More than 50 years ago, the Soviet theoretical physicist L. D. Landau expressed the idea that crystallization and phase transitions in matter can be considered as the appearance or disappearance of certain density waves, which are called critical. These waves generate interference patterns, which ultimately determine the structure of matter. In everyday life, we can also see interference, for example in soap bubbles or in a film of gasoline spread on the surface of water – this is exactly the bright rainbow coloring of the surface, which shimmers amazingly in the light. As scientists of the Faculty of Physics of the Southern Federal University have found out, only those viral shells that correspond to the simplest interference patterns possible on the sphere are realized in nature.

The assembly of protein viral shells from individual proteins or their complexes pre-assembled in solution is in many ways similar to the crystallization process. Using Landau's approach, the scientists explained why small viral shells are assembled from individual proteins, and medium–sized shells from their symmetrical groups (pentamers and hexamers). It also became clear why the sizes of protein shells assembled from pentamers and hexamers are limited.

"We have proposed a new phenomenological theory that describes the structures of both small and medium-sized viral shells with icosahedral symmetry. Within the framework of this theory, for the first time we consider individual proteins as extended structural units, in fact, taking into account their elongated chiral shape. We describe the self-assembly of viral shells as the condensation of a minimum number of density waves on a spherical surface. As we have shown, to describe the structural organization of small viral membranes, it is enough to set two critical density waves: the first wave determines the spatial position of individual protein molecules, and the second wave determines their orientation. Medium-sized viral shells, unlike small ones, always consist of pentamers and hexamers (called capsomers), which are initially assembled from individual proteins. Analyzing all known capsids of medium–sized viruses, we found that the positions of capsomers in such shells are described by combinations of a maximum of two critical density waves," said Sergey Roshal, project manager, Professor of the Department of Nanotechnology at the Faculty of Physics of the Southern Federal University.

Figure: Capsid organization and interference patterns. The device of the Picobirnavirus capsid (a) and the critical density wave (b), similar to its structure. The device of the microcystis phage capsid Mic1(c) and the corresponding interference pattern formed by two critical waves.

Thus, the proposed theory made it possible to identify common features of the device of all known existing small and medium-sized viral shells. It turned out that from the point of view of L. D. Landau's theory of crystallization, these shells are the simplest structures. Density waves on a sphere are described by well-known functions to physicists and mathematicians - spherical harmonics, and the simplicity of virus shells lies in the fact that the corresponding interference patterns are formed by harmonics characterized by a maximum of a pair of neighboring wave numbers. The principle of simplicity also made it possible to explain the restriction observed in nature on the maximum size of viral shells that self-assemble from pentamers and hexamers.

The authors of the study argue that studying the structural organization of viral capsids is important for the development of new antiviral strategies. Moreover, capsids that do not contain the viral genome have many promising applications as nanocontainers and, in particular, can be used in targeted drug delivery and for other bionanotechnology.

The results of the study, supported by a grant from the Russian Science Foundation (RNF), are published in the journal "Physical Chemistry Chemical Physics".