随机基因表达的解析分布
Analytical distributions for stochastic gene expression
摘要：
基因表达具有显著的随机性，这使得遗传网络的建模具有挑战性。我们提出了一个近似，不仅允许计算的平均值和方差，但也分布的蛋白质数量。我们假设蛋白质的衰变速度比它们的mRNA慢得多，并使用芽殖酵母的高通量数据证实许多基因满足这种关系。对于基因表达的两阶段模型，以转录和翻译为一级反应，我们计算了所有时间大于几个mRNA寿命的蛋白质分布，从而定性地预测了蛋白质水平首次跨越任意阈值的时间分布。此外，如果启动子在非活性和活性状态之间波动，我们可以发现稳态蛋白质分布，如果启动子波动缓慢，则其可以是双峰的。我们表明，我们的假设意味着蛋白质合成发生在几何分布的突发，并允许mRNA被淘汰的主方程描述。在一般情况下，我们发现，蛋白质分布是不对称的，可能是穷人的特点，他们的平均值和方差。通过最大似然法，我们的表达式应该因此允许更多的定量比较与实验数据。更一般地说，我们引入了一种技术，通过消除一个快速变量来获得一个更简单，有效的动态随机系统。
英文摘要：
Gene expression is significantly stochastic making modeling of genetic networks challenging. We present an approximation that allows the calculation of not only the mean and variance but also the distribution of protein numbers. We assume that proteins decay substantially slower than their mRNA and confirm that many genes satisfy this relation using high-throughput data from budding yeast. For a two-stage model of gene expression, with transcription and translation as first-order reactions, we calculate the protein distribution for all times greater than several mRNA lifetimes and thus qualitatively predict the distribution of times for protein levels to first cross an arbitrary threshold. If in addition the promoter fluctuates between inactive and active states, we can find the steady-state protein distribution, which can be bimodal if promoter fluctuations are slow. We show that our assumptions imply that protein synthesis occurs in geometrically distributed bursts and allows mRNA to be eliminated from a master equation description. In general, we find that protein distributions are asymmetric and may be poorly characterized by their mean and variance. Through maximum likelihood methods, our expressions should therefore allow more quantitative comparisons with experimental data. More generally, we introduce a technique to derive a simpler, effective dynamics for a stochastic system by eliminating a fast variable.
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