Viral Tiling Theory : a promising insight in the structure and assembly of viral capsids.

Lead Research Organisation: Durham University
Department Name: Mathematical Sciences

Abstract

Viruses are fascinating tiny machines. They are simple organic systems - consisting of a very compact genome and a protective protein shell - which hijack host cells ten times their size in animals and plants to reproduce, and which have the potential to kill.During the replication cycle of a virus, the genome, i.e. the nucleic acid which encodes the genetic information of the virus, is released into a host cell. It is then copied, and encapsulated in new viral shells. The correct assembly of the latter is a crucial factor in the infectiousness of the virus. Scientists worldwide are eager to study the structure of viral shells and unravel the mechanisms of their assembly in order to stop the virus spreading and thereby provide new therapeutic strategies in the battle against diseases. More than 3600 species of viruses exist and their classification provides a first attempt at understanding them. It also yields some clues on the structure of their protein shells. The existing mathematical models cannot account for important classes of viruses, including families of cancer-causing viruses whose study is of prime importance for the health sector. These viruses have spherical protein shells with icosahedral symmetry. For instance, some shells have the shape of a soccer ball. Rotating the ball by 72 degrees about one of six privileged axes gives a configuration of the ball which is indistinguishable from the original one: the soccer ball is said to have six 5-fold symmetry axes. It also has ten 3-fold and fifteen 2-fold symmetry axes. These thirty-one symmetry axes are present in all solids with icosahedral symmetry. Symmetry is a powerful tool in solving problems in many areas of Science. A very promising approach to solve the virus classification puzzle that may provide a brand new and attractive perspective on viral structure is the two-year old Viral Tiling Theory (VTT). The symmetry of the shell provides a way of covering it with a set of tiles. These tilings describe interactions between the protein subunits which are the fabric of the shell. The positions of both the protein subunits and of the bonds between them can be read off from the tilings. Better still, the underlying mathematics provides a plausible explanation of why only certain types of clusters of protein subunits form icosahedral shells. Furthermore, symmetry considerations predict the existence of viral shell structures that have not been found so far in nature. Viral Tiling Theory is also a powerful tool in the exploration of tubular structures that may arise as accidents during assembly. These tubular viruses are not infectious. VTT will be used to model the simultaneous formation of spherical and tubular viruses. This will allow the prediction of the relative concentrations of infectious versus non-infectious particles during assembly, and provide a means of forcing the assembly of the non-infectious tubular species. The project will also study how the genome is inserted and folded in the protein shell. Such analyses may provide clues on how to stop an infection by disturbing the genome packaging and may lead to an efficient packaging of non-native nucleic acids in viral shells for gene therapy.

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