Membrane bending energy selects for compact growth of protein assemblies.

Remodeling of cell membranes into vesicles is essential for receptor transport into cells and viral escape from infected cells. Membranes must be forced into these highly curved vesicles, and this is primarily driven through a structured assembly of multiple, multivalent interacting protein subunits forming a lattice. Lattice assembly from these subunits is a stochastic process, and intermediate structures formed during growth can vary in both structure and stability. Here we show that the membrane bending energy cost per protein rises significantly when remodeling is driven by lattice intermediates that deviate from compact, ideal spherical structures. We use a continuum membrane mechanics model coupled to lattice intermediates assembled from stochastic rigid-body simulations of HIV-1 Gag lattice assembly to quantify the bending energy as it systematically varies with lattice eccentricity. Our results show that highly eccentric lattices induce a higher bending energy cost because the lattices still deform the membrane into an approximate spherical cap, but the radius of the cap is larger due to the imperfect lattice geometry. These quantitative trends are also nearly independent of the density of links to the membrane, emphasizing the importance of the lattice perimeter shape instead. Rescaling thus recovers an approximately universal bending energy cost when evaluated relative to the circumscribing sphere of the lattice intermediates. These results show that assembly pathways coupled to membrane remodeling face much stronger selection pressure for highly compact growth compared to solution assembly pathways due to bending energy costs and provide a tool to characterize these pathways during processes like viral budding and endocytosis.