Skip to main content

Microscopic mechanics of biomolecules in living cells

  • Chapter
Scientific Modeling and Simulations

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

  • 2537 Accesses

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  5. Toulouse G.: Perspectives on neural network models and their relevance to neurobiology. J. Phys. A Math. Gen. 22, 1959–1960 (1989)

    Article  MathSciNet  ADS  Google Scholar 

  6. Svitkina T.M., Borisy G.G.: Correlative light and electron microscopy of the cytoskeleton of cultured cells. Meth. Enzym. 298, 570–576 (1998)

    Article  Google Scholar 

  7. Rudnick J., Bruinsma R.: DNA-protein cooperative binding through variable-range elastic coupling. Biophys. J. 76, 1725–1733 (1999)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  10. Satchey R.I., Dewey C.F.: Theoretical estimates of mechanical properties of the endothelial cell cytoskeleton. J. Biophys. 71, 109–118 (1996)

    Article  Google Scholar 

  11. Dean C., Dresbach T.: Neuroligins and neurexins: linking cell adhesion, synapse formation and cognitive function. Trends Neurosci. 29, 21–29 (2006)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  13. Zamir E., Geiger B.: Molecular complexity and dynamics of cell-matrix adhesions. J. Cell Sci. 114, 3577–3579 (2001)

    Google Scholar 

  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)

    Article  Google Scholar 

  15. Discher D.E., Janmey P., Wang Y.: Tissue cells feel and respond to the stiffness of their substrate. Science 310, 1139–1143 (2005)

    Article  ADS  Google Scholar 

  16. Evans E.A., Calderwood D.: Forces and bond dynamics in cell adhesion. Science 316, 1148–1153 (2007)

    Article  ADS  Google Scholar 

  17. Janmey P.A., Weitz D.A.: Dealing with mechanics: mechanisms of force transduction in cells. Trends Biochem. Sci. 29, 364–370 (2004)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  21. Buiatti M., Buiatti M.: The living state of matter. Riv. Biol. Biol. Forum 94, 59–82 (2001)

    Google Scholar 

  22. Buiatti M., Buiatti M.: Towards a statistical characterisation of the living state of matter. Chaos Sol. Fract. 20, 55–66 (2004)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  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. Buehler M.: Nature designs tough collagen: explaining the nanostructure of collagen fibrils. Proc. Natl. Acad. Sci. USA 103, 12285–12290 (2006)

    Article  ADS  Google Scholar 

  25. Bao G.: Mechanics of biomolecules. J. Mech. Phys. Sol. 50, 2237–2274 (2002)

    Article  ADS  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  28. Frenkel D., Smit B.: Understanding Molecular Simulation, Chap. 7. Academic Press, New York (2006)

    Google Scholar 

  29. McCammon J.A., Harvey S.C.: Dynamics of Proteins and Nucleic Acids. Cambridge University Press, Cambridge (1987)

    Google Scholar 

  30. Aiay R., Murcko M.: Computational methods for predicting binding free energy in ligand-receptor complexes. J. Med. Chem. 38, 4953–4967 (1995)

    Article  Google Scholar 

  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. 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)

    Article  ADS  Google Scholar 

  33. Karplus M., Kushick S.: Method for estimating the configurational entropy of macromolecules. Macromolecules 14, 325–332 (1981)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  35. Schlitter J.: Estimation of absolute and relative entropies of macromolecules using the covariance matrix. Chem. Phys. Lett. 215, 617–621 (1993)

    Article  ADS  Google Scholar 

  36. Schaefer H., Mark A.E., van Gunsteren W.F.: Absolute entropies from molecular dynamics simulations trajectories. J. Chem. Phys. 113, 7809–7817 (2000)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

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

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  47. Jarzynski C.: Nonequilibrium equality for free energy differences. Phys. Rev. Lett. 78, 2690–2693 (1997)

    Article  ADS  Google Scholar 

  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. Crooks G.E.: Path-ensemble averages in systems driven far from equilibrium. Phys. Rev. E 61, 2361–2366 (2000)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  56. Matthews B.: No code for recognition. Nature 335, 294–295 (1988)

    Article  ADS  Google Scholar 

  57. Suzuki M., Brenner S., Gerstein M., Yagi N.: DNA recognition code of transcription factors. Protein Eng. 8, 319–328 (1995)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  60. Doi M., Edwards S.F.: The Theory of Polymer Dynamics. Oxford University Press, Oxford, UK (1986)

    Google Scholar 

  61. Marko J.F., Siggia E.D.: Bending and twisting elasticity of DNA. Macromolecules 27, 981–987 (1994)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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. Dean Astumian R.: Thermodynamics and kinetics of a brownian motor. Science 276, 917–922 (1997)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  79. Mather W.H., Fox R.F.: Kinesin’s biased stepping mechanism: amplification of neck linker zippering. Biophys. J. 91, 2416–2426 (2006)

    Article  ADS  Google Scholar 

  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. Fox R.F.: Rectified brownian movement in molecular and cell biology. Phys. Rev. E 57, 2177–2203 (1998)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  84. Laio A., Parrinello M.: Escaping free energy minima. Proc. Natl. Acad. Sci. USA 99, 12562–12566 (2002)

    Article  ADS  Google Scholar 

  85. Bussi G., Laio A., Parrinello M.: Equilibrium free energies from nonequilibrium metadynamics. Phys. Rev. Lett. 96, 090601 (2006)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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. Lyman E., Ytreberg F.M., Zuckerman D.M.: Resolution exchange simulation. Phys. Rev. Lett. 96, 028105 (2006)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  97. Kmiecik S., Kolinski A.: Characterization of protein-folding pathways by reduced-space modeling. Proc. Natl. Acad. Sci. USA 104, 12330–12335 (2007)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  99. Miao Y., Ortoleva P.J.: Viral structural transitions: an all-atom multiscale theory. J. Chem. Phys. 125, 214901 (2006)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fabrizio Cleri .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Cleri, F. (2008). Microscopic mechanics of biomolecules in living cells. In: Yip, S., de la Rubia, T.D. (eds) Scientific Modeling and Simulations. Lecture Notes in Computational Science and Engineering, vol 68. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9741-6_18

Download citation

Publish with us

Policies and ethics