Frequency spectrum of chemical fluctuation: A probe of reaction mechanism and dynamics

Even in the steady-state, the number of biomolecules in living cells fluctuates dynamically, and the frequency spectrum of this chemical fluctuation carries valuable information about the dynamics of the reactions creating these biomolecules. Recent advances in single-cell techniques enable direct monitoring of the time-traces of the protein number in each cell; however, it is not yet clear how the stochastic dynamics of these time-traces is related to the reaction mechanism and dynamics. Here, we derive a rigorous relation between the frequency-spectrum of the product number fluctuation and the reaction mechanism and dynamics, starting from a generalized master equation. This relation enables us to analyze the time-traces of the protein number and extract information about dynamics of mRNA number and transcriptional regulation, which cannot be directly observed by current experimental techniques. We demonstrate our frequency spectrum analysis of protein number fluctuation, using the gene network model of luciferase expression under the control of the Bmal 1a promoter in mouse fibroblast cells. We also discuss how the dynamic heterogeneity of transcription and translation rates affects the frequency-spectra of the mRNA and protein number.

即便处于稳态，活细胞内的生物分子数量仍会发生动态波动，这类化学波动的频谱携带着与生成这些生物分子的反应动力学相关的宝贵信息。近年来单细胞技术的进步使得我们能够直接监测单个细胞内蛋白质数量的时间轨迹，但目前仍尚未明确这些时间轨迹的随机动力学与反应机制及动力学之间的关联。本文从广义主方程（generalized master equation）出发，推导出了产物数量波动的频谱与反应机制及动力学之间的严格关系。借助这一关系，我们可对蛋白质数量的时间轨迹展开分析，并提取出当前实验技术无法直接观测到的信使RNA（mRNA）数量动力学与转录调控相关信息。我们以小鼠成纤维细胞中受Bmal1a启动子调控的荧光素酶表达基因网络模型为例，演示了蛋白质数量波动的频谱分析方法。此外，我们还探讨了转录与翻译速率的动态异质性如何影响信使RNA及蛋白质数量的频谱。