# Dynamics of particle uptake at cell membranes

## TL;DR

This paper models the dynamics of particle uptake at cell membranes, considering energy barriers, particle shapes, and stochastic effects, providing analytical approximations and dynamical phase diagrams.

## Contribution

It introduces a new analytical approximation for the energy barrier in membrane deformation and explores the effects of particle shape and stochastic fluctuations on endocytosis dynamics.

## Key findings

- Energy barrier resembles line tension but differs in details.
- Particle shape significantly influences uptake dynamics.
- Stochastic fluctuations facilitate membrane wrapping and alter phase diagrams.

## Abstract

Receptor-mediated endocytosis requires that the energy of adhesion overcomes the deformation energy of the plasma membrane. The resulting driving force is balanced by dissipative forces, leading to deterministic dynamical equations. While the shape of the free membrane does not play an important role for tensed and loose membranes, in the intermediate regime it leads to an important energy barrier. Here we show that this barrier is similar to but different from an effective line tension and suggest a simple analytical approximation for it. We then explore the rich dynamics of uptake for particles of different shapes and present the corresponding dynamical state diagrams. We also extend our model to include stochastic fluctuations, which facilitate uptake and lead to corresponding changes in the phase diagrams.