Search efficiency in the Adam-Delbrück reduction-of-dimensionality scenario versus direct diffusive search
arXiv:2206.03887 · doi:10.1088/1367-2630/ac8824
Abstract
The time instant -- the first-passage time (FPT) -- when a diffusive particle (e.g., a ligand such as oxygen or a signalling protein) for the first time reaches an immobile target located on the surface of a bounded three-dimensional domain (e.g., a hemoglobin molecule or the cellular nucleus) is a decisive characteristic time-scale in diverse biophysical and biochemical processes, as well as in intermediate stages of various inter- and intra-cellular signal transduction pathways. Adam and Delbrück put forth the reduction-of-dimensionality concept, according to which a ligand first binds non-specifically to any point of the surface on which the target is placed and then diffuses along this surface until it locates the target. In this work, we analyse the efficiency of such a scenario and confront it with the efficiency of a direct search process, in which the target is approached directly from the bulk and not aided by surface diffusion. We consider two situations: (i) a single ligand is launched from a fixed or a random position and searches for the target, and (ii) the case of "amplified" signals when ligands start either from the same point or from random positions, and the search terminates when the fastest of them arrives to the target. For such settings, we go beyond the conventional analyses, which compare only the mean values of the corresponding FPTs. Instead, we calculate the full probability density function of FPTs for both scenarios and study its integral characteristic -- the "survival" probability of a target up to time . On this basis, we examine how the efficiencies of both scenarios are controlled by a variety of parameters and single out realistic conditions in which the reduction-of-dimensionality scenario outperforms the direct search.
References in corpus (24)
- Kinetics of protein-DNA interaction: facilitated target location in sequence-dependent potential
- Extreme value statistics of correlated random variables: a pedagogical review
- Diffusion-limited reactions in dynamic heterogeneous media
- 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
- Diffusive escape through a narrow opening: new insights into a classic problem
- Full distribution of first exit times in the narrow escape problem
- Distribution of extreme first passage times of diffusion
- Intermittent random walks for an optimal search strategy: One-dimensional case
- From single-particle stochastic kinetics to macroscopic reaction rates: fastest first-passage time of random walkers
- Heterogeneities Shape Passive Intracellular Transport
- Kinetics of active surface-mediated diffusion in spherically symmetric domains
- Search reliability and search efficiency of combined Lévy-Brownian motion: long relocations mingled with thorough local exploration
- Exact mean exit time for surface-mediated diffusion
- Surface Hopping Propagator: An Alternative Approach to Diffusion-Influenced Reactions
- Optimization and universality of Brownian search in quenched heterogeneous media
- Statistics of first-passage Brownian functionals
- Joint distribution of multiple boundary local times and related first-passage time problems with multiple targets
- Depletion of Resources by a Population of Diffusing Species
- Distribution of first-reaction times with target regions on boundaries of shell-like domains
- Resonance scattering in a waveguide with identical thick barriers
- Reversible reactions controlled by surface diffusion on a sphere
- A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes