酶促反应的弗洛凯驱动：计数统计与长时间电流
Floquet Driving of Enzymatic Reactions: Counting Statistics and Long-Time Currents
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中文总结 AI 辅助
研究在时变控制下化学反应动力学，通过发展弗洛凯理论计算电流及其计数统计，以离散弗洛凯驱动的环磷酸腺苷生产生化系统为例，得到相关解析表达式和数值结果，为周期性驱动化学反应的弗洛凯分析奠定基础。
中文摘要 AI 辅助
人工控制化学反应系统的技术如光遗传学迅速发展，理解时变控制下的反应动力学愈发重要。当反应速率调制具有时间周期性时，弗洛凯形式提供了系统框架。本文为经典随机过程发展了弗洛凯理论，能计算周期性调制下的电流及其计数统计。通过计数场表述理论，推导了一阶累积量和相应电流的一般表达式。以离散弗洛凯驱动为例，应用于环磷酸腺苷（cAMP）生产的生化系统，得到反应速率周期性切换产生长时间产物电流的解析表达式和数值结果。这些结果为周期性驱动化学反应的弗洛凯分析提供了基础。
英文摘要
Technologies for artificially controlling chemical reaction systems, such as optogenetics, are rapidly advancing, making it increasingly important to understand reaction dynamics under time-dependent control. When the modulation of reaction rates is periodic in time, the Floquet formalism provides a systematic framework. We develop a Floquet theory for classical stochastic processes that enables the calculation of the current and its counting statistics under such periodic modulation. In particular, we formulate the theory in terms of a counting field and derive general expressions for the first cumulant and the corresponding current. The current is expressed using the effective Floquet generator and the kicked state, and we further obtain general asymptotic expressions for the current in both the high- and low-frequency regimes. As a concrete example to test our analytical expressions, we then apply the results to discrete Floquet driving -- a non-perturbative, stepwise protocol. The setup is motivated by a biochemical system known as cyclic adenosine monophosphate (cAMP) production, which is an enzymatic reaction activated and inhibited by G-proteins. This is formulated as a discretely driven Michaelis--Menten-type reaction model, in which the catalytic activity is switched on and off abruptly in time, and we obtain analytical expressions and numerical results showing how periodic switching of reaction rates generates a long-time product current. In particular, in the high-frequency limit, we show that the effect of the periodic driving can be interpreted through an effective modification of the chemical reaction rates. These results provide a basis for Floquet analysis of periodically driven chemical reactions.
