Symmetry Properties of Icosahedral Viral Capsids: Raman Spectra

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Symmetry Properties of Icosahedral Viral
CapsidsRaman Spectra
Maia Angelova School of Informatics School
Research Conference 2004
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• Motivation
• new area of research
• mathematical biology
• introduced to the idea in January 2004
• R. Twarock, City University
• contribution to Caspar-Klug theory for prediction
  of formation of viral capsids
• fullerenes and carbon onions
• vibrations of molecules and Raman spectra

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Structure of Viruses

• all viruses have genetic material (DNA or RNA)
• all viruses have rigid protein shell that
  surrounds genetic material CAPSIDS
• all capsids are made of smaller protein subunits
  CAPSOMERS
• some viruses are made of smaller protein
  subunits ENVELOPE
• complete infective virus particle - VIRION

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• Viral Capsids
• The viral capsid protects the viral genome of
  single- or double-stranded RNA or DNA. The shape
  of the viral capsids dictates the shape of
  bacterial viruses
• Three types of bacterial viruses based on shape
  of the viral capsids
• Helical viruses
• Icosahedral viruses
• Complex Viruses

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• Icosahedral Viral Capsids
• Capsid proteins assemble into triangle
• Triangle assemble around genetic material
• Round capsid that has 20 triangular faces
  (icosahedron)
• Has antenna- like fibers that meditate
  attachement

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• Some examples
• polyoma virus (cervical cancer in women)
• foot-and-mouth virus
• HIV virus
• TMV virus

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Icosahedron

• 20 identical equilateral triangles
• Each triangular face is made up of three
  identical shapes, capsid contains 60 subunits,
  the five subunits around each vertex are arranged
  in 5-fold symmetry
• Large icosahedral capsid consists of more than 60
  subunits, some of triangular faces are made up of
  4 subunits

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Structure of a subunit in the capsid of
foot-and-mouth disease virus, Each subunit is
made up of four proteins VP1, VP2, VP3,
VP4 (from L. Stannard)
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• Caspar-Klug theory (1962)
• theoretical basis for the structure of isometric
  viruses
• concept of identical elements on
  quasi-equivalent environments
• possible polyhedra are defined in structure
  units
• icosahedron 20 triangular faces 20T structure
  units where T is the triangulation number
• P1,3, 7, 13, 19, 21, 31,..,
• f is an integer
• new theory based on tesselation, that
  accomodates Caspar-Klug theory and explains
  viral structures that Caspar-Klug theory cannot
  explain.

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Fullerene
Truncated Icosahedron 20 hexagons and 12
pentagons,
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Symmetry Group of the Icosahedron I E, 12 C5,
12C5², 20 C3, 15 C2- group of 60 elements
combined in 5 classes 5 irreducible
representations A degeneracy 1 T1 degeneracy
3 T2 degeneracy 3 G degeneracy 4 H degeneracy 5
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Raman Spectroscopy of Viruses

• Raman spectra supplies information about the
  energies of molecular normal modes of vibration.
• serves as an effective structural probe of
  viruses since early 1970
• allows to gain insights into the virus structure
  and viral assembly pathways
• detailed orientation of protein side chains and
  nucleotide bases in the supramolecular virion
• the nature of hydrogen-bonding interactions

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?vib 2A(R) 3T1(IR) 4T2(ia) 6G(ia) 8H(R)
R Raman active vibrations 2 bands A, 8 bands H
IR Infrared Active vibrations T1 ia Inactive
vibrations T2, G A x A A T1 x T1 A T1
H T2 x T2 A T2 H G x G A T1 T2 G
H H x H A T1 T2 G 2H Group-subgroup
chains SO(3) ? I
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• Application to Raman spectroscopy of icosahedral
  viruses
• First Step
• Classification of the lines
• Selection rules
• Transformation properties of the normal modes
• Symmetry and transformation properties of
  functions and their derivatives at the vertices
  of the icosahedron and along the symmetry axes
  C2, C3 and C5

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• Next Step Building a Model
• classical force-constant model
• proteins as points of mass
• determine the force constants

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Conclusion and Discussion

• interesting problem
• initially can be solved as a simple model
• model can help to confirm known viral structures
• model can help to identify unknown viral
  structures
• model can be given to final year students for
  project