Gaussian curvature and the budding kinetics of enveloped viruses

Abstract

The formation of a membrane-enveloped virus such as HIV-1 starts with the assembly of a curved layer of capsid proteins lining the interior of the plasma membrane (PM) of the host cell. This layer grows into a spherical shell enveloped by a lipid membrane that is connected to the PM via a curved neck ("budding"). For many enveloped viruses the scission of this neck is not spontaneous. Instead, the elaborate "ESCRT" cell machinery needs to be recruited to carry out that task. It is not clear why this is necessary since scission is spontaneous for much simpler systems, such as vesiculation driven by phase-separation inside lipid bilayers. Recently, Brownian dynamics simulations of enveloped virus budding reproduced protracted pausing and stalling after formation of the neck [1], which suggest that the origin of pausing/stalling is to be found in the physics of the budding process. Here, we show that the pausing/stalling observed in the simulations can be understood as a purely kinetic phenomenon associated with a "geometrical" energy barrier that must be overcome by capsid proteins diffusing along the membrane prior to incorporation into the viral capsid. This geometrical energy barrier is generated by the conflict between the positive Gauss curvature of the capsid and the large negative Gauss curvature of the neck region. The theory is compared with the Brownian simulations of the budding of enveloped viruses.

Physics of viral dynamics

“…Retroviruses assemble either inside the cytoplasm of an infected cell or on the cytoplasmic membrane (hereafter PM) 91 . In either case, they acquire a lipid envelope when they bud from the PM 92 . The resulting spherical immature particle is not yet infectious.…”

Nanoscale curvature promotes high yield spontaneous formation of cell-mimetic giant vesicles

“…The expression penalizes bending from 0 of a symmetric membrane and for any stretching of the membrane. The Gaussian curvature is invariant absent a topological change 45 . Since the buds remain attached to the surface, the Gaussian curvature of the vesiculating membrane is invariant during the process of budding (See Supplementary Fig.…”

“…4 and Supplementary Text for a discussion of the morphology and connectivity of the buds). A region of negative Gaussian curvature develops at the neck of the bud that equals the positive Gaussian curvature of the spherical bud 45 . We thus only consider changes in elastic energy of the membrane due to changes in the mean curvature.…”

On Gaussian Curvature and Membrane Fission

“…In the synaptic nerve terminals, vesicles are filled with neurotransmitters and released by exocytosis 3 . Moreover, many viruses are enveloped by a lipid membrane which mediates the fusion of the virus with the host cell membrane; some examples are HIV-1, herpesviruses, the Ebola virus 5 , and coronaviruses 7 like SARS-CoV-2.…”

“…There has been extensive research for protein mediated fission. The dynamin superfamily 8,[18][19][20] or the ESCRT machinery 5,21,22 are two different sets of proteins that mediate in budding and fission. For example, the dynamin Drp1 is considered a major component in mitochondrial division; other dynamins are considered to either help or be necessary for the fission process.…”