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Single-molecule Michaelis-Menten equations.

S C Kou1, Binny J Cherayil, Wei Min

  • 1Department of Statistics, Harvard University, Cambridge, Massachusetts 02138, USA.

The Journal of Physical Chemistry. B
|July 21, 2006
PubMed
Summary
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This study explores single-molecule enzyme kinetics, revealing how dynamic disorder affects reaction rates. A new single-molecule Michaelis-Menten equation is derived, offering insights into enzyme behavior beyond traditional ensemble methods.

Area of Science:

  • Biochemistry
  • Chemical Kinetics
  • Enzyme Mechanisms

Background:

  • Enzymatic reactions follow the Michaelis-Menten mechanism.
  • Single-molecule turnover experiments measure waiting times (t) for individual enzymatic events.
  • Ensemble kinetics often mask dynamic disorder, which arises from enzyme conformational changes affecting catalytic rates.

Purpose of the Study:

  • To theoretically understand single-molecule kinetics in enzymatic reactions.
  • To investigate the impact of dynamic disorder on enzyme turnover.
  • To derive and validate a single-molecule Michaelis-Menten equation.

Main Methods:

  • Theoretical analysis of single-molecule enzymatic turnover data.
  • Derivation of a single-molecule Michaelis-Menten equation for the reciprocal of the first moment of waiting times (1/).

Related Experiment Videos

  • Analysis of the probability density function f(t) under varying substrate concentrations and dynamic disorder.

    • Main Results:

    • The probability density function f(t) shows stretched multiexponential decay at high substrate concentrations and monoexponential decay at low concentrations in the presence of dynamic disorder.
    • A single-molecule Michaelis-Menten equation for 1/ exhibits hyperbolic dependence on substrate concentration [S].
    • Apparent kinetic parameters in the single-molecule equation are complex functions of individual conformer rate constants.

    Conclusions:

    • The derived single-molecule Michaelis-Menten equation provides a framework for understanding enzyme kinetics at the single-molecule level.
    • Dynamic disorder significantly influences enzyme behavior and can be quantified using a randomness parameter (r).
    • This work enhances the interpretation of single-molecule enzyme kinetics, particularly concerning enzyme conformational flexibility.