Research interests and recent research highlights

My research in Mathematical Biology focuses on the development and application of novel analytical and computational tools to address open problems in virology. I have pioneered the area of Mathematical Virology, which uses group, graph and tiling theory in combination with biophysics, bioinformatics and computational chemistry to gain new insights into virus structure, assembly and evolution. The new mathematical approaches, originally developed with applications in virology in mind, have found applications also in other areas of science such as carbon chemistry, quasicrystals and nanotechnology. This theoretical work moreover underpins a recent patent for a novel anti-viral strategy, that we have filed in collaboration with experimental collaborators at the universities of Leeds and Helsinki. Our recent article in Nature Communications identifies packaging signals in Human Parechovirus 1.

A number of research highlights are listed below.

A new geometric principle underlying virus architecture: New group theoretical approaches for the modelling of virus structure

Virus structure is more constrained than previously appreciated. Using affine extensions of non-crystallographic Coxeter groups and related tilings, we have been able to show that the surface lattices of Caspar-Klug theory form a subset of a much wider set of structural constraints on virus architecture than previously appreciated.

This novel understanding has opened up new opportunities of modelling the structural transitions in viruses important for infection. Two movies illustrating the expansion of ERAV virus are shown here:

Our novel mathematical techniques have also made an impact also outside of the context of virology for which they had originally been developed. For example, we have been able to demonstrate that similar mathematical principles also account for the organisation of nested carbon cages called carbon onions.

This work was chosen as a cover article by Acta Crystallographica A and was featured as a highlight by Nature Physics (see "Know your onions", Vol. 10, p.244, 2014).

A paradigm shift in our understanding of virus assembly: viral genomes are more than passive passengers.

The formation of a protein container (viral (nucleo)capsid) that encapsulates and hence provides protection for the viral genome is an essentail stage of a viral life cycle. We have demonstrated that viral genomes can play important cooperative roles in this process, and we have developed a new modelling framework for virus assembly as a co-assembly process in which capsid assembly and genome packaging occur in tandem. This work has revealed how single-stranded RNA viruses overcome the viral equivalent of a Levinthal's Paradox, ensuring efficient navigation through the vast network of possible assembly intermediates on the way to a fully formed capsid. It also explains how such viruses ensure specific packaging of their genomes against a backdrop of cellular RNAs. This work, which has recently been pulished in PNAS, combines a Gillespie-type algorithm for the modelling of the assembly process with the mathematical concept of Hamiltonian path, which is the key to understanding the mechanism underpinning complexity reduction in this system. We have also used this approach to demonstrate how drug action can reduce the yield of infectious particleby triggering misincapsidation of cellular RNAs, and how it can delay assembly, hence enabling the immune defenses to better cope with the infection:

The discovery of packaging signal mediated assembly: the foundation of a novel anti-viral strategy.

Our assembly models demonstrate that specific interactions between viral genomes and capsid proteins are essential for a large number of viruses (in particular single-stranded RNA viruses, a major family containing important human patogens), to ensure efficient capsid assembly and specific genome packaging. For decades, the existence of such multiple dispersed contacts between viral RNA and capsid protein had been overlooked, perhaps because of their low sequence identity, and only incidences of single RNA motifs with high affinity for capsid protein, called packaging signals, were known. We have developed a new modelling approach that has allowed us to identify such multiple dispersed packaging signals based on a combination of bioinformatics and graph theory using SELEX data from the Stockley Lab in Leeds. The figure shows our predictions for MS2:

This approach has resulted in the discovery of packaging signals in a number of viruses, including Hepatitis B and C, Human Parecho virus and HIV, as well as a number of plant viruses, and we have filed a patent with our experimental collaborators in Leeds and Helsinki on a novel anti-viral strategy targeting such packaging signals.

Bionanocontainers: generalisations of Viral Tiling theory

Viral Tiling theory had been introduced by us to solve a long-standing problem concerning the surface structures of the cancer-causing papilloma viruses. These viruses fall out of the standard classification scheme introduced by Caspar and Klug, because their surface structures are formed from more than 12 pentagonal protein clusters (pentamers), and they can therefore not be modelled via the hexagonal surface lattices used to define T-numbers in quasiequivalence theory. A similar problem occurs in the design of self-assembling protein nanoparticles (SAPNs) with applications in vaccine design, that form surface structures with 3- and 5-fold clusters.

We have developed a new mathematical theory for the classification of such surface structures, and used it in collaboration with the Burkhard Lab at Connecticut University to identify the surface structures of these nanoparticles.

This research programme is highly interdisciplinary, and members of the team have expertise spanning from mathematics, computational biophysics and bioinformatics to computational chemistry. We are very grateful for funding from the EPSRC, BBSRC, the Leverhulme Trust, the Wellcome Trust, as well as the University of York for patent exemplification.

Our work has been featured as a research highlight by

© Reidun Twarock