A model of HIV budding and self-assembly, role of cell membrane
  Budding from the plasma membrane of the host cell is an indispensable step in the life cycle of the Human Immunodeficiency Virus (HIV), which belongs to a large family of enveloped RNA viruses, retroviruses. Unlike regular enveloped viruses, retrovirus budding happens {\em concurrently} with the self-assembly of retrovirus protein subunits (Gags) into spherical virus capsids on the cell membrane. Led by this unique budding and assembly mechanism, we study the free energy profile of retrovirus budding, taking into account of the Gag-Gag attraction energy and the membrane elastic energy. We find that if the Gag-Gag attraction is strong, budding always proceeds to completion. During early stage of budding, the zenith angle of partial budded capsids, $\alpha$, increases with time as $\alpha \propto t^{1/3}$. However, when Gag-Gag attraction is weak, a metastable state of partial budding appears. The zenith angle of these partially spherical capsids is given by $\alpha_0\simeq(\tau^2/\kappa\sigma)^{1/4}$ in a linear approximation, where $\kappa$ and $\sigma$ are the bending modulus and the surface tension of the membrane, and $\tau$ is a line tension of the capsid proportional to the strength of Gag-Gag attraction. Numerically, we find $\alpha_0<0.3\pi$ without any approximations. Using experimental parameters, we show that HIV budding and assembly always proceed to completion in normal biological conditions. On the other hand, by changing Gag-Gag interaction strength or membrane rigidity, it is relatively easy to tune it back and forth between complete budding and partial budding. Our model agrees reasonably well with experiments observing partial budding of retroviruses including HIV. 
Rui Zhang and Toan T. Nguyen