标题： 零阶超敏感性：在总拟稳态近似下线性噪声 regime 中的临界性和涨落研究 显示英文标题

标题： Zero-order ultrasensitivity: A study of criticality and fluctuations under the total quasi-steady state approximation in the linear noise regime

摘要： 零阶超敏感性（ZOU）是酶网络中一种长期已知且有趣的现象。在这里，底物由两种对抗性酶可逆地修饰（一个“推拉”系统），在饱和条件下，修饰状态的分数会在酶浓度比的一个临界值处从接近零迅速切换到接近一。ZOU及其扩展自Goldbeter和Koshland（1981）的开创性论文以来已经研究了几十年；然而，对于有限种群中波动的研究来说，重要的完整概率处理仍然缺失。在本文中，我们使用模块化方法研究ZOU，类似于总拟稳态近似（tQSSA）。这种方法导致了中间酶结合复合物的概率分布以及底物分子的修饰/未修饰分数的福克-普朗克（漂移-扩散）方程。我们获得了各种平均分数及其在线性噪声近似（LNA）下的波动的显式表达式。开关转变的“临界点”的出现被严格确立。在接近临界区域的各种化学状态下，得到了底物浓度分数的平均值和方差的新解析结果。对于修饰状态的总分数，方差被证明在临界点附近达到最大值，并远离该点时代数衰减，类似于二阶相变。新的解析结果与现有的结果以及使用Gillespie算法进行的详细数值模拟进行了比较。 显示英文摘要

摘要： Zero-order ultrasensitivity (ZOU) is a long known and interesting phenomenon in enzyme networks. Here, a substrate is reversibly modified by two antagonistic enzymes (a "push-pull" system) and the fraction in modified state undergoes a sharp switching from near-zero to near-unity at a critical value of the ratio of the enzyme concentrations, under saturation conditions. ZOU and its extensions have been studied for several decades now, ever since the seminal paper of Goldbeter and Koshland (1981); however, a complete probabilistic treatment, important for the study of fluctuations in finite populations, is still lacking. In this paper, we study ZOU using a modular approach, akin to the total quasi-steady state approximation (tQSSA). This approach leads to a set of Fokker-Planck (drift-diffusion) equations for the probability distributions of the intermediate enzyme-bound complexes, as well as the modified/unmodified fractions of substrate molecules. We obtain explicit expressions for various average fractions and their fluctuations in the linear noise approximation (LNA). The emergence of a "critical point" for the switching transition is rigorously established. New analytical results are derived for the average and variance of the fractional substrate concentration in various chemical states in the near-critical regime. For the total fraction in the modified state, the variance is shown to be a maximum near the critical point and decays algebraically away from it, similar to a second-order phase transition. The new analytical results are compared with existing ones as well as detailed numerical simulations using a Gillespie algorithm.