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Mechanical Characterization in Molecular Simulation

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Book cover Biomateriomics

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 165))

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Abstract

A standardized procedure for extracting mechanical properties from molecular simulation unfortunately does not exist. The challenge is to construct a suitable procedure and extract useful mechanical measures comparable to macroscale metrics (stiffness, strength, fracture toughness, etc.). As a result, there have been many methods developed to exploit the capabilities of atomistic simulation (such as steered molecular dynamics, direct calculation of virial stress and strain, free energy minimization, etc.), and various analytical tools and models to interpret such results (e.g., the classical Bell model for rate dependence, worm-like chain models for entropic unfolding, etc.). Here, we look at a sample of approaches used for mechanical characterization in molecular simulation.

You have your way. I have my way. As for the right way, the correct way, and the only way, it does not exist.

Friedrich Nietzsche (1844–1900)

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Notes

  1. 1.

    MD provides an alternative approach to methods like Monte Carlo (MC), which provide certain advantages as well. However, this point will not be discussed further here as the simulation studies reviewed here are carried out with a MD approach.

References

  1. E.B. Tadmor, M. Ortiz, R. Phillips, Quasicontinuum analysis of defects in solids. Philos. Mag., A, Phys. Condens. Matter, Struct. Defects Mech. Prop. 73(6), 1529–1563 (1996)

    Google Scholar 

  2. W.A. Curtin, R.E. Miller, Atomistic/continuum coupling in computational materials science. Model. Simul. Mater. Sci. Eng. 11(3), R33–R68 (2003)

    Article  CAS  Google Scholar 

  3. W.K. Liu, E.G. Karpov, S. Zhang, H.S. Park, An introduction to computational nanomechanics and materials. Comput. Methods Appl. Mech. Eng. 193(17–20), 1529–1578 (2004)

    Article  Google Scholar 

  4. H.S. Park, P.A. Klein, Surface Cauchy-Born analysis of surface stress effects on metallic nanowires. Phys. Rev. B 75(8) (2007)

    Google Scholar 

  5. B. Liu, H. Jiang, Y. Huang, S. Qu, M.F. Yu, K.C. Hwang, Atomic-scale finite element method in multiscale computation with applications to carbon nanotubes. Phys. Rev. B 72(3) (2005)

    Google Scholar 

  6. G.I. Giannopoulos, P.A. Kakavas, N.K. Anifantis, Evaluation of the effective mechanical properties of single walled carbon nanotubes using a spring based finite element approach. Comput. Mater. Sci. 41(4), 561–569 (2008)

    Article  CAS  Google Scholar 

  7. T.A. Witten, Polymer solutions: a geometric introduction. Rev. Mod. Phys. 70(4), 1531–1544 (1998)

    Article  CAS  Google Scholar 

  8. R.B. Laughlin, D. Pines, The theory of everything. Proc. Natl. Acad. Sci. USA 97(1), 28–31 (2000)

    Article  CAS  Google Scholar 

  9. J.F. Smith, T.P.J. Knowles, C.M. Dobson, C.E. MacPhee, M.E. Welland, Characterization of the nanoscale properties of individual amyloid fibrils. Proc. Natl. Acad. Sci. USA 103(43), 15806–15811 (2006)

    Article  CAS  Google Scholar 

  10. T.P. Knowles, A.W. Fitzpatrick, S. Meehan, H.R. Mott, M. Vendruscolo, C.M. Dobson, M.E. Welland, Role of intermolecular forces in defining material properties of protein nanofibrils. Science 318(5858), 1900–1903 (2007)

    Article  CAS  Google Scholar 

  11. T. Ackbarow, M.J. Buehler, Superelasticity, energy dissipation and strain hardening of vimentin coiled-coil intermediate filaments: atomistic and continuum studies. J. Mater. Sci. 42(21), 8771–8787 (2007)

    Article  CAS  Google Scholar 

  12. T. Ackbarow, X. Chen, S. Keten, M.J. Buehler, Hierarchies, multiple energy barriers, and robustness govern the fracture mechanics of alpha-helical and beta-sheet protein domains. Proc. Natl. Acad. Sci. USA 104(42), 16410–16415 (2007)

    Article  CAS  Google Scholar 

  13. T. Ackbarow, S. Keten, M.J. Buehler, A multi-timescale strength model of alpha helical protein domains. J. Phys., Condens. Matter 21, 035111 (2009)

    Article  Google Scholar 

  14. C.B. Prater, H.J. Butt, P.K. Hansma, Atomic force microscopy. Nature 345(6278), 839–840 (1990)

    Article  Google Scholar 

  15. Y.L. Sun, Z.P. Luo, A. Fertala, K.N. An, Stretching type ii collagen with optical tweezers. J. Biomech. 37(11), 1665–1669 (2004)

    Article  Google Scholar 

  16. K.J. Van Vliet, G. Bao, S. Suresh, The biomechanics toolbox: experimental approaches for living cells and biomolecules. Acta Mater. 51(19), 5881–5905 (2003)

    Article  Google Scholar 

  17. K. Schulten, Manipulating proteins by steered molecular dynamics. J. Mol. Graph. Model. 16(4-6), 289 (1998)

    Google Scholar 

  18. H. Lu, B. Isralewitz, A. Krammer, V. Vogel, K. Schulten, Unfolding of titin immunoglobulin domains by steered molecular dynamics simulation. Biophys. J. 75(2), 662–671 (1998)

    Article  CAS  Google Scholar 

  19. S. Izrailev, S. Stepaniants, K. Schulten, Applications of steered molecular dynamics to protein-ligand/membrane binding. Biophys. J. 74(2), 177 (1998)

    Google Scholar 

  20. B. Isralewitz, M. Gao, K. Schulten, Steered molecular dynamics and mechanical functions of proteins. Curr. Opin. Struct. Biol. 11(2), 224–230 (2001)

    Article  CAS  Google Scholar 

  21. E.B. Walton, S. Lee, K.J. Van Vliet, Extending bell’s model: how force transducer stiffness alters measures unbinding forces and kinetics of molecular complexes. Biophys. J. 94, 2621–2630 (2008)

    Article  CAS  Google Scholar 

  22. M. Sotomayer, K. Schulten, Single-molecule experiments in vitro and in silico. Science 316, 1144–1148 (2007)

    Article  Google Scholar 

  23. S.W. Cranford, C. Ortiz, M.J. Buehler, Mechanomutable properties of a paa/pah polyelectrolyte complex: rate dependence and ionization effects on tunable adhesion strength. Soft Matter 6(17), 4175–4188 (2010)

    Article  CAS  Google Scholar 

  24. S. Keten, J.F.R. Alvarado, S. Muftu, M.J. Buehler, Nanomechanical characterization of the triple beta-helix domain in the cell puncture needle of bacteriophage t4 virus. Cell. Mol. Bioeng. 2(1), 66–74 (2009)

    Article  CAS  Google Scholar 

  25. G.I. Bell, Models for the specific adhesion of cells to cells. Science 200(4342), 618–627 (1978)

    Article  CAS  Google Scholar 

  26. G. Hummer, A. Szabo, Kinetics from nonequilibrium single-molecule pulling experiments. Biophys. J. 85(1), 5–15 (2003)

    Article  CAS  Google Scholar 

  27. O.K. Dudko, G. Hummer, A. Szabo, Intrinsic rates and activation free energies from single-molecule pulling experiments. Phys. Rev. Lett. 96(10) (2006)

    Google Scholar 

  28. H.J. Lin, H.Y. Chen, Y.J. Sheng, H.K. Tsao, Bell’s expression and the generalized garg form for forced dissociation of a biomolecular complex. Phys. Rev. Lett. 98(8) (2007)

    Google Scholar 

  29. R.W. Friddle, Unified model of dynamic forced barrier crossing in single molecules. Phys. Rev. Lett. 100(13) (2008)

    Google Scholar 

  30. O.K. Dudko, G. Hummer, A. Szabo, Theory, analysis, and interpretation of single-molecule force spectroscopy experiments. Proc. Natl. Acad. Sci. USA 105(41), 15755–15760 (2008)

    Article  CAS  Google Scholar 

  31. O.K. Dudko, Single-molecule mechanics: new insights from the escape-over-a-barrier problem. Proc. Natl. Acad. Sci. USA 106(22), 8795–8796 (2009)

    Article  CAS  Google Scholar 

  32. E. Evans, K. Ritchie, Dynamic strength of molecular adhesion bonds. Biophys. J. 72, 1541–1555 (1997)

    Article  CAS  Google Scholar 

  33. E. Evans, Probing the relation between force, lifetime, and chemistry in single molecular bonds. Annu. Rev. Biophys. Biomol. Struct. 30(1), 105–128 (2001)

    Article  CAS  Google Scholar 

  34. R. Merkel, P. Nassoy, A. Leung, K. Ritchie, E. Evans, Energy landscapes of receptor-ligand bonds explored with dynamic force spectroscopy. Nature 397(6714), 50–53 (1999)

    Article  CAS  Google Scholar 

  35. G. Hummer, A. Szabo, Free energy reconstruction from nonequilibrium single-molecule pulling experiments. Proc. Natl. Acad. Sci. USA 98(7), 3658–3661 (2001)

    Article  CAS  Google Scholar 

  36. U. Seifert, Rupture of multiple parallel molecular bonds under dynamic loading. Phys. Rev. Lett. 84(12), 2750–2753 (2000)

    Article  CAS  Google Scholar 

  37. U. Seifert, Dynamic strength of adhesion molecules: role of rebinding and self-consistent rates. Europhys. Lett. 58(5), 792–798 (2002)

    Article  CAS  Google Scholar 

  38. R. Zwanzig, Diffusion in a rough potential. Proc. Natl. Acad. Sci. USA 85(7), 2029–2090 (1988)

    Article  CAS  Google Scholar 

  39. C. Hyeon, D. Thirumalai, Measuring the energy landscape roughness and the transition state location of biomolecules using single molecule mechanical unfolding experiments. J. Phys., Condens. Matter 19(11), 113101 (2007)

    Article  Google Scholar 

  40. S. Keten, Z.P. Xu, B. Ihle, M.J. Buehler, Nanoconfinement controls stiffness, strength and mechanical toughness of beta-sheet crystals in silk. Nat. Mater. 9(4), 359–367 (2010)

    Article  CAS  Google Scholar 

  41. Z.P. Xu, M.J. Buehler, Mechanical energy transfer and dissipation in fibrous beta-sheet-rich proteins. Phys. Rev. E 81(6) (2010)

    Google Scholar 

  42. R. Paparcone, M.J. Buehler, Failure of a beta(1–40) amyloid fibrils under tensile loading. Biomaterials 32(13), 3367–3374 (2011)

    Article  CAS  Google Scholar 

  43. D.J. Brockwell, E. Paci, R.C. Zinober, G.S. Beddard, P.D. Olmsted, D.A. Smith, R.N. Perham, S.E. Radford, Pulling geometry defines the mechanical resistance of a beta-sheet protein. Nat. Struct. Biol. 10(10), 731–737 (2003)

    Article  CAS  Google Scholar 

  44. S. Keten, M.J. Buehler, Geometric confinement governs the rupture strength of h-bond assemblies at a critical length scale. Nano Lett. 8(2), 743–748 (2008)

    CAS  Google Scholar 

  45. C. Bustamante, J.F. Marko, E.D. Siggia, S. Smith, Entropic elasticity of lambda-phage DNA. Science 265(5178), 1599–1600 (1994)

    Article  CAS  Google Scholar 

  46. P.E. Marszalek, H. Lu, H.B. Li, M. Carrion-Vazquez, A.F. Oberhauser, K. Schulten, J.M. Fernandez, Mechanical unfolding intermediates in titin modules. Nature 402(6757), 100–103 (1999)

    Article  CAS  Google Scholar 

  47. M.J. Buehler, S.Y. Wong, Entropic elasticity controls nanomechanics of single tropocollagen molecules. Biophys. J. 93(1), 37–43 (2007)

    Article  CAS  Google Scholar 

  48. J.F. Marko, E.D. Siggia, Stretching DNA. Macromolecules 28(26), 8759–8770 (1995)

    Article  CAS  Google Scholar 

  49. M.D. Wang, H. Yin, R. Landick, J. Gelles, S.M. Block, Stretching DNA with optical tweezers. Biophys. J. 72(3), 1335–1346 (1997)

    Article  CAS  Google Scholar 

  50. T. Odijk, Stiff chains and filaments under tension. Macromolecules 28(20), 7016–7018 (1995)

    Article  CAS  Google Scholar 

  51. M. Rief, J.M. Fernandez, H.E. Gaub, Elastically coupled two-level systems as a model for biopolymer extensibility. Phys. Rev. Lett. 81(21), 4764–4767 (1998)

    Article  CAS  Google Scholar 

  52. D.H. Tsai, Virial theorem and stress calculation in molecular-dynamics. J. Chem. Phys. 70(3), 1375–1382 (1979)

    Article  CAS  Google Scholar 

  53. J.A. Zimmerman, E.B. Webb, J.J. Hoyt, R.E. Jones, P.A. Klein, D.J. Bammann, Calculation of stress in atomistic simulation. Model. Simul. Mater. Sci. Eng. 12(4), 319–332 (2004)

    Article  Google Scholar 

  54. M. Zhou, The virial stress is not a measure of mechanical stress. Model. Numer. Simul. Mater. Behav. Evol. 731, 59–70 (2002)

    CAS  Google Scholar 

  55. M. Born, K. Huang, Dynamical Theory of Crystal Lattices (Oxford University Press, London, 1954)

    Google Scholar 

  56. J. Knap, M. Ortiz, An analysis of the quasicontinuum method. J. Mech. Phys. Solids 49(9), 1899–1923 (2001)

    Article  Google Scholar 

  57. L.M. Dupuy, E.B. Tadmor, R.E. Miller, R. Phillips, Finite-temperature quasicontinuum: molecular dynamics without all the atoms. Phys. Rev. Lett. 95(6) (2005)

    Google Scholar 

  58. H.J. Gao, P. Klein, Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds. J. Mech. Phys. Solids 46(2), 187–218 (1998)

    Article  CAS  Google Scholar 

  59. H.J. Gao, B.H. Ji, Modeling fracture in nanomaterials via a virtual internal bond method. Eng. Fract. Mech. 70(14), 1777–1791 (2003)

    Article  Google Scholar 

  60. J.L. Ericksen, On the Cauchy-Born rule. Math. Mech. Solids 13(3-4), 199–220 (2008)

    Article  Google Scholar 

  61. S. Cranford, D. Sen, M.J. Buehler, Meso-origami: folding multilayer graphene sheets. Appl. Phys. Lett. 95, 123121 (2009)

    Article  Google Scholar 

  62. L.D. Landau, E.M. Lifshitz, Theory of Elasticity, Vol. 7 (Butterworth–Heinemann, Oxford, 1995)

    Google Scholar 

  63. Z. Xu, R. Paparcone, M.J. Buehler, Alzheimer’s a(1–40) amyloid fibrils feature size-dependent mechanical properties. Biophys. J. 98, 2053–2062 (2010)

    Article  CAS  Google Scholar 

  64. N. Du, J. Narayanan, L.A. Li, M.L.M. Lim, D.Q. Li, X.Y. Liu, Design of superior spider silk: from nanostructure to mechanical properties. Biophys. J. 91(12), 4528–4535 (2006)

    Article  CAS  Google Scholar 

  65. S.M. Lee, E. Pippel, U. Gosele, C. Dresbach, Y. Qin, C.V. Chandran, T. Brauniger, G. Hause, M. Knez, Greatly increased toughness of infiltrated spider silk. Science 324(5926), 488–492 (2009)

    Article  CAS  Google Scholar 

  66. W.J. Weaver, S.P. Timoshenko, D.H. Young, Vibration Problems in Engineering (Wiley-Interscience, Hoboken, 2001)

    Google Scholar 

  67. M.M. Tirion, Large amplitude elastic motions in proteins from a single-parameter, atomic analysis. Phys. Rev. Lett. 77(9), 1905–1908 (1996)

    Article  CAS  Google Scholar 

  68. K. Hinsen, Analysis of domain motions by approximate normal mode calculations. Protein. Struct. Funct. Genet. 33, 417–429 (1998)

    Article  CAS  Google Scholar 

  69. K. Hinsen, A. Thomas, M.J. Field, Analysis of domain motions in large proteins. Protein. Struct. Funct. Genet. 34, 369–382 (1999)

    Article  CAS  Google Scholar 

  70. F. Tama, Normal mode analysis with simplified models to investigate the global dynamics of biological systems. Prot. Peptide Letters 10(2), 119–132 (2003)

    Article  CAS  Google Scholar 

  71. F. Tama, Y.H. Sanejouand, Conformational change of proteins arising from normal mode calculations. Protein Eng. 14(1), 1–6 (2001)

    Article  CAS  Google Scholar 

  72. M. Delarue, Y.H. Sanejouand, Simplified normal mode analysis of conformational transitions in DNA-dependent polymerases: the elastic network model. J. Mol. Biol. 320(5), 1011–1024 (2002)

    Article  CAS  Google Scholar 

  73. S.E. Dobbins, V.I. Lesk, M.J.E. Sternberg, Insights into protein flexibility: the relationship between normal modes and conformational change upon protein-protein docking. Proc. Natl. Acad. Sci. USA 105(30), 10390–10395 (2008)

    Article  CAS  Google Scholar 

  74. L.R. Pratt, Fluctuation method for calculation of elastic-constants of solids. J. Chem. Phys. 87(2), 1245–1247 (1987)

    Article  Google Scholar 

  75. S. Sengupta, P. Nielaba, M. Rao, K. Binder, Elastic constants from microscopic strain fluctuations. Phys. Rev. E 61(2), 1072–1080 (2000)

    Article  CAS  Google Scholar 

  76. M. Parrinello, A. Rahman, Strain fluctuations and elastic-constants. J. Chem. Phys. 76(5), 2662–2666 (1982)

    Article  CAS  Google Scholar 

  77. A.A. Gusev, M.M. Zehnder, U.W. Suter, Fluctuation formula for elastic constants. Phys. Rev. B 54(1), 1–4 (1996)

    Article  CAS  Google Scholar 

  78. L.D. Landau, E.M. Lifshitz, L.P. Pitaevskii, Statistical Physics (Pergamon Press, Oxford, 1980)

    Google Scholar 

  79. M.T. Meyers, J.M. Rickman, T.J. Delph, The calculation of elastic constants from displacement fluctuations. J. Appl. Phys. 98(6), (2005)

    Article  Google Scholar 

  80. N.V. Medhekar, A. Ramasubramaniam, R.S. Ruoff, V.B. Shenoy, Hydrogen bond networks in graphene oxide composite paper: structure and mechanical properties. ACS Nano 4(4), 2300–2306 (2010)

    Article  CAS  Google Scholar 

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  1. Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Steven W. Cranford & Markus J. Buehler

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Cranford, S.W., Buehler, M.J. (2012). Mechanical Characterization in Molecular Simulation. In: Biomateriomics. Springer Series in Materials Science, vol 165. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1611-7_7

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