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

1
Testing Models of Virus Capsid Structure for
Emerging and Re-Emerging Viruses

• Aziza Jefferson
• Department of Mathematics
• Rutgers University

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.

11
(No Transcript)
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?