  We examine the budding of a nanoscale particle through a lipid bilayer using
molecular dynamics simulations, free energy calculations, and an elastic
theory, with the aim of determining the extent to which equilibrium elasticity
theory can describe the factors that control the mechanism and efficiency of
budding. The particle is a smooth sphere which experiences attractive
interactions to the lipid head groups. Depending on the parameters, we observe
four classes of dynamical trajectories: particle adhesion to the membrane,
stalled partially wrapped states, budding followed by scission, and membrane
rupture. In most regions of parameter space we find that the elastic theory
agrees nearly quantitatively with the simulated phase behavior as a function of
adhesion strength, membrane bending rigidity, and particle radius. However, at
parameter values near the transition between particle adhesion and budding, we
observe long-lived partially wrapped states which are not captured by existing
elastic theories. These states could constrain the accessible system parameters
for those enveloped viruses or drug delivery vehicles which rely on exo- or
endocytosis for membrane transport.
