Microscopic mechanics of biomolecules in living cells

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 68)


The exporting of theoretical concepts and modelling methods from physics and mechanics to the world of biomolecules and cell biology is increasing at a fast pace. The role of mechanical forces and stresses in biology and genetics is just starting to be appreciated, with implications going from cell adhesion, migration, division, to DNA transcription and replication, to the mechanochemical transduction and operation of molecular motors, and more. Substantial advances in experimental techniques over the past 10 years allowed to get unprecedented insight into the elasticity and mechanical response of many different proteins, cytoskeletal filaments, nucleic acids, both in vitro and, more recently, directly inside the cell. In a parallel effort, also theoretical models and computational methods are evolving into a rather specialized toolbox. However, several key issues need to be addressed when applying to life sciences the theories and methods typically originating from the fields of condensed matter and solid mechanics. The presence of a solvent and its dielectric properties, the many subtle effects of entropy, the non-equilibrium thermodynamics conditions, the dominating role of weak forces such as Van der Waals dispersion, hydrophobic interactions, and hydrogen bonding, impose a special caution and a thorough consideration, up to possibly rethinking some basic physics concepts. Discussing and trying to elucidate at least some of the above issues is the main aim of the present, partial and non-exhaustive, contribution.


Biomolecules Mechanical properties Configurational entropy Molecular dynamics Jarzynski identity 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Doran C.F., McCormack B.A.O., Macey A.: A simplified model to determine the contribution of strain energy in the failure process of thin biological membranes during cutting. Strain 40, 173–179 (2004)CrossRefGoogle Scholar
  2. 2.
    Feng Z., Rho J., Han S., Ziv I.: Orientation and loading condition dependence of fracture toughness in cortical bone. Mat. Sci. Eng. C 11, 41–46 (2000)CrossRefGoogle Scholar
  3. 3.
    Fantner G.E., Hassenkam T., Kindt J.H., Weaver J.C., Birkedal H., Cutroni J.A., Cidade G.A.G., Stucky G.D., Morse D.E., Hansma P.K.: Sacrificial bonds and hidden length dissipate energy as mineralized fibrils separate during bone fracture. Nat. Mater. 4, 612–616 (2005)CrossRefADSGoogle Scholar
  4. 4.
    Elices M., Pérez-Rigueiro J., Plaza G.R., Guinea G.V.: Finding inspiration in argiope trifasciata spider silk fiber. JOM J. 57, 60–66 (2005)CrossRefGoogle Scholar
  5. 5.
    Toulouse G.: Perspectives on neural network models and their relevance to neurobiology. J. Phys. A Math. Gen. 22, 1959–1960 (1989)CrossRefMathSciNetADSGoogle Scholar
  6. 6.
    Svitkina T.M., Borisy G.G.: Correlative light and electron microscopy of the cytoskeleton of cultured cells. Meth. Enzym. 298, 570–576 (1998)CrossRefGoogle Scholar
  7. 7.
    Rudnick J., Bruinsma R.: DNA-protein cooperative binding through variable-range elastic coupling. Biophys. J. 76, 1725–1733 (1999)CrossRefADSGoogle Scholar
  8. 8.
    Wang J., Su M., Fan J., Seth A., McCulloch C.A.: Transcriptional regulation of a contractile gene by mechanical forces applied through integrins in osteoblasts. J. Biol. Chem. 277, 22889–22895 (2002)CrossRefGoogle Scholar
  9. 9.
    Chen Y., Lee S.-H., Mao C.: A DNA nanomachine based on a duplex-triplex transition. Angew. Chem. Int. Ed. 43, 5335–5338 (2004)CrossRefGoogle Scholar
  10. 10.
    Satchey R.I., Dewey C.F.: Theoretical estimates of mechanical properties of the endothelial cell cytoskeleton. J. Biophys. 71, 109–118 (1996)CrossRefGoogle Scholar
  11. 11.
    Dean C., Dresbach T.: Neuroligins and neurexins: linking cell adhesion, synapse formation and cognitive function. Trends Neurosci. 29, 21–29 (2006)CrossRefGoogle Scholar
  12. 12.
    Wijnhoven B.P.L., Dinjens W.N.M., Pignatelli M.: E-cadherin-catenin cell-cell adhesion complex and human cancer. Br. J. Surg. 87, 992–1005 (2000)CrossRefGoogle Scholar
  13. 13.
    Zamir E., Geiger B.: Molecular complexity and dynamics of cell-matrix adhesions. J. Cell Sci. 114, 3577–3579 (2001)Google Scholar
  14. 14.
    Balaban N.Q., Schwarz U.S., Riveline D., Goichberg P., Tzur G., Sabanay I., Mahalu D., Safran S., Bershadsky A., Addadi L., Geiger B.: Force and focal adhesion assembly: a close relationship studied using elastic micropatterned substrates. Nat. Cell Biol. 3, 466–472 (2001)CrossRefGoogle Scholar
  15. 15.
    Discher D.E., Janmey P., Wang Y.: Tissue cells feel and respond to the stiffness of their substrate. Science 310, 1139–1143 (2005)CrossRefADSGoogle Scholar
  16. 16.
    Evans E.A., Calderwood D.: Forces and bond dynamics in cell adhesion. Science 316, 1148–1153 (2007)CrossRefADSGoogle Scholar
  17. 17.
    Janmey P.A., Weitz D.A.: Dealing with mechanics: mechanisms of force transduction in cells. Trends Biochem. Sci. 29, 364–370 (2004)CrossRefGoogle Scholar
  18. 18.
    Shenoy V.B., Freund L.B.: Growth and shape stability of a biological membrane adhesion complex in the diffusion-mediated regime. Proc. Natl. Acad. Sci. USA 102, 3213–3218 (2005)CrossRefADSGoogle Scholar
  19. 19.
    Steinberg, M.: Reconstruction of tissues by dissociated cells. Science 141, 401–408 (1963); see also Steinberg, M.: Adhesion in development: an historical overview. Dev. Biol. 180, 377–388 (1996)Google Scholar
  20. 20.
    Bell G.I.: Models for the specific adhesion of cells to cells. Science 200, 618–627 (1978)CrossRefADSGoogle Scholar
  21. 21.
    Buiatti M., Buiatti M.: The living state of matter. Riv. Biol. Biol. Forum 94, 59–82 (2001)Google Scholar
  22. 22.
    Buiatti M., Buiatti M.: Towards a statistical characterisation of the living state of matter. Chaos Sol. Fract. 20, 55–66 (2004)CrossRefMathSciNetMATHADSGoogle Scholar
  23. 23.
    de Pablo, J.J., Curtin, W.A. (guest eds.): Multiscale modeling in advanced materials research—challenges, novel methods, and emerging applications. MRS Bull. 32(11) (2007)Google Scholar
  24. 24.
    Buehler M.: Nature designs tough collagen: explaining the nanostructure of collagen fibrils. Proc. Natl. Acad. Sci. USA 103, 12285–12290 (2006)CrossRefADSGoogle Scholar
  25. 25.
    Bao G.: Mechanics of biomolecules. J. Mech. Phys. Sol. 50, 2237–2274 (2002)CrossRefADSMATHGoogle Scholar
  26. 26.
    Lecuit T., Lenne P.-F.: Cell surface mechanics and the control of cell shape, tissue patterns and morphogenesis. Nat. Rev. Mol. Cell Biol. 8, 633–644 (2002)CrossRefGoogle Scholar
  27. 27.
    Gilson M.K., Given J.A., Bush B.L., McCammon A.: The statistical-thermodynamic basis for computation of binding affinities: a critical review. Biophys. J. 72, 1047–1069 (1997)CrossRefADSGoogle Scholar
  28. 28.
    Frenkel D., Smit B.: Understanding Molecular Simulation, Chap. 7. Academic Press, New York (2006)Google Scholar
  29. 29.
    McCammon J.A., Harvey S.C.: Dynamics of Proteins and Nucleic Acids. Cambridge University Press, Cambridge (1987)Google Scholar
  30. 30.
    Aiay R., Murcko M.: Computational methods for predicting binding free energy in ligand-receptor complexes. J. Med. Chem. 38, 4953–4967 (1995)CrossRefGoogle Scholar
  31. 31.
    Hermans J., Shankar S.: The free-energy of xenon binding to myoglobin from molecular-dynamics simulation. Isr. J. Chem. 27, 225–227 (1986)Google Scholar
  32. 32.
    Roux B., Nina M., Pomes R., Smith J.C.: Thermodynamic stability of water molecules in the bacteriorhodopsin proton channel: a molecular dynamics free energy perturbation study. Biophys. J. 71, 670–681 (1996)CrossRefADSGoogle Scholar
  33. 33.
    Karplus M., Kushick S.: Method for estimating the configurational entropy of macromolecules. Macromolecules 14, 325–332 (1981)CrossRefADSGoogle Scholar
  34. 34.
    Di Nola A., Berendsen H.J.C., Edholm O.: Free energy determination of polypeptide conformations generated by molecular dynamics simulations. Macromolecules 17, 2044–2050 (1984)CrossRefADSGoogle Scholar
  35. 35.
    Schlitter J.: Estimation of absolute and relative entropies of macromolecules using the covariance matrix. Chem. Phys. Lett. 215, 617–621 (1993)CrossRefADSGoogle Scholar
  36. 36.
    Schaefer H., Mark A.E., van Gunsteren W.F.: Absolute entropies from molecular dynamics simulations trajectories. J. Chem. Phys. 113, 7809–7817 (2000)CrossRefADSGoogle Scholar
  37. 37.
    Izrailev S., Stepaniants S., Balsera M., Oono Y., Schulten K.: Molecular dynamics study of unbinding of the avidin-biotin complex. Biophys. J. 72, 1568–1581 (1997)CrossRefGoogle Scholar
  38. 38.
    Izrailev S., Stepaniants S., Isralewitz B., Kosztin D., Lu H., Molnar F., Wriggers W., Schulten K.: Steered molecular dynamics. In: Deuflhard P., Hermans J., Leimkuhler B., Mark A., Skeel R.D., Reich S. (eds.) Algorithms for Macromolecular Modelling, Lecture Notes in Computational Science and Engineering, Springer-Verlag, New York (1998)Google Scholar
  39. 39.
    Evans E., Ritchie K.: Dynamic strength of molecular adhesion bonds. Biophys. J. 72, 1541–1555 (1997)CrossRefGoogle Scholar
  40. 40.
    Isralewitz B., Izrailev S., Schulten K.: Binding pathway of retinal to bacterio-opsin: a prediction by molecular dynamics simulations. Biophys. J. 73, 2972–2979 (1997)CrossRefGoogle Scholar
  41. 41.
    Wriggers W., Schulten K.: Stability and dynamics of G-actin: back-door water diffusion and behavior of a subdomain 3/4 loop. Biophys. J. 73, 624–639 (1997)CrossRefGoogle Scholar
  42. 42.
    Lu H., Schulten K.: Steered molecular dynamics simulation of conformational changes of immunoglobulin domain I27 interprete atomic force microscopy observations. Chem. Phys. 247, 141–153 (1999)CrossRefADSGoogle Scholar
  43. 43.
    Paci E., Karplus M.: Unfolding proteins by external forces and temperature: the importance of topology and energetics. Proc. Natl. Acad. Sci. USA 97, 6521–6526 (2000)CrossRefADSGoogle Scholar
  44. 44.
    Jensen M.O., Park S., Tajkhorshid E., Schulten K.: Energetics of glycerol conduction through aquaglyceroporin GlpF. Proc. Natl. Acad. Sci. USA 99, 6731–6736 (2002)CrossRefADSGoogle Scholar
  45. 45.
    Park S., Khalili-Araghi F., Tajkhorshid E., Schulten K.: Free energy calculation from steered molecular dynamics simulations using Jarzynski’s equality. J. Chem. Phys. 119, 3559–3566 (2003)CrossRefADSGoogle Scholar
  46. 46.
    Buehler M.J., Wong S.Y.: Entropic elasticity controls nanomechanics of single tropocollagen molecules. Biophys. J. 93, 37–43 (2007)CrossRefADSGoogle Scholar
  47. 47.
    Jarzynski C.: Nonequilibrium equality for free energy differences. Phys. Rev. Lett. 78, 2690–2693 (1997)CrossRefADSGoogle Scholar
  48. 48.
    Jarzynski C.: Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences. Phys. Rev. E 60, 2721–2726 (1997)Google Scholar
  49. 49.
    Crooks G.E.: Path-ensemble averages in systems driven far from equilibrium. Phys. Rev. E 61, 2361–2366 (2000)CrossRefADSGoogle Scholar
  50. 50.
    Cuendet M.A.: The Jarzynski identity derived from general Hamiltonian or non-Hamiltonian dynamics reproducing NVT or NPT ensembles. J. Chem. Phys. 125, 144109 (2006)CrossRefADSGoogle Scholar
  51. 51.
    Rodinger T., Pomés R.: Enhancing the accuracy, the efficiency and the scope of free energy simulations. Curr. Opin. Struct. Biol. 15, 164–170 (2005)CrossRefGoogle Scholar
  52. 52.
    Isralewitz B., Gao M., Schulten K.: Steered molecular dynamics and mechanical functions of proteins. Curr. Opin. Struct. Biol. 11, 224–230 (2001)CrossRefGoogle Scholar
  53. 53.
    Sotomayor M., Schulten K.: Single-molecule experiments in vitro and in silico. Science 316, 1144–1148 (2007)CrossRefADSGoogle Scholar
  54. 54.
    Cleri F., Phillpot S.R., Wolf D., Yip S.: Atomistic simulations of materials fracture and the link between atomic and Continuum length scales. J. Amer. Cer. Soc. 81, 501–516 (1998)CrossRefGoogle Scholar
  55. 55.
    Harris S.A., Sands Z.A., Laughton C.A.: Molecular dynamics simulations of duplex stretching reveal the importance of entropy in determining the biomechanical properties of DNA. Biophys. J. 88, 1684–1691 (2005)CrossRefGoogle Scholar
  56. 56.
    Matthews B.: No code for recognition. Nature 335, 294–295 (1988)CrossRefADSGoogle Scholar
  57. 57.
    Suzuki M., Brenner S., Gerstein M., Yagi N.: DNA recognition code of transcription factors. Protein Eng. 8, 319–328 (1995)CrossRefGoogle Scholar
  58. 58.
    Pabo C., Nekludova L.: Geometric analysis and comparison of protein-DNA interfaces: why is there no simple code for recognition? J. Mol. Biol. 301, 597–624 (2000)CrossRefGoogle Scholar
  59. 59.
    Bustamante C., Marko J.F., Siggia E.D., Smith S.: Entropic elasticity of lambda-phage DNA. Science 265, 1599–1600 (1994)CrossRefADSGoogle Scholar
  60. 60.
    Doi M., Edwards S.F.: The Theory of Polymer Dynamics. Oxford University Press, Oxford, UK (1986)Google Scholar
  61. 61.
    Marko J.F., Siggia E.D.: Bending and twisting elasticity of DNA. Macromolecules 27, 981–987 (1994)CrossRefADSGoogle Scholar
  62. 62.
    Baumann C.G., Bloomfield V.A., Smith S.B., Bustamante C., Wang M.D., Block S.M.: Stretching of single collapsed DNA molecules. Biophys. J. 78, 1965–1978 (2000)CrossRefGoogle Scholar
  63. 63.
    Strick T.R., Allemand J.F., Bensimon D., Croquette V.: Stress-induced Structural transitions in DNA and proteins. Ann. Rev. Biophys. Biomol. Struct. 29, 523–542 (2000)CrossRefGoogle Scholar
  64. 64.
    Whitelam S., Pronk S., Geissler P.L.: There and (slowly) back again: entropy-driven hysteresis in a model of DNA overstretching. Biophys. J. 94, 2452–2469 (2008)CrossRefGoogle Scholar
  65. 65.
    Konrad M.W., Bolonick J.I.: Molecular dynamics simulation of DNA stretching is consistent with the tension observed for extension and strand separation and predicts a novel ladder structure. J. Am. Chem. Soc. 118, 10989–10994 (1996)CrossRefGoogle Scholar
  66. 66.
    MacKerell A.D., Lee G.U.: Structure, force, and energy of a double-stranded DNA oligonucleotide under tensile loads. Eur. Biophys. J. 28, 415–426 (1999)CrossRefGoogle Scholar
  67. 67.
    Strunz T., Oroszlan K., Guntherodt H.J., Henger M.: Model energy landscapes and the force-induced dissociation of ligand-receptor bonds. Biophys. J. 79, 1206–1212 (2000)CrossRefGoogle Scholar
  68. 68.
    in’t Veld P.J., Stevens M.J.: Simulation of the mechanical strength of a single collagen molecule. Biophys. J. 95, 33–39 (2008)CrossRefGoogle Scholar
  69. 69.
    Rief M., Gautel M., Oesterhelt F., Fernandez J.M., Gaub H.: Reversible unfolding of individual titin immunoglobulin domains by AFM. Science 276, 1109–1112 (1997)CrossRefGoogle Scholar
  70. 70.
    Kellermayer M.S.Z., Smith S.B., Granzier H.L., Bustamante C.: Folding-unfolding transitions in single titin molecules characterized with laser tweezers. Science 276, 1112–1116 (1997)CrossRefGoogle Scholar
  71. 71.
    Oberhauser A.F., Marszalek P.E., Erickson H.P., Fernandez J.M.: The molecular elasticity of the extracellular matrix protein tenascin. Nature 393, 181–185 (1998)CrossRefADSGoogle Scholar
  72. 72.
    Marszalek P.E., Lu H., Li H., Carrion-Vazquez M., Oberhauser A.F., Schulten K., Fernandez J.M.: Mechanical unfolding intermediates in titin modules. Nature 402, 100–103 (1999)CrossRefADSGoogle Scholar
  73. 73.
    Carl P., Kwok C.H., Manderson G., Speicher D.W., Discher D.E.: Forced unfolding modulated by disulfide bonds in the Ig domains of a cell adhesion molecule. Proc. Natl. Acad. Sci. USA 98, 1565–1570 (2001)CrossRefADSGoogle Scholar
  74. 74.
    Bhasin N., Carl P., Harper S., Feng G., Lu H., Speicher D.W., Discher D.E.: Chemistry on a single protein, vascular cell adhesion molecule-1, during forced unfolding. J. Biol. Chem. 279, 45865–45874 (2004)CrossRefGoogle Scholar
  75. 75.
    Baumann C.G., Smith S.B., Bloomfield V.A., Bustamante C.: Ionic effects on the elasticity of single DNA molecules. Proc. Natl. Acad. Sci. USA 94, 6185–6190 (1997)CrossRefADSGoogle Scholar
  76. 76.
    Alberts B., Bray D., Lewis J., Raff M., Roberts K., Watson J.D.: Molecular Biology of the Cell. Garland, New York (1994)Google Scholar
  77. 77.
    Dean Astumian R.: Thermodynamics and kinetics of a brownian motor. Science 276, 917–922 (1997)CrossRefGoogle Scholar
  78. 78.
    Walker M.L., Burgess S.A., Sellers J.R., Wang F., Hammer J.A., Trinick J., Knight P.J.: Two-headed binding of a processive myosin to F-actin. Nature 405, 804–807 (2000)CrossRefADSGoogle Scholar
  79. 79.
    Mather W.H., Fox R.F.: Kinesin’s biased stepping mechanism: amplification of neck linker zippering. Biophys. J. 91, 2416–2426 (2006)CrossRefADSGoogle Scholar
  80. 80.
    Huxley, A.F.: Muscle structure and theories of contraction. Prog. Biophys. Biophys. Chem. 7, 255–318 (1957); Huxley, A.F.: Muscular contraction—review lecture. J. Physiol. (London) 243, 1–43 (1974)Google Scholar
  81. 81.
    Fox R.F.: Rectified brownian movement in molecular and cell biology. Phys. Rev. E 57, 2177–2203 (1998)CrossRefADSGoogle Scholar
  82. 82.
    Ackbarow T., Buehler M.J.: Superelasticity, energy dissipation and strain hardening of vimentin coiled-coil intermediate filaments: atomistic and continuum studies. J. Mater. Sci. 42, 8771–8787 (2007)CrossRefADSGoogle Scholar
  83. 83.
    Liphardt J., Dumont S., Smith S.B., Tinoco Jr. I., Bustamante C.: Equilibrium information from nonequilibrium measurements in an experimental test of Jarzynski’s equality. Science 296, 1832–1835 (2002)CrossRefADSGoogle Scholar
  84. 84.
    Laio A., Parrinello M.: Escaping free energy minima. Proc. Natl. Acad. Sci. USA 99, 12562–12566 (2002)CrossRefADSGoogle Scholar
  85. 85.
    Bussi G., Laio A., Parrinello M.: Equilibrium free energies from nonequilibrium metadynamics. Phys. Rev. Lett. 96, 090601 (2006)CrossRefADSGoogle Scholar
  86. 86.
    Praprotnik M., Delle Site L., Kremer K.: Adaptive resolution molecular-dynamics simulation: changing the degrees of freedom on the fly. J. Chem. Phys. 123, 224106 (2005)CrossRefADSGoogle Scholar
  87. 87.
    Neri M., Anselmi C., Cascella M., Maritan A., Carloni P.: Coarse-grained model of proteins incorporating atomistic detail of the active site. Phys. Rev. Lett. 95, 218102 (2005)CrossRefADSGoogle Scholar
  88. 88.
    Shi Q., Izvekov S., Voth G.A.: Mixed atomistic and coarse-grained molecular dynamics: simulation of a membrane-bound ion channel. J. Phys. Chem. B 110, 15045–15048 (2006)CrossRefGoogle Scholar
  89. 89.
    Fan Z.Z., Hwang J.K., Warshel A.: Using simplified protein representation as a reference potential for all-atom calculations of folding free energy. Theor. Chem. Acc. 103, 77–80 (1999)Google Scholar
  90. 90.
    Popoff, M., Cleri, F., Gianese, G., Rosato, V.: Docking of small peptides to inorganic surfaces. Eur. Phys. J. E (2008) (to appear)Google Scholar
  91. 91.
    Lyman E., Ytreberg F.M., Zuckerman D.M.: Resolution exchange simulation. Phys. Rev. Lett. 96, 028105 (2006)CrossRefADSGoogle Scholar
  92. 92.
    Klimov D.K., Thirumalai D.: Native topology determines force-induced unfolding pathways in globular proteins. Proc. Natl. Acad. Sci. USA 97, 7254–7259 (2000)CrossRefADSGoogle Scholar
  93. 93.
    Marrink S.J., de Vries A.H., Mark A.E.: Coarse grained model for semiquantitative lipid simulations. J. Phys. Chem. B 108, 750–760 (2004)CrossRefGoogle Scholar
  94. 94.
    Shillcock J.C., Lipowsky R.: Equilibrium structure and lateral stress distribution of amphiphilic bilayers from dissipative particle dynamics simulations. J. Chem. Phys. 117, 5048–5061 (2002)CrossRefADSGoogle Scholar
  95. 95.
    Chen Q., Li D.Y., Oiwa K.: The coordination of protein motors and the kinetic behavior of microtubule—a computational study. Biophys. Chem. 129, 60–69 (2007)CrossRefGoogle Scholar
  96. 96.
    Ayton G.S., Noid W.G., Voth G.A.: Multiscale modeling of biomolecular systems: in serial and in parallel. Curr. Opin. Struct. Biol. 17, 192–198 (2007)CrossRefGoogle Scholar
  97. 97.
    Kmiecik S., Kolinski A.: Characterization of protein-folding pathways by reduced-space modeling. Proc. Natl. Acad. Sci. USA 104, 12330–12335 (2007)CrossRefADSGoogle Scholar
  98. 98.
    Heath A.P., Kavraki L.E., Clementi C.: From coarse-grain to all-atom: toward multiscale analysis of protein landscapes. Proteins Struct. Funct. Bioinfo. 68, 646–661 (2007)CrossRefGoogle Scholar
  99. 99.
    Miao Y., Ortoleva P.J.: Viral structural transitions: an all-atom multiscale theory. J. Chem. Phys. 125, 214901 (2006)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Institut d’Electronique, Microélectronique et NanotechnologieUniversité des Sciences et Technologies de LilleVilleneuve d’AscqFrance

Personalised recommendations