Coupled Evolution of Viral Protein Density and Membrane Shape in Coronavirus Assembly*

The assembly of coronaviruses in cells proceeds via the aggregation of membrane associated viral capsid proteins, leading to budding encapsulating the genetic material. For this process, the dynamics are controlled by interactions between proteins and their coupling to membrane curvature. To quantitatively understand the dynamics of this process, we propose a generalized analytical model that accounts for the key physical features. We describe the coupled time evolution of the protein density field and the membrane height (above a reference plane), taking into account the diffusion of proteins across the membrane and the effects their spontaneous curvature has on membrane bending. We performed linear stability analysis to determine the behavior of oscillations about various equilibrium configurations, finding stable/unstable/fastest growing modes based on original conditions. Numerical simulations, using the finite difference method, and Monte Carlo simulations, based on the free energy functional of the system, were then used to validate our results and analyze the evolution of the system both within and outside the domains defined by the linear stability analysis.