Testing Models of Virus Capsid Testing Models of Virus Capsid Structure for Emerging and Structure for Emerging and

Re-Emerging VirusesRe-Emerging Viruses

Aziza JeffersonAziza JeffersonDepartment of MathematicsDepartment of Mathematics

Rutgers UniversityRutgers University

Advisor:Professor Stanley Dunn

Virus Structure and FunctionVirus Structure and Function

● Simple viruses include Simple viruses include nucleic acid and a nucleic acid and a capsidcapsid

● The capsid is made up The capsid is made up of proteinsof proteins

● The capsid introduces The capsid introduces the virus to its host the virus to its host cellcell

Problem: Problem: Determining Capsid StructureDetermining Capsid Structure

● Currently the most widely used theory on virus Currently the most widely used theory on virus capsid structure comes from Caspar and Klug.capsid structure comes from Caspar and Klug.

● Twarock has since modified Caspar-Klug theory Twarock has since modified Caspar-Klug theory by taking a Tiling theory approach to the by taking a Tiling theory approach to the problem. problem.

● We would like to determine if emerging or re-We would like to determine if emerging or re-emerging viruses follow these theories.emerging viruses follow these theories.

Caspar-Klug TheoryCaspar-Klug Theory

● Caspar and Klug developed a Caspar and Klug developed a theory and published it in theory and published it in 19621962

● This theory dealt only with This theory dealt only with simple virusessimple viruses

● They developed a They developed a triangulation over an triangulation over an icosahedral shape that defined icosahedral shape that defined the capsid of simple viruses 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

Twarock's TheoryTwarock's Theory

● Twarock refined the Caspar-Twarock refined the Caspar-Klug theory using tilling theory Klug theory using tilling theory

● She stated that Caspar-Klug did She stated that Caspar-Klug did not deal with common pentamer not deal with common pentamer instead of hexamer capsids instead of hexamer capsids such as in the Papovavirdae such as in the Papovavirdae which also has a common which also has a common tubular shape instead of tubular shape instead of icosahedral shapeicosahedral shape

Twarock, R. "Mathematical models for tubular structures in the family of Papovaviridae." _Bulletin of Mathematical Biology_ (2004): 1-15

Selection Criteria for Test VirusesSelection Criteria for Test Viruses

● Emerging or re-emerging virus in resent Emerging or re-emerging virus in resent yearsyears

● A simple virusA simple virus● Experimental data such as crystallographic Experimental data such as crystallographic

analysis available analysis available

● We chose

What is Ebola?What is Ebola?

● There are 4 strains of There are 4 strains of Ebola the first two Ebola the first two were discovered in were discovered in 1976 1976

● The strains have a The strains have a 50%-90% fatality rate50%-90% fatality rate

● Currently the only Currently the only effective way to deal effective way to deal with Ebola is isolationwith Ebola is isolation Ebola Virus

What is Ebola?What is Ebola?

● Ebola is a simple virus Ebola is a simple virus with RNA and a with RNA and a capsidcapsid

● Ebola is pleomorphic Ebola is pleomorphic in shape, it can be in shape, it can be found in a branched, found in a branched, circular, 6 or U shape circular, 6 or U shape or spheroidal shapeor spheroidal shape

● It belongs to the It belongs to the Filoviridae familyFiloviridae family

Caspar-Klug applied to EbolaCaspar-Klug applied to Ebola

● assume a branched shaped Ebola assume a branched shaped Ebola capsidcapsid

● Caspar-Klug Theory can not be Caspar-Klug Theory can not be applied for at least 2 reasonsapplied for at least 2 reasons

● One, Ebola is in a branched shape instead of a One, Ebola is in a branched shape instead of a spherical or icosahedral shapespherical or icosahedral shape

● Two, a main protein in the Ebola capsid, VP40, has Two, a main protein in the Ebola capsid, VP40, has an octamer shape instead of a hexamer shapean octamer shape instead of a hexamer shape

Tiling theory applied to EbolaTiling theory applied to Ebola

● Assume there exists a well-behaved octamer tillingAssume there exists a well-behaved octamer tilling● Assume Ebola is branched shapeAssume Ebola is branched shape● Since VP40 is octamer in shape and there exists an Since VP40 is octamer in shape and there exists an

octamer plane tiling, by Twarock, one can create a octamer plane tiling, by Twarock, one can create a tubular octamer tilling of the capsidtubular octamer tilling of the capsid

● However, since Ebola is branched shaped there However, since Ebola is branched shaped there must exist a section of the capsid which with one must exist a section of the capsid which with one cut will not unfold into a plane.cut will not unfold into a plane.

Tilling theory applied to EbolaTilling theory applied to Ebola

● Assume a well-behaved octamer tilling does not Assume a well-behaved octamer tilling does not exist exist

● Assume Ebola is branched shapedAssume Ebola is branched shaped● By Twarock's tiling theory we must produce a By Twarock's tiling theory we must produce a

plane tiling and since VP40 is octamer shape in plane tiling and since VP40 is octamer shape in shape, we would need an octamer tilingshape, we would need an octamer tiling

● Since an octamer tiling doesn't exist we can not Since an octamer tiling doesn't exist we can not apply tiling theoryapply tiling theory

Further QuestionsFurther Questions

● Do these theories hold for the other 4 shapes of Do these theories hold for the other 4 shapes of Ebola?Ebola?

● Can we modify these theories to encompass Can we modify these theories to encompass emerging viruses as well as existing viruses?emerging viruses as well as existing viruses?

● Does there exist a unified theory that explains the Does there exist a unified theory that explains the capsid structure for all viruses?capsid structure for all viruses?