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

Abstract

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.

Single‐Molecule Kinetics of an Enzyme in the Presence of Multiple Substrates

“…Thus, the non‐MM behavior of the initial rate of product formation as a function of [S 1 ] can distinguish between the ordered and random sequential mechanisms. In a few recent kinetic studies, dynamic cooperativity is observed for a monomeric enzyme in which a single enzyme has multiple reaction pathways that arise due to slow fluctuations between different conformational states of the enzyme …”

“…The equations are solved exactly by using a Laplace transform technique to obtain exact expressions for the waiting time distribution. This theoretical formalism was previously used to study the kinetics of a single fluctuating enzyme that led to product formation by either parallel or off‐pathway mechanisms . We calculate the waiting time distribution, the mean waiting time, and the randomness parameter from the moments of the distribution for all three modes of bisubstrate binding pathways to study the effect of temporal fluctuations in enzymatic turnovers.…”

Dissection of enzymatic kinetics and elucidation of detailed parameters based on the Michaelis‐Menten model. Kinetic and thermodynamic connections

“…Experimental procedures to detect different enzyme species and their properties should confirm these data but require special methods, such as fast kinetic and spectroscopic measurements with fluorescent probes. 45,46 Such analyses can also be done using the present approach by loading and fitting directly the complex or turnover data, as described by Kumar et al 46 A very relevant feature of the proposed approach is the possibility of establishing connections between kinetics and thermodynamics. Such kind of correlation was recently described for metabolic pathway analysis using the flux of intermediary components in response to enzyme concentration perturbations.…”

Enzyme Kinetics at the Molecular Level

“…, is evaluated from the mean and variance of w(τ ; N = 1). This yields r < 1 for all [S] [13]. This result is a specific case of a formal connection between the randomness parameter and network topology, which dictates that a reaction mechanism with n sequentially connected kinetic states, 1…”