Modeling Expanding Viral Capsids

• Joseph Yarbrough, Mechanical Engineering, University of Delaware

• John Jungck, Department of Mathematical Sciences and Department of Biological Sciences, University of Delaware

Viruses often have protein shells known as viral capsids which protect the RNA or DNA found inside. Capsids with icosahedral (20-sided polyhedron) symmetry have been observed expanding and collapsing in a breathing-like motion (Lata et al., 2000; Fang et al., 2022) under certain environmental conditions in order to release their genetic material, and these have been coined as “expandohedra” (Kovacs et al., 2004). Developing macroscopic models for these microscopic organisms is a great way to better understand their function and later reapply these models to concepts beyond virology. What is the best way to model a biotic structure using only abiotic materials while still remaining true to the structure’s nature? Our study is focusing on a particular expandohedron – the icosidodecahedron – which is common among icosahedral capsids. Several different techniques with various materials were applied including origami, kirigami, magnets, and simple mechanics. Models that could demonstrate both the structure and function of the expanding icosidodecahedron were preferred. A jitterbug model, an expanding polyhedron connected by hinges, proved to be the most helpful in illustrating dynamics, while origami and magnets were able to appropriately demonstrate the static forms. The concepts that went into the construction of this jitterbug model could be applied to shapes other than the icosidodecahedron in order to demonstrate the nature of more complex viral capsids. Future models can be made from different materials for better durability and automated to represent the breathing motion previously observed. Better understanding the expansion and collapse of these capsids has immediate implications for the field of virology and medicine as a whole. The tensegrity mechanics of these structures could further be applied to architecture, prosthetics, and disaster relief.