First passage time distribution of multiple impatient particles with reversible binding

Area of Science:

• Statistical Physics
• Chemical Kinetics
• Mathematical Modeling

Background:

• Studying the behavior of diffusing particles that interact with a target is crucial in various scientific fields.
• The first passage time (FPT) for multiple particles to bind to a target, considering reversible binding and particle 'impatience', presents a complex temporal coupling challenge.
• Previous research determined the mean FPT for two particles (N=K=2) in a 1D domain.

Purpose of the Study:

• To approximate the full distribution of the first passage time (FPT) for K out of N independently diffusing particles to bind simultaneously to a target.
• To develop an analytically tractable approximation valid for any N ≥ K ≥ 1 in diverse spatial domains and dimensions.
• To investigate the sensitive and nonlinear dependence of FPT on N and K.

Main Methods:

• Development of an analytical approximation for the FPT distribution.
• Proof of the approximation's exactness in the limit of small target/binding rates.
• Demonstration that the approximation serves as an upper bound across all parameter regimes.
• Derivation of explicit formulas for the mean and distribution of the FPT.
• Validation through detailed numerical simulations.

Main Results:

• An analytically tractable approximation for the FPT distribution of K out of N particles binding to a target was derived.
• The approximation is exact for small target/binding rates and an upper bound generally.
• Explicit formulas for the FPT mean and distribution were obtained, revealing sensitive, nonlinear dependencies on K and N.

Conclusions:

• The developed approximation provides a powerful tool for analyzing complex binding dynamics of multiple diffusing particles.
• The study highlights the significant impact of particle number (N) and required bound particles (K) on the first passage time.
• The findings offer insights into systems with reversible binding and particle 'impatience', with broad applicability.