Before the First Bond: Depletion-Assisted Stochastic Capture at the Onset of Endocytosis
Abstract
In a crowded extracellular environment, viruses and nanoparticles must reach the cell membrane within a few nanometers before the first ligand-receptor bond can form. Crowders generate an entropic depletion attraction, yet continuum models usually assume contact is already established or treat the approach deterministically. We formulate a thermodynamically consistent stochastic theory for this pre-contact stage. The sphere-plane depletion geometry uses the exact Asakur-Oosawa spherical-cap overlap, rather than a fitted cap, with either ideal van 't Hoff or pressure-only Carnahan-Starling osmotic pressure. A spatially varying near-wall mobility introduces a noise-induced drift that is essential for thermodynamic consistency and is often omitted. The first specific reaction is modeled by a Robin radiation boundary; the outer boundary is reflecting or absorbing. Three first-passage problems are solved analytically by quadrature: the mean reaction time, the reaction-before-escape probability, and the conditional success time, the last encoded by a Doob transform that exposes the selection bias of conditioning on capture. The theory separates thermodynamic inputs from conditional parameters and reveals a reaction-limited to diffusion-limited crossover controlled by the local Damköhler number. For typical virus and nanoparticle parameters, the depletion well reaches $2−6\,k_{\rm B}T$, capture times are $0.1−1\,{\rm ms}$, and the conditional success time is measurably shorter than the unconditional mean. Finite-volume and Chebyshev schemes reproduce the analytic results within their discretization errors and satisfy the radiation-boundary mass balance. This provides a quantitative theoretical framework for crowding-assisted capture prior to membrane wrapping and a reference for comparing crowding, near-wall mobility, and surface reactivity in endocytosis.
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BibTeX
@misc{wu2026before,
title = {{Before the First Bond: Depletion-Assisted Stochastic Capture at the Onset of Endocytosis}},
author = {Hao Wu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01321},
eprint = {2611.01321},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01321},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Before the First Bond: Depletion-Assisted Stochastic Capture at the Onset of Endocytosis
AU - Hao Wu
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01321
UR - https://arxiv.org/abs/2611.01321
AB - In a crowded extracellular environment, viruses and nanoparticles must reach the cell membrane within a few nanometers before the first ligand-receptor bond can form. Crowders generate an entropic depletion attraction, yet continuum models usually assume contact is already established or treat the approach deterministically. We formulate a thermodynamically consistent stochastic theory for this pre-contact stage. The sphere-plane depletion geometry uses the exact Asakur-Oosawa spherical-cap overlap, rather than a fitted cap, with either ideal van 't Hoff or pressure-only Carnahan-Starling osmotic pressure. A spatially varying near-wall mobility introduces a noise-induced drift that is essential for thermodynamic consistency and is often omitted. The first specific reaction is modeled by a Robin radiation boundary; the outer boundary is reflecting or absorbing. Three first-passage problems are solved analytically by quadrature: the mean reaction time, the reaction-before-escape probability, and the conditional success time, the last encoded by a Doob transform that exposes the selection bias of conditioning on capture. The theory separates thermodynamic inputs from conditional parameters and reveals a reaction-limited to diffusion-limited crossover controlled by the local Damköhler number. For typical virus and nanoparticle parameters, the depletion well reaches $2−6\,k_{\rm B}T$, capture times are $0.1−1\,{\rm ms}$, and the conditional success time is measurably shorter than the unconditional mean. Finite-volume and Chebyshev schemes reproduce the analytic results within their discretization errors and satisfy the radiation-boundary mass balance. This provides a quantitative theoretical framework for crowding-assisted capture prior to membrane wrapping and a reference for comparing crowding, near-wall mobility, and surface reactivity in endocytosis.
ER -