  Budding allows virus replication and macromolecular secretion in cells. It
involves the formation of a bud, i.e. an outgrowth from the cell membrane that
evolves into an envelope. The largest energetic barrier to bud formation is
membrane deflection and is trespassed primarily thanks to nucleocapsid-membrane
adhesion. Transmembrane proteins (TPs), which later form the virus ligands, are
the main promotors of adhesion and can accommodate membrane bending thanks to
an induced spontaneous curvature. Adhesive TPs must diffuse across the membrane
from remote regions to gather on the bud surface, thus, diffusivity controls
the kinetics. This paper proposes a simple model to describe diffusion-mediated
budding unraveling important size limitations and size-dependent kinetics. The
predicted optimal virion radius, giving the fastest budding, is validated
against experiments for Coronavirus, HIV, Flu, and Hepatitis. Assuming
exponential replication of virions and hereditary size, the model can predict
the size distribution of a virus population. This is verified against
experiments for SARS-CoV-2. All the above comparisons rely on the premise that
budding poses the tightest size constraint. This is true in most cases, as
demonstrated in this paper, where the proposed model is extended to describe
virus infection via receptor- and clathrin-mediated endocytosis, and via
membrane fusion.
