Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-28T11:10:18.082Z Has data issue: false hasContentIssue false
  • English
  • Français

Atomistic and continuum modeling of mechanical properties of collagen: Elasticity, fracture, and self-assembly

Published online by Cambridge University Press:  01 August 2006

Markus J. Buehler
Markus J. Buehler*
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
*
a) Address all correspondence to this author. e-mail: [email protected]
Get access

Abstract

We report studies of the mechanical properties of tropocollagen molecules under different types of mechanical loading including tension, compression, shear, and bending. Our modeling yields predictions of the fracture strength of single tropocollagen molecules and polypeptides, and also allows for quantification of the interactions between tropocollagen molecules. Atomistic modeling predicts a persistence length of tropocollagen molecules ξ ≈ 23.4 nm, close to experimental measurements. Our studies suggest that to describe large-strain or hyperelastic properties, it is critical to include a correct description of the bond behavior and breaking processes at large bond stretch, information that stems from the quantum chemical details of bonding. We use full atomistic calculations to derive parameters for a mesoscopic bead-spring model of tropocollagen molecules. We demonstrate that the mesoscopic model enables one to study the finite temperature, long-time scale behavior of tropocollagen fibers, illustrating the dynamics of solvated tropocollagen molecules for different molecular lengths.

Keywords

BiologicalFractureSelf-assembly
Type
Articles
Information
Journal of Materials Research , Volume 21 , Issue 8 , August 2006 , pp. 1947 - 1961
Copyright
Copyright © Materials Research Society 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Langer, R., Tirrell, D.A.: Designing materials for biology and medicine. Nature 428, 487 (2004).CrossRefGoogle ScholarPubMed
2.Petka, W.A., Harden, J.L., McGrath, K.P., Wirtz, D., Tirrell, D.A.: Reversible hydrogels from self-assembling artificial proteins. Science 281, 389 (1998).CrossRefGoogle ScholarPubMed
3.Maskarinec, S.A., Tirrell, D.A.: Protein engineering approaches to biomaterials design. Curr. Opin. Biotechnol. 16, 422 (2005).CrossRefGoogle ScholarPubMed
4.Smeenk, J.M., Otten, M.B.J., Thies, J., Tirrell, D.A., Stunnenberg, H.G., van Hest, J.C.M.: Controlled assembly of macromolecular beta-sheet fibrils. Angew. Chem., Int. Ed. 44, 1968 (2005).CrossRefGoogle ScholarPubMed
5.Mock, M.L., Michon, T., van Hest, J.C.M., Tirrell, D.A.: Stereoselective incorporation of an unsaturated isoleucine analogue into a protein expressed in E. coli. Chembiochem. 7, 83 (2006).CrossRefGoogle ScholarPubMed
6.Diehl, M.R., Zhang, K.C., Lee, H.J., Tirrell, D.A.: Engineering cooperativity in biomotor-protein assemblies. Science 311, 1468 (2006).CrossRefGoogle ScholarPubMed
7.Bozec, L., Horton, M.: Topography and mechanical properties of single molecules of type I collagen using atomic force microscopy. Biophys. J. 88, 4223 (2005).CrossRefGoogle ScholarPubMed
8.Bhattacharjee, A., Bansal, M.: Collagen structure: The Madras triple helix and the current scenario. IUBMB Life 57, 161 (2005).CrossRefGoogle ScholarPubMed
9.Borel, J.P., Monboisse, J.C.: Collagens—Why such a complicated structure. C. R. Seances Soc. Biol. Fil. 187, 124 (1993).Google Scholar
10.Mithieux, S.M., Elastin, A.S. Weiss, in Fibrous Proteins: Coiled-Coils, Collagen and Elastomers. Advances in Protein Chemistry, Vol. 70, edited by Parry, D.A.D. and Squire, J.M. (Elsevier Academic Press, Amsterdam, 2005), p. 437.Google Scholar
11.Li, B., Daggett, V.: Molecular basis for the extensibility of elastin. J. Muscle Res. Cell Motil. 23, 561 (2002).CrossRefGoogle ScholarPubMed
12.Hellmich, C., Ulm, F.J.: Are mineralized tissues open crystal foams reinforced by crosslinked collagen? Some energy arguments. J. Biomech. 35, 1199 (2002).CrossRefGoogle ScholarPubMed
13.Kramer, R.Z., Venugopal, M.G., Bella, J., Mayville, P., Brodsky, B., Berman, H.M.: Staggered molecular packing in crystals of a collagen-like peptide with a single charged pair. J. Mol. Biol. 301, 1191 (2000).CrossRefGoogle ScholarPubMed
14.Zervakis, M., Gkoumplias, V., Tzaphlidou, M.: Analysis of fibrous proteins from electron microscopy images. Med. Eng. Phys. 27, 655 (2005).CrossRefGoogle ScholarPubMed
15.Layton, B.E., Sullivan, S.M., Palermo, J.J., Buzby, G.J., Gupta, R., Stallcup, R.E.: Nanomanipulation and aggregation limitations of self-assembling structural proteins. Microelectron. J. 36, 644 (2005).CrossRefGoogle Scholar
16.An, K.N., Sun, Y.L., Luo, Z.P.: Flexibility of type I collagen and mechanical property of connective tissue. Biorheology 41, 239 (2004).Google ScholarPubMed
17.Sun, Y.L., Luo, Z.P., Fertala, A., An, K.N.: Stretching type II collagen with optical tweezers. J. Biomech. 37, 1665 (2004).CrossRefGoogle ScholarPubMed
18.Sun, Y.L., Luo, Z.P., Fertala, A., An, K.N.: Direct quantification of the flexibility of type I collagen monomer. Biochem. Biophys. Res. Commun. 295, 382 (2002).CrossRefGoogle ScholarPubMed
19.Arnoux, P.J., Bonnoit, J., Chabrand, P., Jean, M., Pithioux, M.: Numerical damage models using a structural approach: Application in bones and ligaments. Eur. Phys. J. Appl. Phys. 17, 65 (2002).CrossRefGoogle Scholar
20.Waite, J.H., Qin, X.X., Coyne, K.J.: The peculiar collagens of mussel byssus. Matrix Biol. 17, 93 (1998).CrossRefGoogle ScholarPubMed
21.Lorenzo, A.C., Caffarena, E.R.: Elastic properties, Young's modulus determination and structural stability of the tropocollagen molecule: A computational study by steered molecular dynamics. J. Biomech. 38, 1527 (2005).CrossRefGoogle ScholarPubMed
22.Persikov, A.V., Ramshaw, J.A.M., Kirkpatrick, A., Brodsky, B.: Electrostatic interactions involving lysine make major contributions to collagen triple-helix stability. Biochemistry 44, 1414 (2005).CrossRefGoogle ScholarPubMed
23.Israelowitz, M., Rizvi, S.W.H., Kramer, J., von Schroeder, H.P.: Computational modeling of type I collagen fibers to determine the extracellular matrix structure of connective tissues. Protein Eng. Des. Sel. 18, 329 (2005).CrossRefGoogle ScholarPubMed
24.Mooney, S.D., Klein, T.E.: Structural models of osteogenesis imperfecta-associated variants in the COL1A1 gene. Mol. Cell. Proteomics 1, 868 (2002).CrossRefGoogle ScholarPubMed
25.Mooney, S.D., Kollman, P.A., Klein, T.E.: Conformational preferences of substituted prolines in the collagen triple helix. Biopolymers 64, 63 (2002).CrossRefGoogle ScholarPubMed
26.Mooney, S.D., Huang, C.C., Kollman, P.A., Klein, T.E.: Computed free energy differences between point mutations in a collagen-like peptide. Biopolymers 58, 347 (2001).3.0.CO;2-M>CrossRefGoogle Scholar
27.Bischoff, J.E., Arruda, E.M., Grosh, K.: Finite element modeling of human skin using an isotropic, nonlinear elastic constitutive model. J. Biomech. 33, 645 (2000).CrossRefGoogle ScholarPubMed
28.Freeman, J.W., Silver, F.H.: Elastic energy storage in unmineralized and mineralized extracellular matrices (ECMs): A comparison between molecular modeling and experimental measurements. J. Theor. Biol. 229, 371 (2004).CrossRefGoogle ScholarPubMed
29.Buehler, M.J., Abraham, F.F., Gao, H.: Hyperelasticity governs dynamic fracture at a critical length scale. Nature 426, 141 (2003).CrossRefGoogle Scholar
30.Buehler, M.J., Gao, H.: Dynamical fracture instabilities due to local hyperelasticity at crack tips. Nature 439, 307 (2006).CrossRefGoogle ScholarPubMed
31.MacKerell, A.D., Bashford, D., Bellott, M., Dunbrack, R.L., Evanseck, J.D., Field, M.J., Fischer, S., Gao, J., Guo, H., Ha, S., al., et: All-atom empirical potential for molecular modeling and dynamics studies of proteins. J. Phys. Chem. B 102, 3586 (1998).CrossRefGoogle ScholarPubMed
32.Phillips, J.C., Braun, R., Wang, W., Gumbart, J., Tajkhorshid, E., Villa, E., Chipot, C., Skeel, R.D., Kale, L., Schulten, K.: Scalable molecular dynamics with NAMD. J. Comput. Chem. 26, 1781 (2005).CrossRefGoogle ScholarPubMed
33.Nelson, M.T., Humphrey, W., Gursoy, A., Dalke, A., Kale, L.V., Skeel, R.D., Schulten, K.: NAMD: A parallel, object oriented molecular dynamics program. Int. J. Supercomp. Appl. High Perf. Comput. 10, 251 (1996).Google Scholar
34.Anderson, D.Collagen self-assembly: A complementary experimental and theoretical perspective. University of Toronto, 2005.Google Scholar
35.Brenner, D.W., Shenderova, O.A., Harrison, J.A., Stuart, S.J., Ni, B., Sinnott, S.B.: A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys.: Condens. Matter 14, 783 (2002).Google Scholar
36.Stuart, S.J., Tutein, A.B., Harrison, J.A.: A reactive potential for hydrocarbons with intermolecular interactions. J. Chem. Phys. 112, 6472 (2000).CrossRefGoogle Scholar
37.Duin, A.C.T.v., Strachan, A., Stewman, S., Zhang, Q., Xu, X., Goddard, W.A.: ReaxFF SiO: Reactive force field for silicon and silicon oxide systems. J. Phys. Chem. A 107, 3803 (2003).CrossRefGoogle Scholar
38.Duin, A.C.T.v., Dasgupta, S., Lorant, F., Goddard, W.A.: ReaxFF: A reactive force field for hydrocarbons. J. Phys. Chem. A 105, 9396 (2001).CrossRefGoogle Scholar
39.Buehler, M.J., Duin, A.C.T.v., Goddard, W.A.: Multi-paradigm modeling of dynamical crack propagation in silicon using a reactive force field. Phys. Rev. Lett. 96, 09505 (2006).CrossRefGoogle Scholar
40.Strachan, A., van Duin, A.C.T., Chakraborty, D., Dasgupta, S., Goddard, W.A.: Shock waves in high-energy materials: The initial chemical events in nitramine RDX. Phys. Rev. Lett. 91, 098301 (2003).CrossRefGoogle ScholarPubMed
41.Nielson, K.D., Duin, A.C.T.v., Oxgaard, J., Deng, W., Goddard, W.A.: Development of the ReaxFF reactive force field for describing transition metal catalyzed reactions, with application to the initial stages of the catalytic formation of carbon nanotubes. J. Phys. Chem. A 109, 49 (2005).CrossRefGoogle Scholar
42.Han, S.S., van Duin, A.C.T., Goddard, W.A., Lee, H.M.: Optimization and application of lithium parameters for the reactive force field, ReaxFF. J. Phys. Chem. A. 109, 4575 (2005).CrossRefGoogle ScholarPubMed
43.Chenoweth, K., Cheung, S., van Duin, A.C.T., Goddard, W.A., Kober, E.M.: Simulations on the thermal decomposition of a poly(dimethylsiloxane) polymer using the ReaxFF reactive force field. J. Am. Chem. Soc. 127, 7192 (2005).CrossRefGoogle ScholarPubMed
44.Strachan, A., Kober, E.M., van Duin, A.C.T., Oxgaard, J., Goddard, W.A.: Thermal decomposition of RDX from reactive molecular dynamics. J. Chem. Phys. 107, 3803 (2005).Google Scholar
45.Cheung, S., Deng, W.Q., van Duin, A.C.T., Goddard, W.A.: ReaxFF(MgH) reactive force field for magnesium hydride systems. J. Phys. Chem. A 109, 851 (2005).CrossRefGoogle ScholarPubMed
46.Nielson, K.D., van Duin, A.C.T., Oxgaard, J., Deng, W., Goddard, W.A.: Development of the ReaxFF reactive force field for describing transition metal catalyzed reactions, with application to the initial stages of the catalytic formation of carbon nanotubes. J. Phys. Chem. A 109, 493 (2005).CrossRefGoogle Scholar
47.Tao, L., Buehler, M.J., Duin, A.C.T.v., Goddard, W.A. Mixed hybrid Dreiding-ReaxFF calculations for modeling enzymatic reactions in proteins. (2005, unpublished).Google Scholar
48.Datta, D., Duin, A.C.T.V., and Goddard, W.A.: Extending ReaxFF to biomacromolecules. (2005, unpublished).Google Scholar
49.Rappé, A.K., Goddard, W.A.: Charge eqilibration for molecular-dynamics simulations. J. Phys. Chem. 95, 3358 (1991).CrossRefGoogle Scholar
50.Buehler, M.J., Dodson, J., Meulbroek, P., Duin, A., and Goddard, W.A.: The computational materials design facility (CMDF): A powerful framework for multiparadigm multi-scale simulations, in Combinatorial Methods and Informatics in Materials Science edited by Fasolka, M.J., Wang, Q., Potyrailo, R.A., Chikyow, T., Schubert, U.S., and Korkin, A. (Mater. Res. Soc. Symp. Proc.894 Warrendale, PA, 2006), p. 327.Google Scholar
51.Stone, J., Gullingsrud, J., Grayson, P., and Schulten, K.: A system for interactive molecular dynamics simulation, in 2001 ACM Symposium on Interactive 3D Graphics edited by Hughes, J.F. and Sequin, C.H. (ACM Press, New York, 2001), pp. 191–194.CrossRefGoogle Scholar
52.Humphrey, W., Dalke, A., Schulten, K.: VMD: Visual molecular dynamics. J. Mol. Graphics 14, 33 (1996).CrossRefGoogle ScholarPubMed
53.Allen, M.P. and Tildesley, D.J., Computer Simulation of Liquids (Oxford University Press, New York, 1989).Google Scholar
54.Ercolessi, F., Adams, J.B.: Interatomic potentials from 1st principle-calculations—the force matching method. Europhys. Lett. 28, 583 (1994).CrossRefGoogle Scholar
55.Plimpton, S.: Fast parallel algorithms for short-range molecular-dynamics. J. Comput. Phys. 117, 1 (1995).CrossRefGoogle Scholar
56.Ritchie, R.O., Kruzic, J.J., Muhlstein, C.L., Nalla, R.K., Stach, E.A.: Characteristic dimensions and the micro-mechanisms of fracture and fatigue in “nano” and “bio” materials. Int. J. Fract. 128, 1 (2004).CrossRefGoogle Scholar
57.Nalla, R.K., Kruzic, J.J., Kinney, J.H., Ritchie, R.O.: Mechanistic aspects of fracture and R-curve behavior in human cortical bone. Biomaterials 26, 217 (2005).CrossRefGoogle ScholarPubMed
58.Nalla, R.K., Kinney, J.H., Ritchie, R.O.: Effect of orientation on the in vitro fracture toughness of dentin: The role of toughening mechanisms. Biomaterials 24, 3955 (2003).CrossRefGoogle ScholarPubMed
59.Pearlman, D.A., Case, D.A., Caldwell, J.W., Ross, W.S., Cheatham, T.E., Debolt, S., Ferguson, D., Seibel, G., Kollman, P.: AMBER, A package of computer-programs for applying molecular mechanics, normal-mode analysis, molecular-dynamics and free-energy calculations to simulate the structural and energetic properties of molecules. Comput. Phys. Commun. 91, 1 (1995).CrossRefGoogle Scholar