# Membrane penetration and trapping of an active particle

## TL;DR

This paper models the interaction of active particles with membranes, revealing conditions for penetration or trapping, and provides analytical tools to predict membrane behavior relevant to biological and synthetic systems.

## Contribution

It introduces a minimal model for active particle-membrane interactions, combining numerical and analytical methods to predict penetration, trapping, and membrane recovery.

## Key findings

- Active particles can either penetrate or get trapped by membranes.
- Membrane shape and dynamics depend on particle activity and membrane properties.
- Analytical predictions align with numerical simulations across various membrane types.

## Abstract

The interaction between nano- or micro-sized particles and cell membranes is of crucial importance in many biological and biomedical applications such as drug and gene delivery to cells and tissues. During their cellular uptake, the particles can pass through cell membranes via passive endocytosis or by active penetration to reach a target cellular compartment or organelle. In this manuscript, we develop a simple model to describe the interaction of a self-driven spherical particle (moving through an effective constant active force) with a minimal membrane system, allowing for both penetration and trapping. We numerically calculate the state diagram of this system, the membrane shape, and its dynamics. In this context, we show that the active particle may either get trapped near the membrane or penetrates through it, where the membrane can either be permanently destroyed or recover its initial shape by self-healing. Additionally, we systematically derive a continuum description allowing to accurately predict most of our results analytically. This analytical theory helps identifying the generic aspects of our model, suggesting that most of its ingredients should apply to a broad range of membranes, from simple model systems composed of magnetic microparticles to lipid bilayers. Our results might be useful to predict mechanical properties of synthetic minimal membranes.