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Reversible target-binding kinetics of multiple impatient particles.

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This study analyzes reaction times for particles binding to targets. Reversible binding significantly alters reaction time distributions, with exact solutions derived and compared to simulations.

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Area of Science:

  • Biochemistry
  • Chemical Kinetics
  • Statistical Mechanics

Background:

  • Biochemical reactions often require multiple particles to bind to a target site, like an enzyme or protein sensor.
  • The timing of these reactions is crucial for biological processes and can be modeled using particle binding dynamics.

Purpose of the Study:

  • To investigate the probability distribution of reaction times for multiple diffusing particles binding to a target.
  • To analyze the impact of reversible binding kinetics on reaction time distributions and their asymptotic behaviors.
  • To determine the dependence of mean reaction time on unbinding rates and particle numbers.

Main Methods:

  • Derivation of the exact mathematical solution for the reaction time distribution with reversible binding.
  • Analysis of short-time and long-time asymptotic behaviors of the reaction time probability density.
  • Comparison of theoretical results with outcomes from Monte Carlo simulations.

Main Results:

  • Reversible binding drastically alters the reaction time distribution compared to irreversible binding.
  • Exact and asymptotic solutions for reaction time distributions were successfully derived.
  • The mean reaction time was found to be dependent on the unbinding rate and the number of particles.

Conclusions:

  • The study provides a comprehensive theoretical framework for understanding reaction times in systems with reversible particle binding.
  • The derived solutions offer accurate predictions that are validated by computational simulations.
  • This work advances the understanding of molecular binding dynamics and reaction kinetics in biological systems.