此，我们使用化学主方程研究在两种活性状态间随机切换以及状态依赖的产生和降解速率存在下的mRNA积累动力学的广义模型。我们推导了稳态概率分布的精确表达式，并解析计算了平均浓度、Fano因子和熵产生率（EPR）。简化这些表达式，我们识别出由随机切换速率和每个活性状态中向平衡的弛豫动力学产生的贡献。接下来，利用我们的理论结果，我们表征了在由切换速率变化介导的分布模态变化期间，Fano因子和EPR作为平均表达函数的变异。我们还确定了实现最高Fano因子和熵产生率的动力学参数条件。我们的发现建立了一个用于检查随机积累动力学的广义框架，阐明了动力学参数如何决定分子分布、噪声和耗散。这些见解可轻易扩展到将随机切换与积累耦合的更广泛背景，包括蛋白质爆发动力学、表型切换介导的药物摄取和排队理论。
英文摘要
Stochastic switching between gene expression states, coupled with production and degradation dynamics, governs the accumulation of mRNA and proteins in cells. The concentrations of these accumulated entities dictate the phenotypic distribution of genetically identical cells. The underlying accumulation dynamics are well-captured by a two-state promoter switching model, with statistical and thermodynamic properties quantified via the Fano factor and entropy production rates. However, how these measures correlate with concentration distributions and their shifts under varying kinetic parameters remains largely unexplored. To this end, we use chemical master equations to study a generalized model of mRNA accumulation dynamics in the presence of stochastic switching between two activity states and state-dependent production and degradation rates. We derive exact expressions for the steady-state probability distribution and analytically compute the mean concentration, Fano factor, and entropy production rate (EPR). Simplifying these expressions, we identify contributions arising from stochastic switching rates and relaxation dynamics toward equilibrium in each activity state. Next, using our theoretical results, we characterize the variation in the Fano factor and EPR as a function of mean expression during modality changes of the distributions mediated by the variation of switching rates. We also identify the conditions in kinetic parameters that achieve the highest Fano factor and entropy production rates. Our findings establish a generalized framework for examining stochastic accumulation dynamics, clarifying how kinetic parameters dictate molecular distributions, noise, and dissipation. These insights extend readily to broader contexts coupling stochastic switching with accumulation, including protein burst dynamics, phenotype-switching-mediated drug intake, and queuing theory.
