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Department of Mathematical Sciences

Applications of Group Theory to Mathematical Biology

This one-day workshop has explored the application of mathematical physics techniques to the study of biological systems, in particular, viruses. The workshop, sponsored by the Mathematical and Theoretical Physics Group of the Institute of Physics, was organised by Anne Taormina (Durham) and Reidun Twarock (York) at Collingwood College, Durham, to celebrate the involvement of the Department of Mathematical Sciences in the newly established Durham Biophysical Sciences Institute, as well as the launch of a new MSc in Biomathematics, that is scheduled to start in October 2009.

The scientific programme focussed on virus dynamics and assembly, and attracted around 25 researchers, mainly from York and Durham. The speakers contributed to the interdisciplinary atmosphere of the meeting, as we heard talks from two virologists, three biophysicists and a theoretical particle physicist.The opening talk, by Peter Stockley from the Astbury Centre for Structural Molecular Biology at Leeds University, gave us some insights of the crucial role played by RNA in the assembly of some viral capsids, such as the bacteriophage MS2. He emphasized the interplay between virologists and mathematicians when it comes to model such assemblies. An interesting paper is `The Three-dimensional Structure of Genomic RNA in Bacteriophage MS2: Implications for Assembly', by K. Toropova, G. Basnak, R. Twarock, P.G. Stockley and N. Ranson, J. of Mol. Biol., Volume 375 (2008) 824-836.

The second talk, by Kasper Peeters, from the Department of Mathematical Sciences at Durham, described a top-down approach to viral capsid vibrations, which highlights intriguing patterns of vibrational modes in Caspar-Klug viruses. Namely, the occurrence in all capsids studied, of a very low-frequency plateau of 24 non trivial modes, whose presence is rooted in the group theory of the icosahedron and its dual, the dodecahedron. The relevant papers are `The twenty-four near-instabilities of Caspar-Klug viruses', by F. Englert, K. Peeters and A. Taormina, Phys. Rev. E 78 (2008) 031908, arXiv:0804.4275 and `Group theory of icosahedral virus capsids: a dynamical top-down approach', by K. Peeters and A. Taormina, J. of Theor. Biol. (to appear),arXiv:0806.1029.

The third talk was a nice complementary account of virus dynamics, this time from an all-atom perspective. Eric Dykeman, from the York Centre for Complex Systems, explained how the simulations provide insights in the movements of atoms in different regions of the capsid. For instance, the atoms around the 5-fold and the 3-fold axes have small relative displacements, while the beta sheet body shows gliding motion. See `Low frequency mechanical modes of viral capsids: an atomistic approach', by E. Dykeman and O. Sankey, Phys Rev Lett. 100(2)(2008) 028101.

In the fourth talk, by Paul Yeo, from the Department of Biological and Biomedical Sciences, we discovered the interests of the small virology group in Durham, centred on structural studies of the nucleocapsids of the Respiratory Syncytial Virus (RSV) which causes severe affections in children under 6 months of age, as well as on the interaction of RSV with the cytoskeleton and lipid rafts.

Tom McLeish, from the Physics Department in Durham, talked us through physical mechanisms by which proteins could use intramolecular dynamics to communicate signals across large molecular distances. Coarse-grained models are used for the calculation of vibrational modes contributing to allostery in proteins. See `Coarse-Grained Model of Entropic Allostery', Phys. Rev. Lett., 93, (2004)098104,`Dynamic allostery of protein alpha helical coiled-coils', J. R. Soc. Interface, 3, (2005)125-138, `Coupling of Global and Local Vibrational Modes in Dynamic Allostery of Proteins',”, Biophys. J., 91, (2006)2055-2062, all by R.J. Hawkins and T.C.B.McLeish.

Last but not least, Ard Louis from the Rudolph Peierls Centre for Theoretical Physics in Oxford, showed how theoretical and computer simulation techniques were used to study the statistical mechanics of a wide variety of biological and soft matter systems, in particular the self-assembly of viruses and DNA nanostructures. See for instance `Minimal models of DNA and the self-assembly of DNA nanostructures', by T.E. Ouldridge, I. G. Johnston and A. Louis, arXiv:0807.3280.

The audience was composed of established researchers as well as postdocs, graduate students and even Mathematics undergraduates.