Nonequilibrium Dynamic Phase Diagram for Transmembrane Transport of Active Particles

In recent years, there has been considerable push toward the biomedical applications with active particles, which have great potential to revolutionize disease diagnostics and therapy. The direct penetration of active particles through the cell membrane leads to more efficient intracellular delivery than previously considered endocytosis processes but may cause membrane disruption. Understanding fundamental behaviors of cell membranes in response to such extreme impacts by active particles is crucial to develop active particle-based biomedical technologies and manage health and safety issues in this emerging field. Unfortunately, the physical principles underlying the nonequilibrium behaviors from endocytosis to direct penetration remain elusive, and experiments are challenging. Here, we present a computed dynamic phase diagram for transmembrane transport of active particles and identify four characteristic dynamic phases in endocytosis and direct penetration according to the particle activity and membrane tension. The boundaries dividing these phases are analytically obtained with theoretical models, elucidating the nonequilibrium physics and criteria for the transition between different phases. Furthermore, we numerically and experimentally show three distinct dynamic regimes related to the interplay between necking and wrapping during the endocytosis process of active particles, which strikingly contrast the regimes for passive particles. Overall, these findings could be useful for sharpening the understanding of basic principles underlying biological issues related to the safe and efficient biomedical applications of such emerging matters.