Microscopic mechanics of biomolecules in living cells
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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.
Keywords
Biomolecules Mechanical properties Configurational entropy Molecular dynamics Jarzynski identityPreview
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- 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.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.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)PubMedCrossRefADSGoogle 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)CrossRefGoogle Scholar
- 5.Toulouse G.: Perspectives on neural network models and their relevance to neurobiology. J. Phys. A Math. Gen. 22, 1959–1960 (1989)CrossRefADSMathSciNetGoogle 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)PubMedCrossRefGoogle Scholar
- 7.Rudnick J., Bruinsma R.: DNA-protein cooperative binding through variable-range elastic coupling. Biophys. J. 76, 1725–1733 (1999)PubMedADSGoogle 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)PubMedCrossRefGoogle 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)CrossRefGoogle Scholar
- 10.Satchey R.I., Dewey C.F.: Theoretical estimates of mechanical properties of the endothelial cell cytoskeleton. J. Biophys. 71, 109–118 (1996)Google Scholar
- 11.Dean C., Dresbach T.: Neuroligins and neurexins: linking cell adhesion, synapse formation and cognitive function. Trends Neurosci. 29, 21–29 (2006)PubMedCrossRefGoogle 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)PubMedCrossRefGoogle Scholar
- 13.Zamir E., Geiger B.: Molecular complexity and dynamics of cell-matrix adhesions. J. Cell Sci. 114, 3577–3579 (2001)PubMedGoogle 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)PubMedCrossRefGoogle 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)PubMedCrossRefADSGoogle Scholar
- 16.Evans E.A., Calderwood D.: Forces and bond dynamics in cell adhesion. Science 316, 1148–1153 (2007)PubMedCrossRefADSGoogle Scholar
- 17.Janmey P.A., Weitz D.A.: Dealing with mechanics: mechanisms of force transduction in cells. Trends Biochem. Sci. 29, 364–370 (2004)PubMedCrossRefGoogle 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)PubMedCrossRefADSGoogle 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)PubMedCrossRefADSGoogle 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)MATHCrossRefMathSciNetGoogle 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)PubMedCrossRefADSGoogle Scholar
- 25.Bao G.: Mechanics of biomolecules. J. Mech. Phys. Sol. 50, 2237–2274 (2002)MATHCrossRefADSGoogle 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)CrossRefGoogle 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)PubMedADSGoogle 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)CrossRefGoogle 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)PubMedADSGoogle Scholar
- 33.Karplus M., Kushick S.: Method for estimating the configurational entropy of macromolecules. Macromolecules 14, 325–332 (1981)CrossRefADSGoogle 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)CrossRefADSGoogle Scholar
- 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.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.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)PubMedGoogle 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)PubMedGoogle 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)PubMedGoogle 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)PubMedGoogle 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)CrossRefADSGoogle 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)PubMedCrossRefADSGoogle 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)PubMedCrossRefADSGoogle 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)CrossRefADSGoogle Scholar
- 46.Buehler M.J., Wong S.Y.: Entropic elasticity controls nanomechanics of single tropocollagen molecules. Biophys. J. 93, 37–43 (2007)PubMedCrossRefADSGoogle Scholar
- 47.Jarzynski C.: Nonequilibrium equality for free energy differences. Phys. Rev. Lett. 78, 2690–2693 (1997)CrossRefADSGoogle 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)CrossRefADSGoogle 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)PubMedCrossRefADSGoogle 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)PubMedCrossRefGoogle Scholar
- 52.Isralewitz B., Gao M., Schulten K.: Steered molecular dynamics and mechanical functions of proteins. Curr. Opin. Struct. Biol. 11, 224–230 (2001)PubMedCrossRefGoogle Scholar
- 53.Sotomayor M., Schulten K.: Single-molecule experiments in vitro and in silico. Science 316, 1144–1148 (2007)PubMedCrossRefADSGoogle 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)CrossRefGoogle 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)PubMedCrossRefGoogle Scholar
- 56.Matthews B.: No code for recognition. Nature 335, 294–295 (1988)PubMedCrossRefADSGoogle Scholar
- 57.Suzuki M., Brenner S., Gerstein M., Yagi N.: DNA recognition code of transcription factors. Protein Eng. 8, 319–328 (1995)PubMedCrossRefGoogle 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)PubMedCrossRefGoogle Scholar
- 59.Bustamante C., Marko J.F., Siggia E.D., Smith S.: Entropic elasticity of lambda-phage DNA. Science 265, 1599–1600 (1994)PubMedCrossRefADSGoogle 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)CrossRefADSGoogle 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)PubMedGoogle 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)CrossRefGoogle 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)PubMedCrossRefGoogle 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)CrossRefGoogle 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)PubMedCrossRefGoogle 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)PubMedCrossRefGoogle 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)CrossRefGoogle 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)PubMedCrossRefGoogle 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)PubMedCrossRefGoogle 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)PubMedCrossRefADSGoogle 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)PubMedCrossRefADSGoogle 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)PubMedCrossRefADSGoogle 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)PubMedCrossRefGoogle 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)PubMedCrossRefADSGoogle 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)CrossRefGoogle 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)PubMedCrossRefADSGoogle Scholar
- 79.Mather W.H., Fox R.F.: Kinesin’s biased stepping mechanism: amplification of neck linker zippering. Biophys. J. 91, 2416–2426 (2006)PubMedCrossRefADSGoogle 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)CrossRefADSGoogle 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)CrossRefADSGoogle 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)PubMedCrossRefADSGoogle Scholar
- 84.Laio A., Parrinello M.: Escaping free energy minima. Proc. Natl. Acad. Sci. USA 99, 12562–12566 (2002)PubMedCrossRefADSGoogle Scholar
- 85.Bussi G., Laio A., Parrinello M.: Equilibrium free energies from nonequilibrium metadynamics. Phys. Rev. Lett. 96, 090601 (2006)PubMedCrossRefADSGoogle 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)PubMedCrossRefADSGoogle 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)PubMedCrossRefADSGoogle 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)PubMedCrossRefGoogle 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)PubMedCrossRefADSGoogle 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)PubMedCrossRefADSGoogle 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)CrossRefGoogle 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)CrossRefADSGoogle 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)PubMedCrossRefGoogle 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)PubMedCrossRefGoogle Scholar
- 97.Kmiecik S., Kolinski A.: Characterization of protein-folding pathways by reduced-space modeling. Proc. Natl. Acad. Sci. USA 104, 12330–12335 (2007)PubMedCrossRefADSGoogle 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)CrossRefGoogle Scholar
- 99.Miao Y., Ortoleva P.J.: Viral structural transitions: an all-atom multiscale theory. J. Chem. Phys. 125, 214901 (2006)PubMedCrossRefADSGoogle Scholar