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Rate enhancement of gated drift-diffusion process by optimal resetting.

Arup Biswas1, Arnab Pal1, Debasish Mondal2

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Stochastic resetting can speed up gated drift-diffusion processes, which are common in biochemistry. This study identifies conditions where resetting enhances efficiency, even surpassing ungated processes.

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Area of Science:

  • Biochemistry and Biophysics
  • Statistical Mechanics
  • Physical Chemistry

Background:

  • Gating describes ion-channel transitions between open and closed states, crucial for selective transport.
  • Gated transport dynamics inherently slow down diffusion processes, increasing mean completion times.
  • Stochastic resetting is a technique used to counteract delays in transport phenomena.

Purpose of the Study:

  • To investigate the effect of stochastic resetting on gated drift-diffusion processes.
  • To determine if stochastic resetting can accelerate gated transport and under what conditions.
  • To construct a phase diagram illustrating the impact of resetting on completion times.

Main Methods:

  • Modeling a particle undergoing drift-diffusion with a stochastically gated target at the origin.
  • Subjecting the system to rate-limiting resetting dynamics.
  • Calculating the minimal mean completion time using an optimal resetting rate.
  • Analyzing the system's behavior across different resetting rates, gating parameters, and geometric configurations.

Main Results:

  • A phase diagram revealing three distinct regimes based on the resetting rate's effectiveness.
  • Identification of conditions where resetting accelerates gated drift-diffusion beyond ungated processes.
  • Demonstration of non-trivial completion time behaviors influenced by system parameters.

Conclusions:

  • Stochastic resetting can be a powerful strategy to enhance the efficiency of gated drift-diffusion processes.
  • The study provides a framework for predicting when resetting can expedite biochemical reactions modeled by gated transport.
  • This work offers insights into optimizing stochastic processes without sacrificing selectivity.