Reidun Twarock

Twarock originally studied mathematical physics at the universities of Cologne and Bath. During her PhD at Technische Universität Clausthal she experimented with quantum mechanical models confined to the surface of a sphere.

In the early 2000s, while thinking about the Penrose tiling and different ways of dividing the surface of a sphere, Twarock created a model describing the exceptional structure of papovaviridae.{{cite journal | last=Twarock | first=R. | title=A tiling approach to virus capsid assembly explaining a structural puzzle in virology | journal=Journal of Theoretical Biology | publisher=Elsevier BV | volume=226 | issue=4 | year=2004 | issn=0022-5193 | doi=10.1016/j.jtbi.2003.10.006 | pages=477–482| pmid=14759653 | bibcode=2004JThBi.226..477T }} Almost all icosahedral viruses have proteins on their capsids arranged in clusters of five and six, with a structure permitting at most 12 clusters of five, but papovaviridae, including HPV, have 72 clusters of five{{cite journal | last1=Rayment | first1=I. | last2=Baker | first2=T. S. | last3=Caspar | first3=D. L. D. | last4=Murakami | first4=W. T. | title=Polyoma virus capsid structure at 22.5 Å resolution | journal=Nature | publisher=Springer Science and Business Media LLC | volume=295 | issue=5845 | year=1982 | issn=0028-0836 | doi=10.1038/295110a0 | pages=110–115| pmid=6276752 | pmc=4144041 | bibcode=1982Natur.295..110R }} This protein layout did not correspond to any spherical polyhedron known to mathematics.

After this, Twarock entered virology. The structure of the virus HK97 was exceptional too, not being modelled by any goldberg polyhedron. Mathematical virology had previously only studied the surfaces of virus, using models that were tilings of the 2-sphere; Twarock hoped to go further than this, to model the three-dimensional protein structure and interior of viruses where their genome is packaged.{{cite web |url=http://plus.maths.org/content/symmetry-approach-viruses |title=A symmetry approach to viruses |last=West |first=Mark |publisher=plus magazine |date=30 September 2007 |website=Plus Maths |accessdate=30 November 2014}}

It was known that, using rotations, virus protein patterns could be generated from a single shape by making copies of it and moving them around in ways that preserve the symmetry. Twarock added an outward translation to this generating process, which created a quite complex patterns of points in 3D space. These patterns turned out to accurately predict the shape and size of the proteins, as well as the structure of packaged genetic material, for many viruses including Nodaviridae.{{cite journal | last1=Keef | first1=T. | last2=Twarock | first2=R. | title=Affine extensions of the icosahedral group with applications to the three-dimensional organisation of simple viruses | journal=Journal of Mathematical Biology | publisher=Springer Science and Business Media LLC | volume=59 | issue=3 | date=1 November 2008 | issn=0303-6812 | doi=10.1007/s00285-008-0228-5 | pages=287–313| pmid=18979101 | s2cid=37042491 }}

The models turned out to be useful for studying the assembly of RNA viruses, which involves proteins binding to specific parts of the genome that end up in 3-dimensional locations{{cite journal | last1=Rolfsson | first1=Óttar | last2=Middleton | first2=Stefani | last3=Manfield | first3=Iain W. | last4=White | first4=Simon J. | last5=Fan | first5=Baochang | last6=Vaughan | first6=Robert | last7=Ranson | first7=Neil A. | last8=Dykeman | first8=Eric | last9=Twarock | first9=Reidun | last10=Ford | first10=James | last11=Cheng Kao | first11=C. | last12=Stockley | first12=Peter G. | title=Direct Evidence for Packaging Signal-Mediated Assembly of Bacteriophage MS2 | journal=Journal of Molecular Biology | publisher=Elsevier BV | volume=428 | issue=2 | year=2016 | issn=0022-2836 | doi=10.1016/j.jmb.2015.11.014 | pages=431–448| pmid=26608810 | pmc=4751978 }} that can be determined mathematically.Self-Assembly of Viral Capsids via a Hamiltonian Paths Approach: The Case of Bacteriophage MS2{{cite journal | last1=Twarock | first1=Reidun | last2=Valiunas | first2=Motiejus | last3=Zappa | first3=Emilio | title=Orbits of crystallographic embedding of non-crystallographic groups and applications to virology | journal=Acta Crystallographica Section A | publisher=International Union of Crystallography (IUCr) | volume=71 | issue=6 | date=22 September 2015 | issn=2053-2733 | doi=10.1107/s2053273315015326 | pages=569–582| pmid=26522406 | arxiv=1411.2115 | s2cid=36526939 | url=https://eprints.whiterose.ac.uk/98977/1/Orbits_Emilio.pdf }}{{cite journal | last1=Zappa | first1=Emilio | last2=Dykeman | first2=Eric C. | last3=Twarock | first3=Reidun | title=On the subgroup structure of the hyperoctahedral group in six dimensions | journal=Acta Crystallographica Section A | publisher=International Union of Crystallography (IUCr) | volume=70 | issue=5 | date=10 July 2014 | issn=2053-2733 | doi=10.1107/s2053273314007712 | pages=417–428| pmid=25176990 | pmc=4186354 | arxiv=1402.3136 }} More insights were gained using the "cut and project" method of generating penrose tilings. Her models can be thought of as squashed-down three dimensional pictures of the 6-demicubic honeycomb tiling, which is a six-dimensional version of the three-dimensional Tetrahedral-octahedral honeycomb. Different viruses are modelled by different subsets of the vertices of this lattice. The viruses appear to use these patterns because they are the most stable way of connecting multiple interacting layers that all have icosahedral symmetry.

Her work has applications to the study of nanomaterials.Know your onion, Vol 10, p. 244, April 2014

• She was awarded the 2018 IMA Gold Medal {{Cite web|url=https://ima.org.uk/10158/ima-gold-medal-2018-awarded-to-professor-reidun-twarock/|title=IMA Gold Medal 2018 awarded to Professor Reidun Twarock|date=14 August 2018|accessdate=5 January 2022}}

• Papillomaviridae
• Virus

{{Reflist}}

• {{cite web|url=https://pure.york.ac.uk/portal/en/researchers/reidun-twarock(a31ce7ec-b49a-4167-89b4-351a869839da).html|title=The York Research Database - Prof. Reidun Twarock|publisher=The University of York|access-date=2020-02-29}}
• {{cite web|url=https://ima.org.uk/12723/an-interview-with-reidun-twarock-fima/|title=An Interview with Reidun Twarock FIMA|publisher=Institute of Mathematics|date=October 12, 2019|access-date=2020-02-29}}
• {{cite web|url=https://www.youtube.com/watch?v=Qkp0w525n8s|title=Mathematics and the fight against viral infections - Professor Reidun Twarock|publisher=University of York|website=YouTube|date=February 10, 2016|access-date=2020-02-29}}
• {{cite web|url=https://www.gresham.ac.uk/lectures-and-events/geometry-a-new-weapon-in-the-fight-against-viruses|title=Geometry: A New Weapon in the Fight Against Viruses, Professor Reidun Twarock|publisher=Gresham College|date=May 20, 2015|access-date=2020-02-29}}
• {{cite web|url=https://www.youtube.com/watch?v=dsJCv1DOfto|title=LMS Popular Lecture Series 2008, Know your Enemy, Dr Reidun Twarock|publisher=London Mathematical Society|website=YouTube|date=May 15, 2014|access-date=2020-02-29}}
• {{cite web|url=https://www.youtube.com/watch?v=yHnHwTFKM_Q|title=Viruses under the Mathematical Microscope: Deciphering the Code of Viral Geometry|publisher=Cambridge University|website=YouTube|date=May 10, 2011|access-date=2020-02-29}}

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