Modeling HA-protein mediated interaction between an influenza virus and a healthy cell: prefusion membrane deformation

We present a mathematical model for pre-fusion interaction between an influenza virus and a healthy cell. The model describes the role of the force exerted by Hemaglutinin (HA) protein clusters in bringing the viral membrane in close contact with the host cell membrane, as a first step of the fusion process between the two membranes. We model the viral membrane as a lipid bilayer whose shape energy is given by the Helfrich functional. Using the calculus of variation, we compute the deformation of the viral membrane under the influence of the protein force. Our numerical results support the hypothesis of dimple formation in the fusion-site proposed in the literature. We discuss the effects of spontaneous curvature, protein-cluster radius, fusion-site radius and protein-cluster force on the dimple size/shape and the energy stored. We also examine the effects of membrane incompressibility and the presence of the host cell on the dimple shape. Our results on the effects of the membrane incompressibility property and spontaneous curvature support the experimental results.