ZERO, ONE AND TWO-SWITCH MODELS OF GENE REGULATION
ZERO, ONE AND TWO-SWITCH MODELS OF GENE REGULATION
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DOI：
10.3934/dcdsb.2010.14.495
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发表时间：
2010-09-01
影响因子：
1.2
通讯作者：
Higham, Desmond J.
中科院分区：
文献类型：
--
作者：
Intep, Somkid;Higham, Desmond J.
我们比较了基因调控中三种随机模型的层次结构。在每种情况下，基因都会产生 mRNA 分子，而 mRNA 分子又会产生蛋白质。最简单的模型，如 Thattai 和 Van Oudenaarden（Proc. Nat. Acad. Sci.，2001）所描述的，假设通用方式是主动的，并在连续时间、离散空间马尔可夫跳跃（Gillespie）设置中使用一阶化学动力学框架。第二个模型由Raserand O'Shea（《科学》，2004）提出，通过允许基因在活跃和不活跃状态之间切换来概括第一个模型。我们的第三个模型通过使用两个以 AND 模式运行的独立开关来解释其他效应，例如转录因子的结合/解除结合。我们首先关注噪声强度，在生物学文献中将其定义为稳态下方差与均值的比率。我们表明，当合并开关时，三种模型的 mRNA 和蛋白质的稳态方差可能会增加或减少，具体取决于速率常数和初始条件。尽管如此，我们还发现，当添加开关时，总体噪声强度总是更大，从某种意义上说，一个或两个开关的噪声确实比任何一个开关都要大。另一方面，从一个开关改为两个开关可能会增加或减少噪声强度。此外，稳态值可能无法反映瞬态阶段的相对噪声水平。然后我们研究双开关模型的混合版本，该模型使用随机微分方程来描述 mRNA 和蛋白质的演化。这是多尺度建模方法的一个简单示例，可以实现更便宜的数值模拟。尽管潜在的化学动力学似乎是二阶的，但我们表明可以通过应用伊藤引理的广义版本来分析 mRNA 和蛋白质水平的一阶矩和二阶矩。我们发现混合模型始终与底层马尔可夫跳跃模型的矩相匹配。相比之下，通过消除扩散来进一步简化模型以获得由开关驱动的常微分方程会导致 RNA 和蛋白质方差被低估。
We compare a hierarchy of three stochastic models in gene regulation. In each case, genes produce mRNA molecules which inturn produce protein. The simplest model, as described by Thattai and Van Oudenaarden (Proc. Nat. Acad. Sci., 2001), assumes that a geneisal way sactive, and uses a first-order chemical kinetics framework in the continuous-time, discrete-space Markov jump (Gillespie) setting. The second model, proposed by Raserand O'Shea (Science, 2004), generalizes the first by allowing the gene to switchr and omly between active and inactive states. Our third model accounts for other effects, such as the binding/unbinding of a transcription factor, by using two independenton/offswitches operating in AND mode. We focus first on the noise strength, which has been defined in the biological literature as the ratio of the variance to the mean at steady state. We show that the steady state variance in the mRNA and protein for the three models can either increase or decrease when switches are incorporated, depending on the rate constants and initial conditions. Despite this, we also find that the overall noise streng this always greater when switches are added, in the sense that one or two switches a real ways noisier tha nnone. On the other hand, moving from one to two switches may either increase ordecrease the noise strength. Moreover, the steady state values may not reflect the relative noise levels in the transient phase. We then look at a hybrid version of the two-switch model that uses stochastic differential equations to describe the evolution of mRNA and protein. This is a simple example of a multiscale modelling approach that allows for cheaper numerical simulations. Although the underlying chemical kinetics appears to be second order, we show that it is possible to analyse the first and second moments of the mRNA and protein levels by applying a generalized version of Ito's lemma. We find that the hybrid model matches the moments of underlying Markov jump model for all time. By contrast, further simplifying the model by removing the diffusion in order to obtain an ordinary differential equation driven by a switch causes them RNA and protein variances to be under estimated.