Extrinsic noise-induced transitions to bimodal dynamics have been largely investigated in a variety of chemical, physical, and biological systems. In the standard approach in physical and chemical systems, the key properties that make these systems mathematically tractable are that the noise appears linearly in the dynamical equations, and it is assumed Gaussian and white. In biology, the Gaussian approximation has been successful in specific systems, but the relevant noise being usually non-Gaussian, non-white, and nonlinear poses serious limitations to its general applicability. Here we revisit the fundamental features of linear Gaussian noise, pinpoint its limitations, and review recent new approaches based on nonlinear bounded noises, which highlight novel mechanisms to account for transitions to bimodal behaviour. We do this by considering a simple but fundamental gene expression model, the repressed gene, which is characterized by linear and nonlinear dependencies on external parameters. We then review a general methodology introduced recently, so-called nonlinear noise filtering, which allows the investigation of linear, nonlinear, Gaussian and non-Gaussian noises. We also present a derivation of it, which highlights its dynamical origin. Testing the methodology on the repressed gene confirms that the emergence of noise-induced transitions appears to be strongly dependent on the type of noise adopted, and on the degree of nonlinearity present in the system.

中文翻译：

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无反馈的基因表达双峰：从高斯白噪声到对数正态彩色噪声

在各种化学，物理和生物系统中，已经大量研究了外部噪声引起的向双峰动力学的过渡。在物理和化学系统的标准方法中，使这些系统在数学上易于处理的关键特性是噪声在动力学方程中呈线性出现，并假定为高斯和白色。在生物学上，高斯近似已在特定系统中取得成功，但是相关的噪声通常是非高斯，非白色和非线性的，因此对其一般适用性构成了严重限制。在这里，我们将回顾线性高斯噪声的基本特征，查明其局限性，并回顾基于非线性有界噪声的最新方法，这些方法突显了解释向双峰行为过渡的新颖机制。为此，我们考虑了一个简单但基本的基因表达模型，即受压基因，其特征在于对外部参数的线性和非线性依赖性。然后，我们回顾一下最近引入的一种通用方法，即所谓的非线性噪声滤波，它可以研究线性，非线性，高斯和非高斯噪声。我们还介绍了它的派生，突出了它的动态起源。测试抑制基因的方法论证实，噪声诱发的跃迁的出现似乎很大程度上取决于所采用的噪声类型以及系统中存在的非线性程度。然后，我们回顾一下最近引入的一种通用方法，即所谓的非线性噪声滤波，它可以研究线性，非线性，高斯和非高斯噪声。我们还介绍了它的派生，突出了它的动态起源。测试抑制基因的方法论证实，噪声诱发的跃迁的出现似乎很大程度上取决于所采用的噪声类型以及系统中存在的非线性程度。然后，我们回顾一下最近引入的一种通用方法，即所谓的非线性噪声滤波，它可以研究线性，非线性，高斯和非高斯噪声。我们还介绍了它的派生，突出了它的动态起源。测试抑制基因的方法论证实，噪声诱发的跃迁的出现似乎很大程度上取决于所采用的噪声类型以及系统中存在的非线性程度。