Department of Chemistry, Massachusetts Institute of Technology , Cambridge, Massachusetts 02139, United States.
J Phys Chem B. 2017 Aug 24;121(33):7750-7760. doi: 10.1021/acs.jpcb.7b01516. Epub 2017 Aug 10.
Recently, we described a pathway analysis technique (paper 1) for analyzing generic schemes for single-molecule kinetics based upon the first-passage time distribution. Here, we employ this method to derive expressions for the Poisson indicator, a normalized measure of stochastic variation (essentially equivalent to the Fano factor and Mandel's Q parameter), for various renewal (i.e., memoryless) enzymatic reactions. We examine its dependence on substrate concentration, without assuming all steps follow Poissonian kinetics. Based upon fitting to the functional forms of the first two waiting time moments, we show that, to second order, the non-Poissonian kinetics are generally underdetermined but can be specified in certain scenarios. For an enzymatic reaction with an arbitrary intermediate topology, we identify a generic minimum of the Poisson indicator as a function of substrate concentration, which can be used to tune substrate concentration to the stochastic fluctuations and to estimate the largest number of underlying consecutive links in a turnover cycle. We identify a local maximum of the Poisson indicator (with respect to substrate concentration) for a renewal process as a signature of competitive binding, either between a substrate and an inhibitor or between multiple substrates. Our analysis explores the rich connections between Poisson indicator measurements and microscopic kinetic mechanisms.
最近，我们描述了一种途径分析技术（文献 1），用于分析基于首通过时间分布的单分子动力学通用方案。在这里，我们将这种方法应用于推导各种更新（即无记忆）酶反应的泊松指标的表达式，泊松指标是随机变化的归一化度量（本质上等同于福诺因子和曼德尔的 Q 参数）。我们研究了它对底物浓度的依赖性，而无需假设所有步骤都遵循泊松动力学。根据对前两个等待时间矩的函数形式的拟合，我们表明，二阶非泊松动力学通常是不确定的，但在某些情况下可以指定。对于具有任意中间拓扑的酶反应，我们确定了泊松指标的通用最小值作为底物浓度的函数，可以用于调整底物浓度以适应随机波动，并估计周转循环中潜在连续链接的最大数量。我们确定了更新过程中泊松指标（相对于底物浓度）的局部最大值，这是竞争结合的特征，无论是在底物和抑制剂之间还是在多个底物之间。我们的分析探讨了泊松指标测量值和微观动力学机制之间的丰富联系。
