Briony Thomas, Adam Arstall and Motiejus Valiunas
Briony Thomas is an academic and designer working in the area of shape-based design, with a specialism in geometric structure. Her current practice explores cross-disciplinary concepts in structural/mechanical design and complex biological systems.
In collaboration with the Twarock group (University of York), and mathematicians Adam Arstall (University of Oxford) and Motiejus Valiunas (University of Cambridge), this project explored the mathematical and artistic complexities of virus structure . The work was made possible thanks to the generous support of the Centre for Chronic Diseases and Disorders (C2D2) and York Centre for Complex Systems Analysis (YCCSA).
The Caspar–Klug theory of virus structure represents viral capsids via icosahedrally symmetric surface lattices modelled by icosideltahedra. To represent and predict information about the capsid structure it is necessary to explore polyhedra related by extensions of icosahedral symmetry. Due to noncrystallographic properties of the icosahedral group these polyhedra are constructed through the projection of points from a cubic lattice in 6D (the minimal dimension where this construction is possible). The double shell of 'Pariacoto structure #1' is related to an orbit of a symmetry group of the 6D lattice. The 3D printed region that fits between the two shells shows the biological protein structure fitting within the nested polyhedra.
A large class of viruses undergo a maturation process that involves an expansion of the capsid. Many open questions remain about the way this process works. In the case of ERAV experimental observations show that although the native and the expanded states retain full icosahedral symmetry, it is more likely for the expansion pathway to be non-icosahedral. It is possible to model transition through expandable polyhedra. These polyhedra consist of rigid pentagonal faces connected by filaments that are able to rotate and translate. The filament contact points between adjacent pentamers lie across the 2-fold axes and hold the expanded particle together. 'ERAV Expansion #1' illustrates two stages of this expansions process for the ERAV virus.