A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes

Abstract

We consider a sequential cascade of molecular first-reaction events towards a terminal reaction centre in which each reaction step is controlled by diffusive motion of the particles. The model studied here represents a typical reaction setting encountered in diverse molecular biology systems, in which, e.g., a signal transduction proceeds via a series of consecutive "messengers": the first messenger has to find its respective immobile target site triggering a launch of the second messenger, the second messenger seeks its own target site and provokes a launch of the third messenger and so on, resembling a relay race in human competitions. For such a molecular relay race taking place in infinite one-, two- and three-dimensional systems, we find exact expressions for the probability density function of the time instant of the terminal reaction event, conditioned on preceding successful reaction events on an ordered array of target sites. The obtained expressions pertain to the most general conditions: number of intermediate stages and the corresponding diffusion coefficients, the sizes of the target sites, the distances between them, as well as their reactivities are arbitrary.

References in corpus (16)

• Diffusion-limited reactions in dynamic heterogeneous media
• Universal relation between instantaneous diffusivity and radius of gyration of proteins in aqueous solution
• Leapover lengths and first passage time statistics for Lévy flights
• First passages for a search by a swarm of independent random searchers
• Strong defocusing of molecular reaction times results from an interplay of geometry and reaction control
• Paradigm shift in diffusion-mediated surface phenomena
• Mortality, Redundancy, and Diversity in Stochastic Search
• First-passage and first-hitting times of Levy flights and Levy walks
• Diffusive escape through a narrow opening: new insights into a classic problem
• Full distribution of first exit times in the narrow escape problem
• Survival probability of a particle in a sea of mobile traps: A tale of tails
• From single-particle stochastic kinetics to macroscopic reaction rates: fastest first-passage time of $N$ random walkers
• Kinetics of active surface-mediated diffusion in spherically symmetric domains
• Statistics of boundary encounters by a particle diffusing outside a compact planar domain
• First-encounter time of two diffusing particles in confinement
• First-passage properties of mortal random walks: ballistic behavior, effective reduction of dimensionality, and scaling functions for hierarchical graphs

Cited by in corpus (3)

• Search efficiency in the Adam-Delbrück reduction-of-dimensionality scenario versus direct diffusive search
• Distribution of first-reaction times with target regions on boundaries of shell-like domains
• Exact calculation of the mean first-passage time of continuous-time random walks by nonhomogeneous Wiener-Hopf integral equations