Recent fluorescence spectroscopy measurements of single-enzyme kinetics have shown that enzymatic turnovers form a renewal stochastic process in which the inverse of the mean waiting time between turnovers follows the Michaelis-Menten equation. We study enzyme kinetics at physiologically relevant mesoscopic concentrations using a master equation. From the exact solution of the master equation we find that the waiting times are neither independent nor identically distributed, implying that enzymatic turnovers form a nonrenewal stochastic process. The inverse of the mean waiting time shows strong departure from the Michaelis-Menten equation. The waiting times between consecutive turnovers are anticorrelated, where short intervals are more likely to be followed by long intervals and vice versa. Correlations persist beyond consecutive turnovers indicating that multiscale fluctuations govern enzyme kinetics. © 2011 American Physical Society.

Arti Dua

Department Of Chemistry

Soma Saha

ENZYMATIC TURNOVER

ENZYME MOLECULES

Exact solution

master equations

MEAN WAITING TIME

Mesoscopics

MICHAELIS-MENTEN EQUATIONS

Multiscales

SHORT-INTERVAL

stochastic process

Waiting time

Catalyst activity

Enzyme kinetics

fluorescence spectroscopy

Kinetics

Random processes

Stochastic systems

Superconducting materials

enzyme activity

Fulltext

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Physical Review Letters

The catalytic conversion of substrates to products at the surface of a single nanoparticle cluster can now be resolved at the molecular scale and the waiting time between individual product turnovers measured with precision. The distribution of waiting times and, in particular, their means and variances can thus be obtained experimentally. Here, we show how theoretical modeling based on the chemical master equation (CME) provides a powerful tool to extract catalytic mechanisms and rate parameters from such experimental data. Conjecturing a family of mechanisms that both include and exclude surface restructuring, we obtain the mean and variance of their waiting times from the CME. A detailed analysis of the link between mechanism topology and waiting time dispersion, then, allows us to select several candidate mechanisms, with branched topologies, that can reproduce experimental data. From these, the least complex model that best matches experimental data is chosen as the minimum model. The CME modeling extracts the Langmuir-Hinshelwood mechanism for product formation and two-pathway mechanism for product dissociation, with substantial off-pathway state fluctuations due to surface restructuring dynamics, as the minimal model consistent with data. Our work, thus, provides a mechanistic origin of the coupling between the kinetics of catalytic turnovers and surface restructuring dynamics and yields a systematic way to compute catalytic rates from distributions of waiting times between product turnovers in the presence of surface restructuring. © 2019 Author(s).

Journal of Chemical Physics

Unraveling mechanisms from waiting time distributions in single-nanoparticle catalysis

The celebrated Michaelis-Menten (MM) expression provides a fundamental relation between the rate of enzyme catalysis and substrate concentration. The validity of this classical expression is, however, restricted to macroscopic amounts of enzymes and substrates and, thus, to processes with negligible fluctuations. Recent experiments have measured fluctuations in the catalytic rate to reveal that the MM equation, though valid for bulk amounts, is not obeyed at the molecular level. In this review, we show how new statistical measures of fluctuations in the catalytic rate identify a regime in which the MM equation is always violated. This regime, characterized by temporal correlations between enzymatic turnovers, is absent for a single enzyme and is unobservably short in the classical limit. © 2019, Indian Academy of Sciences.

Resonance

Enzyme Kinetics at the Molecular Level

Kumar, Adhikari, and Dua Reply

Dynamic co-operativity 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 co-operativity in terms of a slowing down of the Michaelis-Menten (MM) kinetics resulting in negative co-operativity. For fewer enzymes, dynamic co-operativity 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 co-operativity 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 single-pathway 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. © 2016 Author(s).

Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes

Recent fluorescence spectroscopy measurements of the turnover time distribution of single-enzyme turnover kinetics of β-galactosidase provide evidence of Michaelis-Menten kinetics at low substrate concentration. However, at high substrate concentrations, the dimensionless variance of the turnover time distribution shows systematic deviations from the Michaelis-Menten prediction. This difference is attributed to conformational fluctuations in both the enzyme and the enzyme-substrate complex and to the possibility of both parallel- and off-pathway kinetics. Here, we use the chemical master equation to model the kinetics of a single fluctuating enzyme that can yield a product through either parallel- or off-pathway mechanisms. An exact expression is obtained for the turnover time distribution from which the mean turnover time and randomness parameters are calculated. The parallel- and off-pathway mechanisms yield strikingly different dependences of the mean turnover time and the randomness parameter on the substrate concentration. In the parallel mechanism, the distinct contributions of enzyme and enzyme-substrate fluctuations are clearly discerned from the variation of the randomness parameter with substrate concentration. From these general results, we conclude that an off-pathway mechanism, with substantial enzyme-substrate fluctuations, is needed to rationalize the experimental findings of single-enzyme turnover kinetics of β-galactosidase (Chemical Equation). © 2015 American Chemical Society. All rights reserved.

Journal of Physical Chemistry B

Parallel versus Off-Pathway Michaelis-Menten Mechanism for Single-Enzyme Kinetics of a Fluctuating Enzyme

Nonrenewal statistics in the catalytic activity of enzyme molecules at mesoscopic concentrations

Nature Chemical Biology

Not all quiet on the noise front

Stochastic Processes in Physics and Chemistry

STOCHASTIC PROCESSES

Ever-fluctuating single enzyme molecules: Michaelis-Menten equation revisited

Comptes Rendus Biologies

Théorie générale de l'action de quelques diastases par Victor Henri [C. R. Acad. Sci. Paris 135 (1902) 916–919]

Journal	Physical Review Letters
ISSN	00319007
Open Access	Yes