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.

在这里，我们研究一种酶反应系统，该系统受到加性和乘性噪声以及微弱的周期性信号的作用。通过数值模拟，我们发现，不仅通过调节噪声强度（即，噪声引起的跃迁），而且通过调节系统参数，平稳概率分布函数的结构从一个峰变为两个峰。作为乘性噪声强度的函数的平均第一次通过时间表现出最大值，表明噪声可以增强系统的稳定性。此外，利用二态理论，推导了在绝热极限下系统的信噪比（SNR）的解析表达式。结果表明：（1）SNR作为噪声强度的函数表现出最大值，即随机共振（SR）现象；（2）当噪声强度保持不变时，SNR相对于系统参数的曲线将显示一个峰值，即类似SR的现象。因为噪声和参数分别反映了酶促反应的温度和速率，所以选择最佳温度和速率可以增强系统的响应。该发现对于控制酶促反应系统将是有益的。