Nonequilibrium\nDynamic Phase Diagram for Transmembrane\nTransport of Active Particles

In\nrecent years, there has been considerable push toward the biomedical\napplications with active particles, which have great potential to\nrevolutionize disease diagnostics and therapy. The direct penetration\nof active particles through the cell membrane leads to more efficient\nintracellular delivery than previously considered endocytosis processes\nbut may cause membrane disruption. Understanding fundamental behaviors\nof cell membranes in response to such extreme impacts by active particles\nis crucial to develop active particle-based biomedical technologies\nand manage health and safety issues in this emerging field. Unfortunately,\nthe physical principles underlying the nonequilibrium behaviors from\nendocytosis to direct penetration remain elusive, and experiments\nare challenging. Here, we present a computed dynamic phase diagram\nfor transmembrane transport of active particles and identify four\ncharacteristic dynamic phases in endocytosis and direct penetration\naccording to the particle activity and membrane tension. The boundaries\ndividing these phases are analytically obtained with theoretical models,\nelucidating the nonequilibrium physics and criteria for the transition\nbetween different phases. Furthermore, we numerically and experimentally\nshow three distinct dynamic regimes related to the interplay between\nnecking and wrapping during the endocytosis process of active particles,\nwhich strikingly contrast the regimes for passive particles. Overall,\nthese findings could be useful for sharpening the understanding of\nbasic principles underlying biological issues related to the safe\nand efficient biomedical applications of such emerging matters.