Before revision:  We conduct a series of numerical experiments about `regulating' the likelihood of gene transcription by tuning asymmetric stable L\'evy noise indexes.
After revision:  While in the multiplicative noise case, non-Gaussianity index value \alpha=1 is a separating point or line for both the mean first exit time (MFET) and the first escape probability (FEP). We also investigate the noise enhanced stability phenomenon. Additionally, we are able to specify the regions in the whole parameter space for the asymmetric noise, in which we attain desired likelihood for transcription. We have conducted a series of numerical experiments about `regulating' the likelihood of gene transcription by tuning asymmetric stable L\'evy noise indexes.