Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania 16802, USA.
J Chem Phys. 2010 Jul 21;133(3):034104. doi: 10.1063/1.3459111.
Following the discovery of slow fluctuations in the catalytic activity of an enzyme in single-molecule experiments, it has been shown that the classical Michaelis-Menten (MM) equation relating the average enzymatic velocity and the substrate concentration may hold even for slowly fluctuating enzymes. In many cases, the average velocity is that given by the MM equation with time-averaged values of the fluctuating rate constants and the effect of enzyme fluctuations is simply averaged out. The situation is quite different for a sequence of reactions. For colocalization of a pair of enzymes in a sequence to be effective in promoting reaction, the second must be active when the first is active or soon after. If the enzymes are slowly varying and only rarely active, the product of the first reaction may diffuse away before the second enzyme is active, and colocalization may have little value. Even for single-step reactions the interplay of reaction and diffusion with enzyme fluctuations leads to added complexities, but for multistep reactions the interplay of reaction and diffusion, cell size, compartmentalization, enzyme fluctuations, colocalization, and segregation is far more complex than for single-step reactions. In this paper, we report the use of stochastic simulations at the level of whole cells to explore, understand, and predict the behavior of single- and multistep enzyme-catalyzed reaction systems exhibiting some of these complexities. Results for single-step reactions confirm several earlier observations by others. The MM relationship, with altered constants, is found to hold for single-step reactions slowed by diffusion. For single-step reactions, the distribution of enzymes in a regular grid is slightly more effective than a random distribution. Fluctuations of enzyme activity, with average activity fixed, have no observed effects for simple single-step reactions slowed by diffusion. Two-step sequential reactions are seen to be slowed by segregation of the enzymes for each step, and results of the calculations suggest limits for cell size. Colocalization of enzymes for a two-step sequence is seen to promote reaction, and rates fall rapidly with increasing distance between enzymes. Low frequency fluctuations of the activities of colocalized enzymes, with average activities fixed, can greatly reduce reaction rates for sequential reactions.
在单分子实验中发现酶的催化活性存在缓慢波动之后，已经表明，即使对于缓慢波动的酶，经典的米氏-门捷列夫（MM）方程将平均酶速度与底物浓度相关联也是成立的。在许多情况下，平均速度是由 MM 方程给出的，其中波动的速率常数的时间平均值和酶波动的影响被平均掉了。对于一系列反应，情况就完全不同了。为了使一对酶在序列中的共定位有效地促进反应，第二个酶必须在第一个酶活跃或之后不久活跃。如果酶是缓慢变化的，并且只有很少的时间是活跃的，那么第一个反应的产物可能在第二个酶活跃之前扩散掉，并且共定位可能没有什么价值。即使对于单步反应，反应和扩散与酶波动的相互作用也会导致额外的复杂性，但对于多步反应，反应和扩散、细胞大小、隔室化、酶波动、共定位和隔离的相互作用比单步反应复杂得多。在本文中，我们报告了在整个细胞水平上使用随机模拟来探索、理解和预测表现出这些复杂性的单步和多步酶催化反应系统的行为。单步反应的结果证实了其他人的一些早期观察结果。发现对于扩散减慢的单步反应，MM 关系（常数改变）仍然成立。对于单步反应，在规则网格中酶的分布比随机分布稍微更有效。对于扩散减慢的简单单步反应，平均活性固定的酶活性波动没有观察到影响。两步连续反应由于每个步骤的酶的隔离而被减慢，并且计算结果表明了细胞大小的限制。对于两步序列的酶共定位被观察到促进反应，并且随着酶之间距离的增加，反应速率迅速下降。共定位酶的低频率活性波动，平均活性固定，可以大大降低连续反应的反应速率。
