Multiscale Modeling of Virus Structure, Assembly, and Dynamics

  • Eric R. May
  • Karunesh Arora
  • Ranjan V. Mannige
  • Hung D. Nguyen
  • Charles L. BrooksIII
Chapter
Part of the Biological and Medical Physics, Biomedical Engineering book series (BIOMEDICAL)

Abstract

Viruses are traditionally considered as infectious agents that attack cells and cause illnesses like AIDS, Influenza, Hepatitis, etc. However, recent advances have illustrated the potential for viruses to play positive roles for human health, instead of causing disease [1, 2]. For example, viruses can be employed for a variety of biomedical and biotechnological applications, including gene therapy[3], drug delivery[4], tumor targeting[5], and medical imaging[6]. Therefore, it is important to understand quantitatively how viruses operate such that they can be engineered in a predictive manner for beneficial roles.

References

  1. 1.
    Uchida, M., Klem, M.T., Allen, M., Suci, P., Flenniken, M., Gillitzer, E., Varpness, Z., Liepold, L.O., Young, M., Douglas, T.: Biological containers: protein cages as multifunctional nanoplatforms. Adv. Mater. 19(8), 1025–1042 (2007)CrossRefGoogle Scholar
  2. 2.
    Maham, A., Tang, Z., Wu, H., Wang, J., Lin, Y.: Protein-based nanomedicine platforms for drug delivery. Small 5(15), 1706–1721 (2009)CrossRefGoogle Scholar
  3. 3.
    Miller, A.D.: Human gene therapy comes of age. Nature 357(6378), 455–460 (1992)ADSCrossRefGoogle Scholar
  4. 4.
    Douglas, T., Young, M.: Host-guest encapsulation of materials by assembled virus protein cages. Nature 393(6681), 152–155 (1998)ADSCrossRefGoogle Scholar
  5. 5.
    Destito, G., Yeh, R., Rae, C.S., Finn, M.G., Manchester, M.: Folic acid-mediated targeting of cowpea mosaic virus particles to tumor cells. Chem. Biol. 14(10), 1152–1162 (2007)CrossRefGoogle Scholar
  6. 6.
    Gupta, S.S., Raja, K.S., Kaltgrad, E., Strable, E., Finn, M.G.: Virus-glycopolymer conjugates by copper(i) catalysis of atom transfer radical polymerization and azide-alkyne cycloaddition. Chem. Commun. (Camb.) (34), 4315–4317 (2005)Google Scholar
  7. 7.
    Smith, D.E., Tans, S.J., Smith, S.B., Grimes, S., Anderson, D.L., Bustamante, C.: The bacteriophage straight phi29 portal motor can package dna against a large internal force. Nature 413(6857), 748–752 (2001)ADSCrossRefGoogle Scholar
  8. 8.
    Ivanovska, I., Wuite, G., Jnsson, B., Evilevitch, A.: Internal dna pressure modifies stability of wt phage. Proc. Natl. Acad. Sci. USA 104(23), 9603–9608 (2007)ADSCrossRefGoogle Scholar
  9. 9.
    Roos, W.H., Bruinsma, R., Wuite, G.J.L.: Physical virology. Nature Phys. 6(10), 733–743 (2010)ADSCrossRefGoogle Scholar
  10. 10.
    Bancroft, J.B., Hills, G.J., Markham, R.: A study of the self-assembly process in a small spherical virus. Formation of organized structures from protein subunits in vitro. Virology 31(2), 354–379 (1967)Google Scholar
  11. 11.
    Rose, R.C., Bonnez, W., Reichman, R.C., Garcea, R.L.: Expression of human papillomavirus type l1 (HPV-l1) protein in insect cells: in vivo and in vitro assembly of viruslike particles. J. Virol. 67(4), 1936–1944 (1993)Google Scholar
  12. 12.
    Conway, J.F., Duda, R.L., Cheng, N., Hendrix, R.W., Steven, A.C.: Proteolytic and conformational control of virus capsid maturation: the bacteriophage hk97 system. J. Mol. Biol. 253(1), 86–99 (1995)CrossRefGoogle Scholar
  13. 13.
    Lata, R., Conway, J.F., Cheng, N., Duda, R.L., Hendrix, R.W., Wikoff, W.R., Johnson, J.E., Tsuruta, H., Steven, A.C.: Maturation dynamics of a viral capsid: visualization of transitional intermediate states. Cell 100(2), 253–263 (2000)CrossRefGoogle Scholar
  14. 14.
    Adolph, K.W., Butler, P.J.: Studies on the assembly of a spherical plant virus. I. States of aggregation of the isolated protein. J. Mol. Biol. 88(2), 327–41 (1974)Google Scholar
  15. 15.
    Rossmann, M.G.: Constraints on the assembly of spherical virus particles. Virology 134(1), 1–11 (1984)CrossRefGoogle Scholar
  16. 16.
    Ceres, P., Zlotnick, A.: Weak protein–protein interactions are sufficient to drive assembly of hepatitis b virus capsids. Biochemistry 41, 11525–11531 (2002)CrossRefGoogle Scholar
  17. 17.
    Johnson, J.M., Willits, D.A., Young, M.J., Zlotnick, A.: Interaction with capsid protein alters rna structure and the pathway for in vitro assembly of cowpea chlorotic mottle virus. J. Mol. Biol. 335(2), 455–64 (2004)CrossRefGoogle Scholar
  18. 18.
    Schwartz, R., Shor, P.W., Prevelige, P.E., Berger, B.: Local rules simulation of the kinetics of virus capsid self-assembly. Biophys. J. 75, 2626–2636 (1998)CrossRefGoogle Scholar
  19. 19.
    Zlotnick, A., Johnson, J.M., Wingfield, P.W., Stahl, S.J., Endres, D.: A theoretical model successfully identifies features of hepatitis b virus capsid assembly. Biochemistry 38(44), 14644–14652 (1999)CrossRefGoogle Scholar
  20. 20.
    Bruinsma, R.F., Gelbart, W.M., Reguera, D., Rudnick, J., Zandi, R.: Viral self-assembly as a thermodynamic process. Phys. Rev. Lett. 90(24), 248101 (2003)ADSCrossRefGoogle Scholar
  21. 21.
    Arkhipov, A., Freddolino, P.L., Schulten, K.: Stability and dynamics of virus capsids described by coarse-grained modeling. Structure 14(12), 1767–1777 (2006)CrossRefGoogle Scholar
  22. 22.
    Zink, M., Grubmller, H.: Mechanical properties of the icosahedral shell of southern bean mosaic virus: a molecular dynamics study. Biophys. J. 96(4), 1350–1363 (2009)ADSCrossRefGoogle Scholar
  23. 23.
    Caspar, D.L.D.: Structure of bushy stunt virus. Nature 177(4506), 476–477 (1956)ADSCrossRefGoogle Scholar
  24. 24.
    Crick, F.H., Watson, J.D.: Structure of small viruses. Nature 177(4506), 473–475 (1956)ADSCrossRefGoogle Scholar
  25. 25.
    Horne, R.W., Wildy, P.: Symmetry in virus architecture. Virology 15, 348–373 (1961)Google Scholar
  26. 26.
    Caspar, D.L., Klug, A.: Physical principles in the construction of regular viruses. Cold Spring Harb. Symp. Quant. Biol. 27, 1–24 (1962)CrossRefGoogle Scholar
  27. 27.
    Schwartz, R.S., Garcea, R.L., Berger, B.: ‘local rules’ theory applied to polyomavirus polymorphic capsid assemblies. Virology 268(2), 461–470 (2000)CrossRefGoogle Scholar
  28. 28.
    Rapaport, D.C.: Self-assembly of polyhedral shells: a molecular dynamics study. Phys. Rev. E 70(5), 1539–1555 (2004)CrossRefGoogle Scholar
  29. 29.
    Endres, D., Miyahara, M., Moisant, P., Zlotnick, A.: A reaction landscape identifies the intermediates critical for self-assembly of virus capsids and other polyhedral structures. Prot. Sci. 14, 1518–1525 (2005)CrossRefGoogle Scholar
  30. 30.
    Keef, T., Taormina, A., Twarock, R.: Assembly models for papovaviridae based on tiling theory. Phys. Biol. 2(3), 175–188 (2005)ADSCrossRefGoogle Scholar
  31. 31.
    Keef, T., Micheletti, C., Twarock, R.: Master equation approach to the assembly of viral capsids. J. Theor. Biol. 242(3), 713–721 (2006)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Hagan, M.F., Chandler, D.: Dynamic pathways for viral capsid assembly. Biophys. J. 91, 42–54 (2006)ADSCrossRefGoogle Scholar
  33. 33.
    Nguyen, H.D., Reddy, V.S., Brooks III, C.L. Deciphering the kinetic mechanism of spontaneous self-assembly of icosahedral capsids. Nano Lett. 7(2), 338–344 (2007)ADSCrossRefGoogle Scholar
  34. 34.
    Workum, K.V., Douglas, J.F.: Symmetry, equivalence, and molecular self-assembly. Phys. Rev. E 73, 031502 (2006)ADSCrossRefGoogle Scholar
  35. 35.
    Chen, T., Zhang, Z., Glotzer, S.C.: A precise packing sequence for self-assembled convex structures. Proc. Natl. Acad. Sci. USA 104(3), 717–722 (2007)ADSCrossRefGoogle Scholar
  36. 36.
    Mannige, R.V., Brooks III, C.L.: Geometric considerations in virus capsid size specificity, auxiliary requirements, and buckling. Proc. Natl. Acad. Sci. USA 106(21), 8531–8536 (2009)ADSCrossRefGoogle Scholar
  37. 37.
    Mannige, R.V., Brooks III, C.L.: Periodic table of virus capsids: implications for natural selection and design. PLoS One 5(3), e9423 (2010)ADSCrossRefGoogle Scholar
  38. 38.
    Twarock, R.: A tiling approach to virus capsid assembly explaining a structural puzzle in virology. J. Theor. Biol. 226(4), 477–482 (2004)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Twarock, R.: Mathematical virology: a novel approach to the structure and assembly of viruses. Phil. Trans. R. Soc. A 364, 3357–3373 (2006)MathSciNetADSMATHCrossRefGoogle Scholar
  40. 40.
    Mannige, R.V., Brooks III, C.L.: Tilable nature of virus capsids and the role of topological constraints in natural capsid design. Phys. Rev. E 77(5), 051902 (2008)ADSCrossRefGoogle Scholar
  41. 41.
    Lidmar, J., Mirny, L., Nelson, D.R.: Virus shapes and buckling transitions in spherical shells. Phys. Rev. E 68, 051910–051919 (2003)ADSCrossRefGoogle Scholar
  42. 42.
    Nguyen, T.T., Bruinsma, R.F., Gelbart, W.M.: Elasticity theory and shape transitions of viral shells. Phys. Rev. E Stat. Nonlin. Soft. Matter Phys. 72(5 Pt 1), 051923 (2005)MathSciNetADSCrossRefGoogle Scholar
  43. 43.
    Zandi, R., Reguera, D.: Mechanical properties of viral capsids. Phys. Rev. E Stat. Nonlin. Soft. Matter Phys. 72, 021917 (2005)Google Scholar
  44. 44.
    Zandi, R., Reguera, D., Bruinsma, R.F., Gelbart, W.M., Rudnick, J.: Origin of icosahedral symmetry in viruses. Proc. Natl. Acad. Sci. USA 101(44), 15556–15560 (2004)ADSCrossRefGoogle Scholar
  45. 45.
    Bamford, D.H., Grimes, J.M., Stuart, D.I.: What does structure tell us about virus evolution? Curr. Opin. Struct. Biol. 15(6), 655–663 (2005)CrossRefGoogle Scholar
  46. 46.
    Johnson, J.E., Speir, J.A.: Quasi-equivalent viruses: a paradigm for protein assemblies. J. Mol. Biol. 269(5), 665–75 (1997)CrossRefGoogle Scholar
  47. 47.
    Dokland, T., McKenna, R., Ilag, L.L., Bowman, B.R., Incardona, N.L., Fane, B.A., Rossmann, M.G.: Structure of a viral procapsid with molecular scaffolding. Nature 389(6648), 308–313 (1997)ADSCrossRefGoogle Scholar
  48. 48.
    Douglas, T., Young, M.: Viruses: making friends with old foes. Science 312(5775), 873–875 (2006)ADSCrossRefGoogle Scholar
  49. 49.
    Koutsky, L.A., Ault, K.A., Wheeler, C.M., Brown, D.R., Barr, E., Alvarez, F.B., Chiacchierini, L.M., Jansen, K.U.: A controlled trial of a human papillomavirus type 16 vaccine. N. Engl. J. Med. 347(21), 1645–1651 (2002)CrossRefGoogle Scholar
  50. 50.
    Shank-Retzlaff, M., Wang, F., Morley, T., Anderson, C., Hamm, M., Brown, M., Rowland, K., Pancari, G., Zorman, J., Lowe, R., Schultz, L., Teyral, J., Capen, R., Oswald, C.B., Wang, Y., Washabaugh, M., Jansen, K., Sitrin, R.: Correlation between mouse potency and in vitro relative potency for human papillomavirus type 16 virus-like particles and gardasil vaccine samples. Hum. Vaccin. 1(5), 191–7 (2005)CrossRefGoogle Scholar
  51. 51.
    Shi, L., Sings, H.L., Bryan, J.T., Wang, B., Wang, Y., Mach, H., Kosinski, M., Washabaugh, M.W., Sitrin, R., Barr, E.: Gardasil: prophylactic human papillomavirus vaccine development–from bench top to bed-side. Clin. Pharmacol. Ther. 81(2), 259–64 (2007)CrossRefGoogle Scholar
  52. 52.
    Wales, D.J.: Closed-shell structures and the building game. Chem. Phys. Lett. 141, 478–484 (1987)ADSCrossRefGoogle Scholar
  53. 53.
    Berger, B., Shor, P.W., Tucker-Kellogg, L., King, J.: Local rule-based theory of virus shell assembly. Proc. Natl. Acad. Sci. USA. 91, 7732–7736 (1994)ADSMATHCrossRefGoogle Scholar
  54. 54.
    Zlotnick, A.: To build a virus capsid. An equilibrium model of the self assembly of polyhedral protein complexes. J. Mol. Biol. 241(1), 59–67 (1994)Google Scholar
  55. 55.
    Endres, D., Zlotnick, A.: Model-based analysis of assembly kinetics for virus capsids or other spherical polymers. Biophys. J. 83, 1217–1230 (2002)ADSCrossRefGoogle Scholar
  56. 56.
    Reddy, V.S., Giesing, H.A., Morton, R.T., Kumar, A., Post, C.B., Brooks III, C.L., Johnson, J.E.: Energetics of quasiequivalence: computational analysis of protein-protein interactions in icosahedral viruses. Biophys. J. 74(1), 546–558 (1998)ADSCrossRefGoogle Scholar
  57. 57.
    Shepherd, C.M., Borelli, I.A., Lander, G., Natarajan, P., Siddavanahalli, V., Bajaj, C., Johnson, J.E., Brooks III, C.L., Reddy, V.S.: Viperdb: a relational database for structural virology. Nucleic Acids Res. 34, D386–D389. (2006)CrossRefGoogle Scholar
  58. 58.
    Zlotnick, A., Aldrich, R., Johnson, J.M., Ceres, P., Young, M.J.: Mechanism of capsid assembly for an icosahedral plant virus. Virology 277, 450–456 (2000)CrossRefGoogle Scholar
  59. 59.
    Casini, G.L., Graham, D., Heine, D., Garcea, R.L., Wu, D.L.: In vitro papillomavirus capsid assembly analyzed by light scattering. Virology 325, 320–327 (2004)CrossRefGoogle Scholar
  60. 60.
    Zhang, T., Schwartz, R.: Simulation study of the contribution of oligomer/oligomer binding to capsid assembly kinetics. Biophys. J. 90, 57–64 (2006)ADSCrossRefGoogle Scholar
  61. 61.
    Hicks, S.D., Henley, C.L.: Irreversible growth model for virus capsid assembly. Phys. Rev. E Stat. Nonlin. Soft. Matter Phys. 74(3 Pt 1), 031912 (2006)ADSCrossRefGoogle Scholar
  62. 62.
    Alder, B.J., Wainwright, T.E.: Studies in molecular dynamics. I. General method. J. Chem. Phys. 31, 459–466 (1959)MathSciNetADSGoogle Scholar
  63. 63.
    Rapaport, D.C.: Molecular dynamics simulation of polymer chains with excluded volume. J. Phys. A 11, L213–L217 (1978)ADSCrossRefGoogle Scholar
  64. 64.
    Bellemans, A., Orban, J., Belle, D.V.: Molecular dynamics of rigid and non-rigid necklaces of hard discs. Mol. Phys. 39, 781–782 (1980)ADSCrossRefGoogle Scholar
  65. 65.
    Nguyen, H.D., Reddy, V.S., Brooks III, C.L. Invariant polymorphism in virus capsid assembly. J. Am. Chem. Soc. 131(7), 2606–14 (2009)CrossRefGoogle Scholar
  66. 66.
    Sorger, P.K., Stockley, P.G., Harrison, S.C.: Structure and assembly of turnip crinkle virus. ii. mechanism of reassembly in vitro. J. Mol. Biol. 191(4), 639–658 (1986)Google Scholar
  67. 67.
    Earnshaw, W., King, J.: Structure of phage p22 coat protein aggregates formed in the absence of the scaffolding protein. J. Mol. Biol. 126, 721–747 (1978)CrossRefGoogle Scholar
  68. 68.
    Bancroft, J.B., Bracker, C.E., Wagner, G.W.: Structures derived from cowpea chlorotic mottle and brome mosaic virus protein. Virology 38(2), 324–35 (1969)CrossRefGoogle Scholar
  69. 69.
    Salunke, D.M., Caspar, D.L., Garcea, R.L.: Polymorphism in the assembly of polyomavirus capsid protein vp1. Biophys. J. 56(5), 887–900 (1989)CrossRefGoogle Scholar
  70. 70.
    Kanesashi, S.N., Ishizu, K., Kawano, M.A., Han, S.I., Tomita, S., Watanabe, H., Kataoka, K., Handa, H.: Simian virus 40 vp1 capsid protein forms polymorphic assemblies in vitro. J. Gen. Virol. 84(Pt 7), 1899–905 (2003)CrossRefGoogle Scholar
  71. 71.
    Zhao, Q., Guo, H.H., Wang, Y., Washabaugh, M.W., Sitrin, R.D.: Visualization of discrete l1 oligomers in human papillomavirus 16 virus-like particles by gel electrophoresis with coomassie staining. J. Virol. Methods 127(2), 133–40 (2005)CrossRefGoogle Scholar
  72. 72.
    Fu, C.Y., Morais, M.C., Battisti, A.J., Rossmann, M.G., Jr. Prevelige, P.E.: Molecular dissection of o29 scaffolding protein function in an in vitro assembly system. J. Mol. Biol. 366(4), 1161–1173 (2007)CrossRefGoogle Scholar
  73. 73.
    Dong, X.F., Natarajan, P., Tihova, M., Johnson, J.E., Schneemann, A.: Particle polymorphism caused by deletion of a peptide molecular switch in a auasiequivalent icosahedral virus. J. Virol. 72(7), 6024–6033 (1998)Google Scholar
  74. 74.
    Cusack, S., Oostergetel, G.T., Krijgsman, P.C., Mellema, J.E.: Structure of the top a-t component of alfalfa mosaic virus. A non-icosahedral virion. J. Mol. Biol. 171(2), 139–55 (1983)Google Scholar
  75. 75.
    Nguyen, H.D., Brooks III, C.L.: Generalized structural polymorphism in self-assembled viral particles. Nano Lett. 8, 4574–81 (2008)ADSCrossRefGoogle Scholar
  76. 76.
    Xie, Z., Hendrix, R.W.: Assembly in vitro of bacteriophage hk97 proheads. J. Mol. Biol. 253(1), 74–85 (1995)CrossRefGoogle Scholar
  77. 77.
    Duda, R.L., Hempel, J., Michel, H., Shabanowitz, J., Hunt, D., Hendrix, R.W.: Structural transitions during bacteriophage hk97 head assembly. J. Mol. Biol. 247(4), 618–635 (1995)Google Scholar
  78. 78.
    Wikoff, W.R., Liljas, L., Duda, R.L., Tsuruta, H., Hendrix, R.W., Johnson, J.E.: Topologically linked protein rings in the bacteriophage hk97 capsid. Science 289(5487), 2129–2133 (2000)ADSCrossRefGoogle Scholar
  79. 79.
    Conway, J.F., Wikoff, W.R., Cheng, N., Duda, R.L., Hendrix, R.W., Johnson, J.E., Steven, A.C.: Virus maturation involving large subunit rotations and local refolding. Science 292(5517), 744–748 (2001)ADSCrossRefGoogle Scholar
  80. 80.
    Ross, P.D., Conway, J.F., Cheng, N., Dierkes, L., Firek, B.A., Hendrix, R.W., Steven, A.C., Duda, R.L.: A free energy cascade with locks drives assembly and maturation of bacteriophage hk97 capsid. J. Mol. Biol. 364(3), 512–525 (2006)CrossRefGoogle Scholar
  81. 81.
    Gertsman, I., Gan, L., Guttman, M., Lee, K., Speir, J.A., Duda, R.L., Hendrix, R.W., Komives, E.A., Johnson, J.E.: An unexpected twist in viral capsid maturation. Nature 458(7238), 646–650 (2009)ADSCrossRefGoogle Scholar
  82. 82.
    Gan, L., Conway, J.F., Firek, B.A., Cheng, N., Hendrix, R.W., Steven, A.C., Johnson, J.E., Duda, R.L.: Control of crosslinking by quaternary structure changes during bacteriophage hk97 maturation. Mol. Cell 14(5), 559–569 (2004)CrossRefGoogle Scholar
  83. 83.
    Steven, A.C., Heymann, J.B., Cheng, N., Trus, B.L., Conway, J.F.: Virus maturation: dynamics and mechanism of a stabilizing structural transition that leads to infectivity. Curr. Opin. Struct. Biol. 15(2), 227–236 (2005)CrossRefGoogle Scholar
  84. 84.
    Lee, K.K., Gan, L., Tsuruta, H., Hendrix, R.W., Duda, R.L., Johnson, J.E.: Evidence that a local refolding event triggers maturation of hk97 bacteriophage capsid. J. Mol. Biol. 340(3), 419–433 (2004)CrossRefGoogle Scholar
  85. 85.
    May, E.R., Brooks III, C.L.: Determination of viral capsid elastic properties from equilibrium thermal fluctuations. Phys. Rev. Lett. 106, 188101–188104 (2011)ADSCrossRefGoogle Scholar
  86. 86.
    May, E.R., Aggarwal, A., Klug, W.S., Brooks III, C.L.: Viral capsid equilibrium dynamics reveals nonuniform elastic properties. Biophys. J. 100, L59–L61 (2011)CrossRefGoogle Scholar
  87. 87.
    Ivanovska, I.L., de Pablo, P.J., Ibarra, B., Sgalari, G., MacKintosh, F.C., Carrascosa, J.L., Schmidt, C.F., Wuite, G.J.L.: Bacteriophage capsids: tough nanoshells with complex elastic properties. Proc. Natl. Acad. Sci. USA 101(20), 7600–7605 (2004)ADSCrossRefGoogle Scholar
  88. 88.
    Michel, J.P., Ivanovska, I.L., Gibbons, M.M., Klug, W.S., Knobler, C.M., Wuite, G.J.L., Schmidt, C.F.: Nanoindentation studies of full and empty viral capsids and the effects of capsid protein mutations on elasticity and strength. Proc. Natl. Acad. Sci. USA 103(16), 6184–6189 (2006)ADSCrossRefGoogle Scholar
  89. 89.
    Kol, N., Gladnikoff, M., Barlam, D., Shneck, R.Z., Rein, A., Rousso, I.: Mechanical properties of murine leukemia virus particles: effect of maturation. Biophys. J. 91(2), 767–774 (2006)ADSCrossRefGoogle Scholar
  90. 90.
    Carrasco, C., Carreira, A., Schaap, I.A.T., Serena, P.A., Gmez-Herrero, J., Mateu, M.G., de Pablo, P.J.: Dna-mediated anisotropic mechanical reinforcement of a virus. Proc. Natl. Acad. Sci. USA 103(37), 13706–13711 (2006)ADSCrossRefGoogle Scholar
  91. 91.
    Roos, W.H., Gibbons, M.M., Arkhipov, A., Uetrecht, C., Watts, N.R., Wingfield, P.T., Steven, A.C., Heck, A.J.R., Schulten, K., Klug, W.S., Wuite, G.J.L.: Squeezing protein shells: how continuum elastic models, molecular dynamics simulations, and experiments coalesce at the nanoscale. Biophys. J. 99(4), 1175–1181 (2010)ADSCrossRefGoogle Scholar
  92. 92.
    Tama, F., Brooks, C.L.: Symmetry, form, and shape: guiding principles for robustness in macromolecular machines. Annu. Rev. Biophys. Biomol. Struct. 35, 115–133 (2006)CrossRefGoogle Scholar
  93. 93.
    Tirion, M.M.: Large amplitude elastic motions in proteins from a single-parameter, atomic analysis. Phys. Rev. Lett. 77(9), 1905–1908 (1996)ADSCrossRefGoogle Scholar
  94. 94.
    Landau, L.D., Lifshitz, E.M.: Theory of Elasticity. Pergamon Press, London (1959)Google Scholar
  95. 95.
    Cagin, T., Holder, M., Pettitt, B.M.: A method for modeling icosahedral virions rotational symmetry boundary-conditions. J. Comput. Chem. 12(5), 627–634 (1991)CrossRefGoogle Scholar
  96. 96.
    Tama, F., Brooks III, C.L.: Diversity and identity of mechanical properties of icosahedral viral capsids studied with elastic network normal mode analysis. J. Mol. Biol. 345(2), 299–314 (2005)CrossRefGoogle Scholar
  97. 97.
    Khavrutskii, I.V., Arora, K., Brooks III, C.L.: Harmonic fourier beads method for studying rare events on rugged energy surfaces. J. Chem. Phys. 125(17), 174108 (2006)ADSCrossRefGoogle Scholar
  98. 98.
    Arora, K., Brooks III, C.L. Large-scale allosteric conformational transitions of adenylate kinase appear to involve a population-shift mechanism. Proc. Natl. Acad. Sci. USA 104(47), 18496–18501 (2007)ADSCrossRefGoogle Scholar
  99. 99.
    Arora, K., Brooks III, C.L. Functionally important conformations of the met20 loop in dihydrofolate reductase are populated by rapid thermal fluctuations. J. Am. Chem. Soc. 131, 5642–5647 (2009)CrossRefGoogle Scholar
  100. 100.
    Lee, M.S., Salsbury, F.R., Brooks III, C.L. Constant-pH molecular dynamics using continuous titration coordinates. Proteins 56(4), 738–752 (2004)CrossRefGoogle Scholar
  101. 101.
    Khandogin, J., Brooks III, C.L. Constant pH molecular dynamics with proton tautomerism. Biophys. J. 89(1), 141–157 (2005)CrossRefGoogle Scholar
  102. 102.
    May, E.R., Armen, R.S., Mannan, A.M., Brooks III, C.L.: The flexible c-terminal arm of the lassa arenavirus z-protein mediates interactions with multiple binding partners. Proteins 78(10), 2251–2264 (2010)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Eric R. May
    • 1
  • Karunesh Arora
    • 1
  • Ranjan V. Mannige
    • 2
  • Hung D. Nguyen
    • 3
  • Charles L. BrooksIII
    • 1
  1. 1.Department of Chemistry and Biophysics ProgramUniversity of MichiganAnn ArborUSA
  2. 2.Department of Chemistry and Chemical BiologyHarvard UniversityCambridgeUSA
  3. 3.Department of Chemical Engineering and Materials ScienceUniversity of California, IrvingIrvineUSA

Personalised recommendations