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 .
We investigate the dynamical effects of non-Gaussian asymmetric stable L\'evy fluctuations on the evolution of the transcription factor activator in a genetic regulation system. The noisy fluctuations arise from the synthesis reaction rate . We compute two deterministic quantities, the mean first exit time (MFET) and the first escape probability (FEP), in order to examine the likelihood for transcriptions: The mean time scale for the system exits the low concentration state (the longer the exit time, the less likely for transcription) and the switch probability from low concentration states to high concentration states (corresponding to likelihood for transcription). By focusing on the impact of skewness (i.e., non-symmetry) in the probability distributions of noise, we find that the fluctuations in the synthesis reaction rate lead to peculiar transitions to high concentrations and thus to possible transcriptions , such as realizing higher likelihood of transcription for larger positive skewness (i.e., asymmetry) index \beta, causing a bifurcation for the likelihood of transcription at the critical non-Gaussianity index value \alpha = 1 (i.e., beyond which the likelihood for transcription suddenly increases), and achieving a turning point at the threshold value \beta \approx 0.55 (i.e., beyond which the likelihood for transcription reversed for \alpha values). The bifurcation and turning point phenomena do not occur in the symmetric noise case (\beta =0). We conduct a series of numerical experiments about `regulating' the likelihood of gene transcription by tuning asymmetric stable L\'evy noise indexes. These offer insights for possible ways of achieving gene regulation in experimental research .
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indexes. These offer insights for possible ways of achieving gene regulation in experimental research