modeling virus capsids using tiling theory
DESCRIPTION
Aziza Jefferson Department of Mathematics Rutgers University Advisor: Professor Stanley Dunn. Modeling Virus Capsids using Tiling Theory. How do viruses effect us?. Several viruses that effect humans are Rhinoviruses (common cold) Orthomyxoviridae (Influenza) Rhabdoviridae (Rabies) - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Modeling Virus Capsids using Tiling Theory](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568159f0550346895dc73970/html5/thumbnails/1.jpg)
Modeling Virus Capsids using Tiling Theory
Aziza JeffersonDepartment of Mathematics
Rutgers University
Advisor:Professor Stanley Dunn
![Page 2: Modeling Virus Capsids using Tiling Theory](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568159f0550346895dc73970/html5/thumbnails/2.jpg)
How do viruses effect us?
Several viruses that effect humans are
● Rhinoviruses (common cold)
● Orthomyxoviridae (Influenza)
● Rhabdoviridae (Rabies)
● Hepadnaviridae (Hepatitis B)
● Flaviviridae (Yellow Fever)
![Page 3: Modeling Virus Capsids using Tiling Theory](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568159f0550346895dc73970/html5/thumbnails/3.jpg)
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
![Page 4: Modeling Virus Capsids using Tiling Theory](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568159f0550346895dc73970/html5/thumbnails/4.jpg)
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
![Page 5: Modeling Virus Capsids using Tiling Theory](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568159f0550346895dc73970/html5/thumbnails/5.jpg)
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
![Page 6: Modeling Virus Capsids using Tiling Theory](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568159f0550346895dc73970/html5/thumbnails/6.jpg)
![Page 7: Modeling Virus Capsids using Tiling Theory](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568159f0550346895dc73970/html5/thumbnails/7.jpg)
![Page 8: Modeling Virus Capsids using Tiling Theory](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568159f0550346895dc73970/html5/thumbnails/8.jpg)
![Page 9: Modeling Virus Capsids using Tiling Theory](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568159f0550346895dc73970/html5/thumbnails/9.jpg)
![Page 10: Modeling Virus Capsids using Tiling Theory](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568159f0550346895dc73970/html5/thumbnails/10.jpg)
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
![Page 11: Modeling Virus Capsids using Tiling Theory](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568159f0550346895dc73970/html5/thumbnails/11.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
![Page 12: Modeling Virus Capsids using Tiling Theory](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568159f0550346895dc73970/html5/thumbnails/12.jpg)
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
![Page 13: Modeling Virus Capsids using Tiling Theory](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568159f0550346895dc73970/html5/thumbnails/13.jpg)
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
![Page 14: Modeling Virus Capsids using Tiling Theory](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568159f0550346895dc73970/html5/thumbnails/14.jpg)
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
![Page 15: Modeling Virus Capsids using Tiling Theory](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568159f0550346895dc73970/html5/thumbnails/15.jpg)
Twarock 2004
● Looked at tubular shaped capsids the family of Papovaviridae
● Compared predicted results with experimental results
● Predicted locations and orientations of the pentamers
![Page 16: Modeling Virus Capsids using Tiling Theory](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568159f0550346895dc73970/html5/thumbnails/16.jpg)
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
![Page 17: Modeling Virus Capsids using Tiling Theory](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568159f0550346895dc73970/html5/thumbnails/17.jpg)
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
![Page 18: Modeling Virus Capsids using Tiling Theory](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568159f0550346895dc73970/html5/thumbnails/18.jpg)
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
![Page 19: Modeling Virus Capsids using Tiling Theory](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568159f0550346895dc73970/html5/thumbnails/19.jpg)
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