Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes

Abstract

Dynamic cooperativity in monomeric enzymes is characterized in terms of a non-Michaelis-Menten kinetic behaviour. The latter is believed to be associated with mechanisms that include multiple reaction pathways due to enzymatic conformational fluctuations. Recent advances in single-molecule fluorescence spectroscopy have provided new fundamental insights on the possible mechanisms underlying reactions catalyzed by fluctuating enzymes. Here, we present a bottom-up approach to understand enzyme turnover kinetics at physiologically relevant mesoscopic concentrations informed by mechanisms extracted from single-molecule stochastic trajectories. The stochastic approach, presented here, shows the emergence of dynamic cooperativity in terms of a slowing down of the Michaelis-Menten (MM) kinetics resulting in negative cooperativity. For fewer enzymes, dynamic cooperativity emerges due to the combined effects of enzymatic conformational fluctuations and molecular discreteness. The increase in the number of enzymes, however, suppresses the effect of enzymatic conformational fluctuations such that dynamic cooperativity emerges solely due to the discrete changes in the number of reacting species. These results confirm that the turnover kinetics of fluctuating enzyme based on the parallel-pathway MM mechanism switches over to the singlepathway MM mechanism with the increase in the number of enzymes. For large enzyme numbers, convergence to the exact MM equation occurs in the limit of very high substrate concentration as the stochastic kinetics approaches the deterministic behaviour.

Substrate inhibition versus product feedback inhibition: In the perspective of single molecule enzyme kinetics

“…Whereas competing parallel and off‐parallel corridors led to a broad and highly stretched distribution function for the network. We here emphasize once again that dynamic disorder arises in this case even in the absence of a distinct inhibitor as discussed in a few recent articles 10,20,21 …”

“…However, one can extract valuable information on the kinetic mechanisms of a single enzyme from the inverse of the randomness and associate it to the number of rate‐limiting steps of the kinetic cycle, including identification of off‐pathways within the network if any. 10,19,20 So is the minimum amount of randomness that can be summarized. Hence, or and in the perspective of statistical kinetics brings insight into the emergent features of the dynamics at the stochastic level.…”

“…Additionally, we also calculate first and second moments given in Equations (A4) and (A5). We also numerically compute the inverse Laplace transformation of and then go on to calculate the first and second moments to present our results 20 …”

“…In an enzyme‐catalyzed reaction, enzymatic conformational fluctuations influence the turnover time of a single enzyme and the fluctuations carry important information about the mechanistic pathway 12 . This aspect of the single molecule study has been widely discussed under the purview of dynamic disorder, 13–17 which is believed to be associated with mechanisms that involve multiple reaction off‐pathways including dynamic cooperativity 18–21 …”

Variability and its types: the differential approach

“…К типичным примерам данной формы изменчивости относятся способность любого многоклеточного организма к возникновению случайных соматических мутаций или способность клеток женского эмбриона у плацентарных млекопитающих претерпевать случайную инактивацию одной из X-хромосом (Allis et al 2007;Clerc and Avner 2011). К этой же форме изменчивости следует отнести способность к стохастическому варьированию экспрессии генов (Paldi 2003;Raj et al 2010;Pilpel 2011), способность к спонтанным изменениям конформации белков (Kumar et al 2016) и т.п. Под онтогенетической изменчивостью мы понимаем способность живых существ претерпевать изменения в связи с закономерностями индивидуального развития.…”