线性反馈二元遗传开关模型的统计物理
Statistical physics of a model binary genetic switch with linear feedback
摘要：
我们研究了一个简单的遗传调控网络的统计特性，该网络提供了细胞群体内的异质性。这个网络由一个二进制的遗传开关，其中两个开关状态之间的随机翻转是由一个“翻转”酶介导的。开关状态和翻转速率之间的反馈由线性反馈机制提供：翻转酶仅在打开开关状态下产生，并且开关速率线性依赖于酶的拷贝数。这项工作概括了[物理学评论快报，101，118104]到更广泛的一类线性反馈系统。我们提出了一个完整的分析解决方案的稳态统计的酶分子的数量在开和关状态，酶可以介导翻转在任何一个方向的一般情况下。对于这种一般情况下，我们也解决了翻转时间分布，使连接到统计物理学中的第一通道和持久性问题。我们表明，该模型的统计是非泊松，导致翻转时间分布的峰值。这种峰值的发生被分析为参数空间的函数。我们提出了一个新的翻转时间分布之间的关系测量两个相关的初始条件的选择。我们还引入了一个新的相关性措施，表明该模型可以表现出长寿命的时间相关性，从而提供了一个原始形式的细胞记忆。受DNA复制以及基因复制的进化机制的启发，我们研究了同一细胞中两个开关的情况。这导致两个开关之间的相关性;这些相关性可以是正的或负的，这取决于参数状态。
英文摘要：
We study the statistical properties of a simple genetic regulatory network that provides heterogeneity within a population of cells. This network consists of a binary genetic switch in which stochastic flipping between the two switch states is mediated by a "flipping" enzyme. Feedback between the switch state and the flipping rate is provided by a linear feedback mechanism: the flipping enzyme is only produced in the on switch state and the switching rate depends linearly on the copy number of the enzyme. This work generalises the model of [Phys. Rev. Lett., 101, 118104] to a broader class of linear feedback systems. We present a complete analytical solution for the steady-state statistics of the number of enzyme molecules in the on and off states, for the general case where the enzyme can mediate flipping in either direction. For this general case we also solve for the flip time distribution, making a connection to first passage and persistence problems in statistical physics. We show that the statistics of the model are non-Poissonian, leading to a peak in the flip time distribution. The occurrence of such a peak is analysed as a function of the parameter space. We present a new relation between the flip time distributions measured for two relevant choices of initial condition. We also introduce a new correlation measure to show that this model can exhibit long-lived temporal correlations, thus providing a primitive form of cellular memory. Motivated by DNA replication as well as by evolutionary mechanisms involving gene duplication, we study the case of two switches in the same cell. This results in correlations between the two switches; these can either positive or negative depending on the parameter regime.
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