virus-examples

virus-examples - (2003) Subdivision Surface Approximation...

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Icosahedral Virus Structure CCMV Speir, et al. Capsids self-assemble from multiple copies of similar or identical protein subunits http://en.wikipedia.org/wiki/Icosahedron 3 2 5 5 2 3 5 2 3 5 2 3 Spherical capsids assemble with symmetries of an icosahedron
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AFM nanoindentation of Viral capsids pH 6 pH 5 ~3.5 nm ~20 nm Loading Unloading Z Indentation Z
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The Caspar-Klug Construction Nguyen, et al. Form a closed shell by aligning an icosahedron template onto a hexahedral sheet of “capsomers” Triangulation number: (3,1) T =13
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“Buckling” of thin shells with disclinations 2-D thin shell model Add/remove a slice from hexagonal sheet stretching needed to keep it flat. Buckling may alleviate stretching. Stabilitiy of planar sheet controlled by Föppl-von Kármán number: Buckled disclinations implicated in determining the “facetedness” of capsids Seung & Nelson, Phys. Rev. A (1988) 2-D Young’s modulus bending modulus 5-fold disclination Lidmar, Mirny, & Nelson, Phys. Rev. E
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Unformatted text preview: (2003) Subdivision Surface Approximation Limit of a sequence of refinements Computer Graphics Shell Mechanics C 1 Subdivision finite elements FEM Control mesh Smooth computational surface (crucial for membrane curvatures) Infinite refinement Control mesh Limit surface Subdivision Surfaces in Character Animation Pixar Animation Studios Offline limit analysis basis functions for control vertices refinement Finite Element Approximation Surface defined by subdivision basis functions (splines) Minimize bending energy (Rayleigh-Ritz) Nonlinear equations Pentons are Foci of Elastic Stress Stretching Energy Bending Energy Maturation of Bacteriophage HK97 Expansion from subunits conformational changes leads to final stable mature capsid Chainmail in HII Different phases during HK97 maturation (Wikoff et. al. 2006) Elastic Shells with Pre-sheared Hexons Hexon skewing in PII: Minimizes aspherity, energy Makes penton assembly more favorable (Gertsman, et. al. 2009)...
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virus-examples - (2003) Subdivision Surface Approximation...

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