Exactly solvable models of stochastic gene expression
Exactly solvable models of stochastic gene expression
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DOI：
10.1101/2020.01.05.895359
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发表时间：
2020-01
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影响因子：
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通讯作者：
Lucy Ham;David Schnoerr;Rowan D. Brackston;M. Stumpf
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文献类型：
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作者：
Lucy Ham;David Schnoerr;Rowan D. Brackston;M. Stumpf
随机模型是理解基因表达复杂动态的关键。但最简单的模型仅考虑例如基因的活性和非活性状态无法捕获原核生物和真核生物中的常见观察结果。在这里，我们考虑基因表达的多态模型，它概括了规范的电报过程，并且能够捕获例如的联合效应。转录因子、异染色质状态和 DNA 可及性（或在原核生物中，Sigma 因子活性）对转录本丰度的影响。我们提出了两种解决这些广义系统的类的方法。第一种方法为一般类型的多状态模型提供了新的视角，并允许我们将更复杂的系统“分解”为更简单的过程，每个过程都可以通过分析来解决。这使我们能够从此类中获得任何模型的解决方案。我们进一步表明，在没有外部噪声的情况下，这些模型不能具有重尾分布。接下来，我们为更广泛的基因转录多态模型类别开发了一种基于平稳分布的幂级数展开的近似方法。这些现实基因表达模型的分析和计算解决方案的结合也具有设计合成系统的潜力，并控制自然进化的基因表达系统的行为，例如指导细胞命运的决定。
Stochastic models are key to understanding the intricate dynamics of gene expression. But the simplest models which only account for e.g. active and inactive states of a gene fail to capture common observations in both prokaryotic and eukaryotic organisms. Here we consider multistate models of gene expression which generalise the canonical Telegraph process, and are capable of capturing the joint effects of e.g. transcription factors, heterochromatin state and DNA accessibility (or, in prokaryotes, Sigma-factor activity) on transcript abundance. We propose two approaches for solving classes of these generalised systems. The first approach offers a fresh perspective on a general class of multistate models, and allows us to “decompose” more complicated systems into simpler processes, each of which can be solved analytically. This enables us to obtain a solution of any model from this class. We further show that these models cannot have a heavy-tailed distribution in the absence of extrinsic noise. Next, we develop an approximation method based on a power series expansion of the stationary distribution for an even broader class of multistate models of gene transcription. The combination of analytical and computational solutions for these realistic gene expression models also holds the potential to design synthetic systems, and control the behaviour of naturally evolved gene expression systems, e.g. in guiding cell-fate decisions.