Testing Models of Virus Capsid Structure for Emerging and Re-Emerging Viruses

1. Aziza Jefferson Department of Mathematics Rutgers University Testing Models of Virus Capsid Structure for Emerging and Re-Emerging Viruses Advisor: Professor Stanley Dunn

2. Virus Structure and Function • Simple viruses include nucleic acid and a capsid • The capsid is made up of proteins • The capsid introduces the virus to its host cell

3. Problem: Determining Capsid Structure • Currently the most widely used theory on virus capsid structure comes from Caspar and Klug. • Twarock has since modified Caspar-Klug theory by taking a Tiling theory approach to the problem. • We would like to determine if emerging or re-emerging viruses follow these theories.

4. Caspar-Klug Theory • Caspar and Klug developed a theory and published it in 1962 • This theory dealt only with simple viruses • They developed a triangulation over an icosahedral shape that defined the capsid of simple viruses Caspar, D.L.D., and A Klug. "Physical Principles in the Construction of Regular Viruses." _Cold Spring Harbor Symposia on Quantitative Biology_ 27 (1962): 1-24

5. Twarock's Theory • Twarock refined the Caspar-Klug theory using tilling theory • She stated that Caspar-Klug did not deal with common pentamer instead of hexamer capsids such as in the Papovavirdae which also has a common tubular shape instead of icosahedral shape Twarock, R. "Mathematical models for tubular structures in the family of Papovaviridae." _Bulletin of Mathematical Biology_ (2004): 1-15

6. Selection Criteria for Test Viruses • Emerging or re-emerging virus in resent years • A simple virus • Experimental data such as crystallographic analysis available • We chose

7. What is Ebola? • There are 4 strains of Ebola the first two were discovered in 1976 • The strains have a 50%-90% fatality rate • Currently the only effective way to deal with Ebola is isolation Ebola Virus

8. What is Ebola? • Ebola is a simple virus with RNA and a capsid • Ebola is pleomorphic in shape, it can be found in a branched, circular, 6 or U shape or spheroidal shape • It belongs to the Filoviridae family

9. Caspar-Klug applied to Ebola • assume a branched shaped Ebola capsid • Caspar-Klug Theory can not be applied for at least 2 reasons • One, Ebola is in a branched shape instead of a spherical or icosahedral shape • Two, a main protein in the Ebola capsid, VP40, has an octamer shape instead of a hexamer shape

10. Tiling theory applied to Ebola • Assume there exists a well-behaved octamer tilling • Assume Ebola is branched shape • Since VP40 is octamer in shape and there exists an octamer plane tiling, by Twarock, one can create a tubular octamer tilling of the capsid • However, since Ebola is branched shaped there must exist a section of the capsid which with one cut will not unfold into a plane.

12. Tilling theory applied to Ebola • Assume a well-behaved octamer tilling does not exist • Assume Ebola is branched shaped • By Twarock's tiling theory we must produce a plane tiling and since VP40 is octamer shape in shape, we would need an octamer tiling • Since an octamer tiling doesn't exist we can not apply tiling theory

13. Further Questions • Do these theories hold for the other 4 shapes of Ebola? • Can we modify these theories to encompass emerging viruses as well as existing viruses? • Does there exist a unified theory that explains the capsid structure for all viruses?