2021/04/19 by Ryan D. Schumm, Schumm, Ryan D., Paul C. Bressloff +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Materials Science · #Advanced biosensing and bioanalysis techniques #Diffusion and Search Dynamics #FOS: Physical sciences #Gold and Silver Nanoparticles Synthesis and Applications #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2104.09372
openalex publication_date 2021/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend the theoretical framework used to study search processes with\nstochastic resetting to the case of partially absorbing targets. Instead of an\nabsorption event occurring when the search particle reaches the boundary of a\ntarget, the particle can diffuse freely in and out of the target region and is\nabsorbed at a rate \κ when inside the target. In the context of cell\nbiology, the target could represent a chemically reactive substrate within a\ncell or a region where a particle can be offloaded onto a nearby compartment.\nWe apply this framework to a partially absorbing interval and to spherically\nsymmetric targets in Rd. In each case, we determine how the mean first\npassage time (MFPT) for absorption depends on \κ, the resetting rate r,\nand the target geometry. For the given examples, we find that the MFPT is a\nmonotonically decreasing function of \κ, whereas it is a unimodal\nfunction of r with a unique minimum at an optimal resetting rate r rm\nopt. The variation of r rm opt with \κ depends on the spatial\ndimension d, decreasing in sensitivity as d increases. For finite \κ,\n r rm opt is a non-trivial function of the target size and distance\nbetween the target and the reset point. We also show how our results converge\nto those obtained previously for problems with totally absorbing targets and\nsimilar geometries when the absorption rate becomes infinite. Finally, we\ngeneralize the theory to take into account an extended chemical reaction scheme\nwithin a target.\n