# Stochastic Dynamics of Nanoparticle and Virus Uptake

## TL;DR

This paper investigates how stochastic effects and particle geometry influence cellular uptake, revealing that spherical particles may be taken up faster than cylindrical ones due to noise effects, contrary to deterministic predictions.

## Contribution

It introduces a stochastic model showing geometry-dependent effects on nanoparticle and virus uptake, highlighting the role of noise in favoring spherical shapes.

## Key findings

- Spherical particles can have faster uptake due to stochastic effects.
- Deterministic theory predicts cylindrical particles are faster for the same volume.
- Stochastic effects depend strongly on particle geometry.

## Abstract

The cellular uptake of nanoparticles or viruses requires that the gain of adhesion energy overcomes the cost of plasma membrane bending. It is well known that this leads to a minimal particle size for uptake. Using a simple deterministic theory for this process, we first show that, for the same radius and volume, cylindrical particles should be taken up faster than spherical particles, both for normal and parallel orientations. We then address stochastic effects, which are expected to be relevant due to small system size, and show that, now, spherical particles can have a faster uptake, because the mean first passage time profits from the multiplicative noise induced by the spherical geometry. We conclude that stochastic effects are strongly geometry dependent and may favor spherical shapes during adhesion-driven particle uptake.