Kundu Prasanta, Saha Soma, Gangopadhyay Gautam
S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India.
Department of Chemistry, Presidency University, 86/1 College Street, Kolkata 700073, India.
J Phys Chem B. 2020 Dec 31;124(52):11793-11801. doi: 10.1021/acs.jpcb.0c08392. Epub 2020 Dec 17.
Single-molecule experiment probed the catalytic conversions of Amplex Red to resorufin by horseradish peroxidase in which the product molecules were found to act as the allosteric inhibitor for the individual enzyme. While broad distributions of the initial reaction velocities and the number of product molecules required to cease the reaction unraveled the underlying dynamic disorder in the reaction pathway, bulk experimental measurements established the particularity of noncompetitive inhibition of the enzyme species. In this work, to rationalize the observed phenomena, we present a stochastic kinetic model of the enzymatic reaction taking into account the inhibitions of the enzyme and enzyme-substrate complex in the circumstance of their structural fluctuations. Starting from a chemical master equation that can further be reduced into a set of ordinary differential equations for the case of single-enzyme kinetics, we derived an analytical expression for the turnover time distribution, the first moment of which yielded the mean turnover time. The inverse of the latter showed excellent agreement with the bulk data of the initial enzymatic velocities measured in the presence of varying inhibitor concentrations. This supports the observed nature of inhibition which we further confirmed by constructing double-reciprocal plots for the inhibited kinetics. In addition, we successfully recovered ensemble data from another experiment that redesigned the aforesaid single-molecule catalysis to investigate the effects of molecular crowders on reaction velocity; the latter was greatly alleviated with increasing the molecular weight of the crowders. On the other hand, the calculated randomness parameter, determined from the higher moment of the turnover time distribution, clearly inferred dynamic disorder in the catalytic turnovers. Our work under a unified framework provides a robust theoretical description for the experimental kinetic study and eradicates the necessity of assuming an alternative mode of inhibition in analyzing the data, not consistent with the experiments, considered earlier.
单分子实验研究了辣根过氧化物酶催化Amplex Red转化为试卤灵的过程，发现产物分子对单个酶起变构抑制剂的作用。虽然初始反应速度和终止反应所需产物分子数的广泛分布揭示了反应途径中潜在的动态无序，但大量实验测量确定了该酶物种非竞争性抑制的特殊性。在这项工作中，为了解释观察到的现象，我们提出了一个酶促反应的随机动力学模型，该模型考虑了酶和酶 - 底物复合物在其结构波动情况下的抑制作用。从一个化学主方程出发，对于单酶动力学的情况，该方程可进一步简化为一组常微分方程，我们推导出了周转时间分布的解析表达式，其第一矩给出了平均周转时间。后者的倒数与在不同抑制剂浓度下测量的初始酶促速度的大量数据显示出极好的一致性。这支持了观察到的抑制性质，我们通过构建抑制动力学的双倒数图进一步证实了这一点。此外，我们成功地从另一个实验中恢复了总体数据，该实验重新设计了上述单分子催化过程，以研究分子拥挤剂对反应速度的影响；随着拥挤剂分子量的增加，反应速度的减缓得到了极大缓解。另一方面，根据周转时间分布的高阶矩计算出的随机性参数清楚地推断出催化周转过程中的动态无序。我们在一个统一框架下的工作为实验动力学研究提供了一个强有力的理论描述，并且消除了在分析与早期实验不一致的数据时假设另一种抑制模式的必要性。
