  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.
