Before revision: 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.
After revision: We investigate the dynamical effects of non-Gaussian asymmetric stable L\'evy noisy fluctuations on the evolution of the transcrip- tion factor activator in the kinetic model of a single genetic regulation system.