Biomedical subjects

Brian P English

Publications and source records attributed to Brian P English.

5 recordsLinked to original sources

PubMed2006

When does the Michaelis-Menten equation hold for fluctuating enzymes?

Enzymes are dynamic entities: both their conformation and catalytic activity fluctuate over time. When such fluctuations are relatively fast, it is not surprising that the classical Michaelis-Menten (MM) relationship between the steady-state enzymatic velocity and the substrate concentration still holds. However, recent single-molecule experiments have shown that this is the case even for an enzyme whose catalytic activity fluctuates on the 10(-4)-10 s range. The purpose of this paper is to examine various scenarios in which slowly fluctuating enzymes would still obey the MM relationship. Specifically, we consider (1) the quasi-static condition (e.g., the conformational fluctuation of the enzyme-substrate complex is much slower than binding, catalysis, and the conformational fluctuations of the free enzyme), (2) the quasi-equilibrium condition (when the substrate dissociation is much faster than catalysis, irrespective of the time scales or amplitudes of conformational fluctuations), and (3) the conformational-equilibrium condition (when the dissociation and catalytic rates depend on the conformational coordinate in the same way). For each of these scenarios, the physical meaning of the apparent Michaelis constant and catalytic rate constant is provided. Finally, as an example, the theoretical analysis of a recent single-molecule enzyme assay is considered in light of the perspectives presented in this paper.

Biophysics↗

PubMed2005

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

Enzymes are biological catalysts vital to life processes and have attracted century-long investigation. The classic Michaelis-Menten mechanism provides a highly satisfactory description of catalytic activities for large ensembles of enzyme molecules. Here we tested the Michaelis-Menten equation at the single-molecule level. We monitored long time traces of enzymatic turnovers for individual beta-galactosidase molecules by detecting one fluorescent product at a time. A molecular memory phenomenon arises at high substrate concentrations, characterized by clusters of turnover events separated by periods of low activity. Such memory lasts for decades of timescales ranging from milliseconds to seconds owing to the presence of interconverting conformers with broadly distributed lifetimes. We proved that the Michaelis-Menten equation still holds even for a fluctuating single enzyme, but bears a different microscopic interpretation.

Catalysis↗

PubMed2005

Single-molecule Michaelis-Menten equations.

This paper summarizes our present theoretical understanding of single-molecule kinetics associated with the Michaelis-Menten mechanism of enzymatic reactions. Single-molecule enzymatic turnover experiments typically measure the probability density f(t) of the stochastic waiting time t for individual turnovers. While f(t) can be reconciled with ensemble kinetics, it contains more information than the ensemble data; in particular, it provides crucial information on dynamic disorder, the apparent fluctuation of the catalytic rates due to the interconversion among the enzyme's conformers with different catalytic rate constants. In the presence of dynamic disorder, f(t) exhibits a highly stretched multiexponential decay at high substrate concentrations and a monoexponential decay at low substrate concentrations. We derive a single-molecule Michaelis-Menten equation for the reciprocal of the first moment of f(t), 1/ , which shows a hyperbolic dependence on the substrate concentration [S], similar to the ensemble enzymatic velocity. We prove that this single-molecule Michaelis-Menten equation holds under many conditions, in particular when the intercoversion rates among different enzyme conformers are slower than the catalytic rate. However, unlike the conventional interpretation, the apparent catalytic rate constant and the apparent Michaelis constant in this single-molecule Michaelis-Menten equation are complicated functions of the catalytic rate constants of individual conformers. We also suggest that the randomness parameter r, defined as <(t - )2> / t2, can serve as an indicator for dynamic disorder in the catalytic step of the enzymatic reaction, as it becomes larger than unity at high substrate concentrations in the presence of dynamic disorder.

Algorithms↗

PubMed2005

Fluctuating enzymes: lessons from single-molecule studies.

Recent single-molecule enzymology measurements with improved statistics have demonstrated that a single enzyme molecule exhibits large temporal fluctuations of the turnover rate constant at a broad range of time scales (from 1 ms to 100 s). The rate constant fluctuations, termed as dynamic disorder, are associated with fluctuations of the protein conformations observed on the same time scales. We discuss the unique information extractable from these experiments and the reconciliation of these observations with ensemble-averaged Michaelis-Menten equation. A theoretical model based on the generalized Langevin equation (GLE) treatment of Kramers' barrier crossing problem for chemical reactions accounts naturally for the observation of dynamic disorder and highly dispersed kinetics.

Enzymes↗

PubMed2002

Development of a novel method to populate native disulfide-bonded intermediates for structural characterization of proteins: implications for the mechanism of oxidative folding of RNase A.

RNase A, a model protein for oxidative folding studies, has four native disulfide bonds. The roles of des [40-95] and des [65-72], the two native-like structured three-disulfide-bonded intermediates populated between 8 and 25 degrees C during the oxidative folding of RNase A, are well characterized. Recent work focuses on both the formation of these structured disulfide intermediates from their unstructured precursors and on the subsequent oxidation of the structured species to form the native protein. The major obstacles in this work are the very low concentration of the precursor species and the difficulty of isolating some of the structured intermediates. Here, we demonstrate a novel method that enables the native disulfide-bonded intermediates to be populated and studied regardless of whether they have stable structure and/or are present at low concentrations during the oxidative folding or reductive unfolding process. The application of this method enabled us to populate and, in turn, study the key intermediates with two native disulfide bonds on the oxidative folding pathway of RNase A; it also facilitated the isolation of des [58-110] and des [26-84], the other two native-like structured des species whose isolation had thus far not been possible.

Animals↗