Noise-enhanced stability and resonance effect of a termolecular enzymatic reaction

Here, we investigate an enzymatic reaction system subjected to additive and multiplicative noises and a weak periodic signal. By means of numerical simulations, we find that structure of stationary probability distribution function changes from one peak to two peaks by regulating not only the noise intensities (i.e., noise-induced transition), but also system parameters. The mean first passage time as a function of the multiplicative noise intensity exhibits a maximum, showing that the noise can enhance stability of the system. Moreover, by using the two-states theory, analytically expression of signal-to-noise ratio (SNR) of the system in the adiabatic limit is derived. The results indicate that: (1) The SNR as a function of noise intensity exhibits a maximal value, i.e., a stochastic resonance (SR) phenomenon; (2) as the noise intensities remain unchanged, the curve of the SNR with respect to the parameters of the system displays a peak, i.e., a SR-like phenomenon. Because the noise and the parameters reflect, respectively, temperature and rates of the enzymatic reactions, choosing optimal temperature and rates can enhance response of the system. This findings will be beneficial for controlling enzymatic reaction systems.