Influenza Viral Membrane Deformation due to Re- folding of HA-protein: Two-dimensionalModel and Analysis

In this paper we study influenza viral membrane deformation related to the refolding of Hemagglutinin (HA) protein. The focus of the paper is to understand membrane deformation and budding due to experimentally observed linear HA-protein clusters, which have not been mathematically studied before. The viral membrane is modeled as a two dimensional incompressible lipid bilayer with bending rigidity. For tensionless membranes, we derive an analytical solution while for membrane under tension we solve the problem numerically. Our solution for tensionless membranes shows that the height of membrane deformation increases monotonically with the bending moment exerted by HA-proteins and attains its maximum when the size of the protein cluster reaches a critical value. Our results also show that the hypothesis of dimple formation proposed in the literature is valid in the two dimensional setting. Our comparative study of axisymmetric HA-clusters and linear HA-clusters reveals that the linear HA-clusters are not favorable to provide a sufficient energy required to overcome an energy barrier for a successful fusion, despite their capability to cause membrane deformation and budding.