DELAYS INDUCE DIFFERENT SWITCH IN A STOCHASTIC SINGLE GENETIC REGULATION SYSTEM WITH A POSITIVE AUTOREGULATORY FEEDBACK LOOP

Abstract

The steady properties of a stochastic single genetic regulation system with the different time delays, which appear in the deterministic and fluctuating forces, are investigated based on the small delay time approximation method. Using the approximation probability density approach, the delayed Fokker–Planck equation is obtained. The effects of two different time delays on the stationary probability distribution and the mean value are discussed. It is found that with the time delay τ1 in the deterministic force increasing, the TF-A monomer concentration shifts from "off" state to "on" state. However, with the time delay τ2 in the fluctuating force increasing, the TF-A monomer concentration shifts from "on" state to "off" state. In the switch process, two kinds of time delays play an opposite role. The theoretical predictions are found to be in good agreement with numerical results.