Electrostatic interactions and structural transformations in viral shells

Structural transformations occurring in proteinaceous viral shells (capsids) can be induced by changing the pH of bathing solution, thus modifying the dissociation equilibrium of ionizable amino acids in proteins. To analyze the effects of electrostatic interactions on viral capsids, we construct a model of 2D isotropic elastic shells with embedded point charges located in the centers of mass of individual proteins. We find that modification of the electrostatic interactions between proteins affects not only the size and shape of capsids, but in addition induces substantial deformations of hexamers in capsid structures. Using bacteriophage P22 and Nudarelia capensis omega virus (NωV) as examples, we analyze the capsid faceting and propose an explanation as to why the hexamers in spherical procapsid are skewed, while they acquire a regular shape in the faceted state. Also, we examine the electrostatic and elastic effects that can explain different shapes of coronavirus shells decorated with spikes, which are often localized in compact areas over the shell surface. The proposed mechanism of local curvature generation is supported by the remarkable correspondence between the shell shape and the distribution of spikes in model and observed shells. Considering the simplest energy of electrostatic interactions between proteins together with the mechanical energy of the continuum shell, one can model various structural transformations possible in viral capsids.