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In a multistep reaction mechanism, one of the elementary steps progresses significantly slower than the others. This slowest step is called the rate-limiting step (or rate-determining step). A reaction cannot proceed faster than its slowest step, and hence, the rate-determining step limits the overall reaction rate.
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The rate-determining step, or RDS, in a chemical reaction is the slowest step that determines the overall reaction rate. It is identified by using the observed rate law and typically involves approximation methods like the RDS approximation or the steady-state approximation.In the RDS approximation, also known as the rate-limiting-step or equilibrium approximation, the reaction mechanism consists of one or more reversible reactions near equilibrium, followed by a slower RDS, and then one or...
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Precisely and Accurately Inferring Single-Molecule Rate Constants.

C D Kinz-Thompson1, N A Bailey1, R L Gonzalez1

  • 1Columbia University, New York, NY, United States.

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|October 30, 2016
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Calculating stochastic rate constants from single-molecule data requires idealizing signal trajectories. New methods enhance precision and accuracy, rigorously assessing limitations from finite trajectory lengths and time resolution.

Keywords:
Bayesian inferenceDwell time distribution analysisFluorescence resonance energy transferHidden Markov modelMarkovian reactionsSingle-molecule rate constant

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Area of Science:

  • Biophysics
  • Biochemistry
  • Physical Chemistry

Background:

  • Biomolecular kinetics are quantified by stochastic rate constants governing molecular trajectories.
  • Experimental signal trajectories are often idealized to state trajectories using methods like thresholding or hidden Markov modeling.

Purpose of the Study:

  • To discuss methods for idealizing single-molecule signal trajectories.
  • To calculate stochastic rate constants from idealized state trajectories.
  • To analyze and improve the precision and accuracy of these calculations.

Main Methods:

  • Idealization of experimental signal trajectories (e.g., thresholding, hidden Markov modeling).
  • Calculation of stochastic rate constants from state trajectories.
  • Bayesian inference for rigorous precision determination.
  • Methods accounting for finite trajectory length and limited time resolution.

Main Results:

  • Analysis of how finite signal trajectory length impacts precision.
  • Demonstration of Bayesian inference for precise assessment.
  • Analysis of how finite length and time resolution affect accuracy.
  • Development of methods to substantially improve accuracy.

Conclusions:

  • The discussed methods enable rigorous assessment of precision in stochastic rate constant calculations.
  • Accuracy of stochastic rate constants is significantly enhanced by accounting for trajectory limitations.
  • These approaches improve the reliability of kinetic parameter estimation from single-molecule data.