Reversible Target-Binding Kinetics of Multiple Impatient Particles
arXiv:2112.15069 · doi:10.1063/5.0083849
Abstract
Certain biochemical reactions can only be triggered after binding of a sufficient number of particles to a specific target region such as an enzyme or a protein sensor. We investigate the distribution of the reaction time, i.e., the first instance when all independently diffusing particles are bound to the target. When each particle binds irreversibly, this is equivalent to the first-passage time of the slowest (last) particle. In turn, reversible binding to the target renders the problem much more challenging and drastically changes the distribution of the reaction time. We derive the exact solution of this problem and investigate the short-time and long-time asymptotic behaviors of the reaction time probability density. We also analyze how the mean reaction time depends on the unbinding rate and the number of particles. Our exact and asymptotic solutions are compared to Monte Carlo simulations.
References in corpus (30)
- First-passage times in complex scale-invariant media
- Geometry-controlled kinetics
- Geometrical structure of Laplacian eigenfunctions
- Extreme value statistics of correlated random variables: a pedagogical review
- Diffusion-limited reactions in dynamic heterogeneous media
- First passages in bounded domains: When is the mean first passage time meaningful?
- Optimal reaction time for surface-mediated diffusion
- Strong defocusing of molecular reaction times results from an interplay of geometry and reaction control
- First passage time distribution in heterogeneity controlled kinetics: going beyond the mean first passage time
- Paradigm shift in diffusion-mediated surface phenomena
- Kinetics of stochastically-gated diffusion-limited reactions and geometry of random walk trajectories
- Diffusive escape through a narrow opening: new insights into a classic problem
- Universal formula for the mean first passage time in planar domains
- Full distribution of first exit times in the narrow escape problem
- Towards a full quantitative description of single-molecule reaction kinetics in biological cells
- Distribution of extreme first passage times of diffusion
- From single-particle stochastic kinetics to macroscopic reaction rates: fastest first-passage time of random walkers
- Spectral theory of imperfect diffusion-controlled reactions on heterogeneous catalytic surfaces
- First passage statistics for diffusing diffusivity
- Explicit Construction of the Brownian Self-Transport Operator
- Interlacing Relaxation and First-Passage Phenomena in Reversible Discrete and Continuous Space Markovian Dynamics
- Asymptotics of extreme statistics of escape time in 1,2 and 3-dimensional diffusions
- Exit time distribution in spherically symmetric two-dimensional domains
- Extreme value statistics of ergodic Markov processes from first passage times in the large deviation limit
- Partially Reflected Brownian Motion: A Stochastic Approach to Transport Phenomena
- A probabilistic approach to extreme statistics of Brownian escape times in dimensions 1, 2, and 3
- Competition between slow and fast regimes for extreme first passage times of diffusion
- Diffusion toward non-overlapping partially reactive spherical traps: fresh insights onto classic problems
- A first-passage approach to diffusion-influenced reversible binding: insights into nanoscale signaling at the presynapse
- Survival probability of stochastic processes beyond persistence exponents