We investigate the dynamical effects of non-Gaussian  noisy fluctuations on the evolution of the transcrip- tion factor activator in the kinetic  model of a single genetic regulation system. The noisy fluctuations arise from the determination of the synthesis rate and degradation rate , and are modeled by asymmetric stable L\'evy motions. We use two deterministic quantities, the mean first exit time (MFET) and the first escape probability (FEP), to examine the transition events from low to concentration states under the influences of two types of noise. In the first case, the noise is multiplicative and symmetric, and we conclude that the fluctuations of the degradation reaction rate induce different switching processes for different noise param- eters.For the second case, the noise is additive and asymmetric, and we find that the fluctuations of the synthesis reaction rate lead to interesting transitions. The mean first exit time can be shortened and first escape probability can be increased by adjusting the noise parameters.
We investigate the dynamical effects of non-Gaussian asymmetric stable L\'evy noisy fluctuations on the evolution of the transcription factor activator in the kinetic concentration model of a single genetic regulation system. The noisy fluctuations arise from the determination of the synthesis reaction rate , and are modeled by asymmetric stable L\'evy motions. We compute two deterministic quantities, the mean first exit time (MFET) and the first escape probability (FEP), to examine the transition events from low to high concentration state under the influence of L\'evy noise. We find that the fluctuations of the synthesis reaction rate lead to peculiar transitions to higher concentrations (i.e., higher likelihood for transcriptions), such as higher likelihood of transcription for larger positive skewness parameter (asymmetry index) \beta, achieving the minimum likelihood of transcription by tuning skewness parameter \beta, achieving the higher likelihood of transcription by tuning non-Gaussianity index \alpha, and a bifurcation for transcription at the critical value \alpha=1. We conduct a series of numerical experiments about `regulating' the likelihood of gene transcription by tuning asymmetric stable L\'evy noise parameters.
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asymmetric stable L\'evy
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transcrip- tion
transcription
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concentration
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rate and degradation rate
reaction rate
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use
compute
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concentration states under the influences of two types of noise. In the first case, the noise is multiplicative and symmetric, and we conclude
high concentration state under the influence of L\'evy noise. We find
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degradation reaction rate induce different switching processes for different noise param- eters.For the second case, the noise is additive and asymmetric, and we find that the fluctuations of the synthesis reaction rate lead to interesting transitions. The mean first exit time can be shortened and first escape probability can be increased by adjusting the
synthesis reaction rate lead to peculiar transitions to higher concentrations (i.e., higher likelihood for transcriptions), such as higher likelihood of transcription for larger positive skewness parameter (asymmetry index) \beta, achieving the minimum likelihood of transcription by tuning skewness parameter \beta, achieving the higher likelihood of transcription by tuning non-Gaussianity index \alpha, and a bifurcation for transcription at the critical value \alpha=1. We conduct a series of numerical experiments about `regulating' the likelihood of gene transcription by tuning asymmetric stable L\'evy