Probing Wrapping Dynamics of Spherical Nanoparticles by 3D Vesicles Using Force-based Simulations

Nanoparticles present in various environments can interact with living organisms, potentially leading to deleterious effects. Understanding how these nanoparticles interact with cell membranes is crucial for rational assessment of their impact on diverse biological processes. While previous research has explored particle-membrane interactions, the dynamic processes of particle wrapping by fluid vesicles remain incompletely understood. In this study, we introduce a force-based, continuum-scale model utilizing triangulated mesh representation and discrete differential geometry to investigate particle-vesicle interaction dynamics. Our model captures the transformation of cell membrane shapes and nanoparticle wrapping by calculating the forces arising from membrane bending energy and particle adhesion energy. The simulation is validated through comparisons with theoretically predicted minimal bending energy and corresponding vesicle shapes. We then examine the interactions between spherical vesicles and individual nanospheres, both externally and internally, and quantify energy landscapes across different wrapping fractions of the nanoparticles. Furthermore, we explore multiple particle interactions with biologically relevant fluid vesicles with nonspherical shapes. Our study reveals that initial particle positions and interaction sequences are critical in determining the final equilibrium shapes of the vesicle-particle complex in these interactions. These findings emphasize the importance of nanoparticle positioning and wrapping fractions in the dynamics of particle-vesicle interactions, providing crucial insights for future research in the field.