Membrane particle wrapping across methods and shapes

Understanding the passive wrapping of adhesive particles by lipid membranes is a crucial step in untangling more complex endocytotic processes. However, despite the variety of computational approaches used to study passive endocytosis, a direct comparison of results across different modeling methods has never been performed. In this work, we present a comparative analysis of three distinct frameworks: numerical solutions of the axisymmetric membrane shape equation, a particle-based molecular dynamics model (MesoMem), and an energy-based triangulated surface model (FreeDTS). First, we validated our numerical solver for spherical particles against established literature and extended the implementation to include closed vesicle membranes and non-spherical particles. Next, we studied the same system with our two simulation methods, and found that the phase plots obtained from our numerical solution agree with those from our simulations. We then extended our study to anisotropic particles. By tracking engulfment pathways in MesoMem and FreeDTS, we observed a dynamic rotational transition where non-spherical particles initially bind in a horizontal ('submarine') orientation and subsequently rotate to a vertical ('rocket') orientation to complete wrapping - a behavior impossible to capture with standard axisymmetric models. Lastly, we considered the wrapping of soft vesicles with FreeDTS. Our simulations of a deformable, fixed-connectivity particle show that stronger adhesion promotes wrapping, whereas increasing membrane tension suppresses it. Complete engulfment is accompanied by a substantial reduction in particle volume, suggesting that particle compressibility provides an additional pathway for wrapping.