Mathematical model for force and energy of virion-cell interactions during full engulfment in HIV: Impact of virion maturation and host cell morphology.

Viral endocytosis involves elastic cell deformation, driven by chemical adhesion energy, and depends on physical interactions between the virion and cell membrane. These interactions are not easy to quantify experimentally. Hence, this study aimed to develop a mathematical model of the interactions of HIV particles with host cells and explore the effects of mechanical and morphological parameters during full virion engulfment. The invagination force and engulfment energy were described as viscoelastic and linear-elastic functions of radius and elastic modulus of virion and cell, ligand-receptor energy density and engulfment depth. The influence of changes in the virion-cell contact geometry representing different immune cells and ultrastructural membrane features and the decrease in virion radius and shedding of gp120 proteins during maturation on invagination force and engulfment energy was investigated. A low invagination force and high ligand-receptor energy are associated with high virion entry ability. The required invagination force was the same for immune cells of different sizes but lower for a local convex geometry of the cell membrane at the virion length scale. This suggests that localized membrane features of immune cells play a role in viral entry ability. The available engulfment energy decreased during virion maturation, indicating the involvement of additional biological or biochemical changes in viral entry. The developed mathematical model offers potential for the mechanobiological assessment of the invagination of enveloped viruses towards improving the prevention and treatment of viral infections.