Before revision:  Here, we investigate the dynamics of switching between metastable states of a feedback based on/off switch , by employing the WKB theory to treat the underlying master equations. This technique, applicable for any generic feedback function, yields accurate results for the quasi-stationary distributions of mRNA and protein copy numbers and  mean switching time, starting from either state.
After revision:  Here, we investigate the dynamics of switching between metastable states of a feedback based on/off switch , by employing the WKB theory to treat the underlying chemical master equations, we obtain accurate results for the quasi-stationary distributions of mRNA and protein copy numbers and mean switching time, starting from either state.