Extrinsic noise-induced transitions  have been largely investigated in a variety of chemical and physicalsystems. The key properties that make these systems mathematically tractable is that the noise appears linearly in the dynamical equations  and it is assumed Gaussian and white. Here we consider the simplest unit of gene regulation ,  the repressed gene, which is instead characterized by nonlinear dependencies on external parameters , leading to corresponding nonlinear extrinsic noise. We adopt a general methodology to address this nonlinearity based on assuming that the fluctuations exhibit a finite and large correlation time . We also relax the Gaussian assumption, and consider the more biologically relevant log-normal noise. We find that in contrast to Gaussian noise, log-normal noise leads to noise-induced transitions, with the system becoming bimodal. We emphasize that no feedback loops are present in the system, and therefore our findings identify a novel class of noise-induced transitions , based on both features of noise nonlinearity and boundedness .
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 .
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Here we consider the simplest unit of gene regulation
In biology, the Gaussian approximation has been successful in specific systems, but the relevant noise being usually non-Gaussian
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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,
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to address this nonlinearity based on assuming that the fluctuations exhibit a finite and large correlation time
introduced recently, so-called nonlinear noise filtering, which allows the investigation of linear, nonlinear, Gaussian and non-Gaussian noises
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relax the Gaussian assumption, and consider the more biologically relevant log-normal noise. We find that in contrast to Gaussian noise, log-normal noise leads to noise-induced transitions, with the system becoming bimodal. We emphasize that no feedback loops are present in the system, and therefore our findings identify a novel class
present a derivation of it, which highlights its dynamical origin. Testing the methodology on the repressed gene confirms that the emergence
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, based on both features of noise nonlinearity and boundedness
appears to be strongly dependent on the type of noise adopted, and on the degree of nonlinearity present in the system