Modeling Virus Capsids using Tiling Theory Aziza Jefferson Department of Mathematics Rutgers...
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Transcript of Modeling Virus Capsids using Tiling Theory Aziza Jefferson Department of Mathematics Rutgers...
Modeling Virus Capsids using Tiling Theory
Aziza JeffersonDepartment of Mathematics
Rutgers University
Advisor:Professor Stanley Dunn
How do viruses effect us?
Several viruses that effect humans are
● Rhinoviruses (common cold)
● Orthomyxoviridae (Influenza)
● Rhabdoviridae (Rabies)
● Hepadnaviridae (Hepatitis B)
● Flaviviridae (Yellow Fever)
Virus Structure
● A simple virus contains nucleic acid and a capsid
● The nucleic acid is normally RNA or DNA
● The capsid is made up of proteins.
http://www.pinkmonkey.com/studyguides/subjects/biology-edited/chap14/b1400001.asp
Virus Structure
Other viruses such as the HIV virus have a more complex structure and may include
●Virus membrane
●Shell membrane
●Reverse transcriptase
http://www.schoolscience.co.uk/content/4/biology/abpi/immune/immune10.htm
Importance of the Capsid
● The virus is fragile inside of the capsid
● The capsid introduces the virus to its host cell
● Once the structure is known anti-viral medications to penetrate the capsid can be developed.
http://www.microbiology.wustl.edu/sindbis/sin_genes
Capsid structure● In a simple virus the
capsid is created from a tiling of one type of protein
● Because of the size of a virus, the nucleic acid can only code for several proteins maximum
● The capsid can contain one or two layers of proteins
http://pathmicro.med.sc.edu/int6.jpg
Theoretical Problem
● We need to know all possible configurations of the capsid in order to design effective anti-viral therapy.
● Experimental evidence alone can not effectively give us every possible capsid structure
● We need a mathematical theory that will allow us to predict the number and types of capsids for each virus
Background
Several people have examined the virus capsid and developed a mathematical theory from experimental findings
● 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, R. "A tiling approach to virus capsid assembly explaining a structural puzzle in virology." Journal of Theoretical Biology226 (2004): 477-482.
● Twarock, R. "Mathematical models for tubular structures in the family of Papovaviridae." Bulletin of Mathematical Biology (2004): 1-15
Caspar-Klug Theory● Studied simple viruses
with Icosahedral shaped capsids
● Used triangulation to predict the shape and position of proteins in the capsid
● T=Pf 2
● P=h2+hk+k2
http://www.tulane.edu/~dmsander/WWW/335/335Structure.html
Twarock 2004
● Relaxed the assumption of triangular shaped subunits of proteins
● Re-evaluated the family of Icosahedral shaped capsids
● Uses tiling theory to determine the structure of the capsid
Twarock 2004
● Looked at tubular shaped capsids the family of Papovaviridae
● Compared predicted results with experimental results
● Predicted locations and orientations of the pentamers
Tiling Theory
● Tilings- tessellations in terms of a set of basic building blocks
● Decorations- Location of protein subunits on tiles
● Plane tiling(TT)- countable family of closed sets which cover the plane without gaps or overlaps
● Simply connected- tile does not enclose any holes
● Topological disk- bounded, connected and simply connected set
● Patch- finite number of tiles of the tiling such that their union is a topological disk
● Incident- the relation of a tile to each of its edges or vertices and also of an edge to each of its endpoints
Definitions
Tiling Theory
● Well-behaved tiles, tilings- each tile is a closed topological disk
● Monohedral tilings- every tile in tiling T is congruent to one fixed set T
● Prototile of T- the set T
The number of viruses being discovered is increasing at a faster rate then our ability to develop anti-viral therapies. What we do not know is if these theories of virus capsid structure apply to or are made up of newer viruses such as the emerging viruses:●E. coli O157:H7 disease●Cryptosporidiosis ●Human Immunodeficiency Virus●Ebola
Motivation
This Summer...
● Identify a emerging or re-merging virus which crystallographic information about its structure exists
● Gain a better understanding of the underlying assumptions of the virus capsid tile theories and see if the current theories apply to this target virus
● Generalize the theory as appropriate