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Extrinsic noise-induced transitions to bimodal dynamics have been largelyinvestigated in a variety of chemical, physical, and biological systems. In thestandard approach in physical and chemical systems, the key properties thatmake these systems mathematically tractable are that the noise appears linearlyin the dynamical equations, and it is assumed Gaussian and white. In biology,the Gaussian approximation has been successful in specific systems, but therelevant noise being usually non-Gaussian, non-white, and nonlinear posesserious limitations to its general applicability. Here we revisit thefundamental features of linear Gaussian noise, pinpoint its limitations, andreview recent new approaches based on nonlinear bounded noises, which highlightnovel mechanisms to account for transitions to bimodal behaviour. We do this byconsidering a simple but fundamental gene expression model, the repressed gene,which is characterized by linear and nonlinear dependencies on externalparameters. We then review a general methodology introduced recently, so-callednonlinear noise filtering, which allows the investigation of linear, nonlinear,Gaussian and non-Gaussian noises. We also present a derivation of it, whichhighlights its dynamical origin. Testing the methodology on the repressed geneconfirms that the emergence of noise-induced transitions appears to be stronglydependent on the type of noise adopted, and on the degree of nonlinearitypresent in the system.

Bimodality in gene expression without feedback: From Gaussian white noise to log-normal coloured noise