Stochasticity in gene expression impacts the dynamics and functions of gene regulatory circuits. Intrinsic noises, including those that are caused by low copy number of molecules and transcriptional bursting, are usually studied by stochastic simulations. However, the role of extrinsic factors, such as cell-to-cell variability and heterogeneity in the microenvironment, is still elusive. To evaluate the effects of both the intrinsic and extrinsic noises, we develop a method, named sRACIPE, by integrating stochastic analysis with random circuit perturbation (RACIPE) method. RACIPE uniquely generates and analyzes an ensemble of models with random kinetic parameters. Previously, we have shown that the gene expression from random models form robust and functionally related clusters. In sRACIPE we further develop two stochastic simulation schemes, aiming to reduce the computational cost without sacrificing the convergence of statistics. One scheme uses constant noise to capture the basins of attraction, and the other one uses simulated annealing to detect the stability of states. By testing the methods on several synthetic gene regulatory circuits and an epithelial–mesenchymal transition network in squamous cell carcinoma, we demonstrate that sRACIPE can interpret the experimental observations from single-cell gene expression data. We observe that parametric variation (the spread of parameters around a median value) increases the spread of the gene expression clusters, whereas high noise merges the states. Our approach quantifies the robustness of a gene circuit in the presence of noise and sheds light on a new mechanism of noise-induced hybrid states. We have implemented sRACIPE as an R package.

基因表达的随机性影响基因调控回路的动力学和功能。通常通过随机模拟研究内在的噪声，包括由低分子拷贝数和转录爆发引起的内在噪声。但是，外部因素的作用，如微环境中的细胞间变异性和异质性，仍然难以捉摸。为了评估内部和外部噪声的影响，我们通过将随机分析与随机电路扰动（RACIPE）方法集成在一起，开发了一种名为sRACIPE的方法。RACIPE唯一地生成和分析具有随机动力学参数的模型集合。以前，我们已经表明，来自随机模型的基因表达形成了功能强大且功能相关的簇。在sRACIPE中，我们进一步开发了两种随机仿真方案，目的是在不牺牲统计收敛性的情况下降低计算成本。一种方案使用恒定噪声来捕获吸引盆地，另一种方案使用模拟退火来检测状态的稳定性。通过在鳞状细胞癌中对几种合成基因调控电路和上皮-间充质转化网络的方法进行测试，我们证明了sRACIPE可以从单细胞基因表达数据中解释实验观察结果。我们观察到，参数变化（参数在中值附近的扩散）增加了基因表达簇的扩散，而高噪声合并了状态。我们的方法量化了在存在噪声的情况下基因电路的鲁棒性，并阐明了噪声诱导的混合态的新机制。