Mechanisms of viral budding through cellular membranes.

Budding is a fundamental membrane-remodeling process central to many cellular functions and is exploited by numerous enveloped viruses to acquire their lipid envelopes. Despite extensive molecular characterization, the physical mechanisms that determine whether budding proceeds to completion or becomes stalled remain unclear. Here, we develop a theoretical model based on the Helfrich elastic formalism to investigate how membrane geometry and boundary conditions regulate the elastic energy of viral budding. We analyze two representative cases: budding from a flat membrane, characteristic of human immunodeficiency virus and alphaviruses, and budding from a vesicle, as observed for severe acute respiratory syndrome coronavirus 2 in the ER-Golgi intermediate compartment. Our results reveal distinct energetic pathways: vesicle-like geometries exhibit a stronger energetic bias toward closure, whereas flat membranes develop extended low-slope regions in the energy landscape that can hinder completion. Relaxing far-field boundary constraints reduces the energetic cost associated with membrane area conservation and renders the flat-membrane case energetically comparable to the vesicle case, providing a physical explanation for why viruses frequently bud adjacent to one another or within pre-curved membrane regions. Comparison with thin-section TEM images of alphavirus budding shows results consistent with the theoretical membrane profiles. Together, these findings establish how curvature coupling, boundary flexibility, and local membrane geometry cooperate to control the efficiency and completion of membrane budding.