Mugler Andrew, Walczak Aleksandra M, Wiggins Chris H
Department of Physics, Columbia University, New York, New York 10027, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 1):041921. doi: 10.1103/PhysRevE.80.041921. Epub 2009 Oct 20.
Signal-processing molecules inside cells are often present at low copy number, which necessitates probabilistic models to account for intrinsic noise. Probability distributions have traditionally been found using simulation-based approaches which then require estimating the distributions from many samples. Here we present in detail an alternative method for directly calculating a probability distribution by expanding in the natural eigenfunctions of the governing equation, which is linear. We apply the resulting spectral method to three general models of stochastic gene expression: a single gene with multiple expression states (often used as a model of bursting in the limit of two states), a gene regulatory cascade, and a combined model of bursting and regulation. In all cases we find either analytic results or numerical prescriptions that greatly outperform simulations in efficiency and accuracy. In the last case, we show that bimodal response in the limit of slow switching is not only possible but optimal in terms of information transmission.
细胞内的信号处理分子通常以低拷贝数存在，这就需要概率模型来解释内在噪声。传统上，概率分布是通过基于模拟的方法来确定的，然后需要从许多样本中估计分布。在这里，我们详细介绍一种替代方法，即通过在控制方程的自然本征函数中展开来直接计算概率分布，该控制方程是线性的。我们将所得的谱方法应用于随机基因表达的三个通用模型：具有多个表达状态的单个基因（通常用作两种状态极限下的爆发模型）、基因调控级联以及爆发与调控的组合模型。在所有情况下，我们都得到了分析结果或数值公式，其在效率和准确性方面都大大优于模拟。在最后一种情况下，我们表明在慢切换极限下的双峰响应不仅是可能的，而且在信息传输方面是最优的。
