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Mapping Molecular Diffusion in the Plasma Membrane by Multiple-Target Tracing MTT
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Random search for a partially reactive target by multiple diffusive searchers.

Byeong Guk Go1, Juyeon Yi2, Yong Woon Kim1

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This study investigates how multiple searchers find a target in a limited space, finding their search time decreases with more searchers. The efficiency depends on space dimensions and target reactivity.

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Area of Science:

  • Statistical Physics
  • Physical Chemistry
  • Mathematical Biology

Background:

  • First-passage time problems are crucial for understanding diffusion-controlled processes.
  • Investigating partially reactive targets with excluded searchers is key to real-world phenomena.
  • The influence of multiple searchers on reaction kinetics is a complex, yet vital area of study.

Purpose of the Study:

  • To analyze the first-passage problem for N identical diffusive particles targeting a partially reactive region.
  • To determine the impact of partial reactivity and initial exclusion from the target zone.
  • To elucidate the relationship between searcher number, dimensionality, and reactivity.

Main Methods:

  • Solving the Fokker-Planck equation to derive analytical expressions.
  • Analyzing the mean first-passage time (MFPT) behavior.
  • Utilizing Langevin dynamics simulations for validation.

Main Results:

  • The mean first-passage time (τN) shows a power-law relationship with the number of searchers (N), τN∼N^{-α}.
  • The exponent α is dependent on dimensionality, reactivity, and searcher number.
  • Identified conditions leading to crossovers between different exponent behaviors.

Conclusions:

  • The study provides a comprehensive understanding of multi-particle diffusion to partially reactive targets.
  • Analytical findings are robustly confirmed by numerical simulations.
  • The research offers insights into optimizing search strategies in various scientific domains.