Skip to main content
Log in

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

  • Article
  • Published:
Journal of Materials Research Aims and scope Submit manuscript

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.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. Langer, D.A. Tirrell: Designing materials for biology and medicine. Nature 428, 487 (2004).

    CAS  Google Scholar 

  2. W.A. Petka, J.L. Harden, K.P. McGrath, D. Wirtz, D.A. Tirrell: Reversible hydrogels from self-assembling artificial proteins. Science 281, 389 (1998).

    CAS  Google Scholar 

  3. S.A. Maskarinec, D.A. Tirrell: Protein engineering approaches to biomaterials design. Curr. Opin. Biotechnol. 16, 422 (2005).

    CAS  Google Scholar 

  4. J.M. Smeenk, M.B.J Otten, J. Thies, D.A. Tirrell, H.G. Stunnenberg, J.C.M. van Hest: Controlled assembly of macromolecular beta-sheet fibrils. Angew. Chem., Int. Ed. 44, 1968 (2005).

    CAS  Google Scholar 

  5. M.L. Mock, T. Michon, J.C.M. van Hest, D.A. Tirrell: Stereoselective incorporation of an unsaturated isoleucine analogue into a protein expressed in E. coli. Chembiochem. 7, 83 (2006).

    CAS  Google Scholar 

  6. M.R. Diehl, K.C. Zhang, H.J. Lee, D.A. Tirrell: Engineering cooperativity in biomotor-protein assemblies. Science 311, 1468 (2006).

    CAS  Google Scholar 

  7. L. Bozec, M. Horton: Topography and mechanical properties of single molecules of type I collagen using atomic force microscopy. Biophys. J. 88, 4223 (2005).

    CAS  Google Scholar 

  8. A. Bhattacharjee, M. Bansal: Collagen structure: The Madras triple helix and the current scenario. IUBMB Life 57, 161 (2005).

    CAS  Google Scholar 

  9. J.P. Borel, J.C. Monboisse: Collagens—Why such a complicated structure. C. R. Seances Soc. Biol. Fil. 187, 124 (1993).

    CAS  Google Scholar 

  10. S.M. Mithieux, A.S. Weiss Elastin: Elastin, in Fibrous Proteins: Coiled-Coils, Collagen and Elastomers. Advances in Protein Chemistry, Vol. 70, edited by D.A.D Parry and J.M. Squire (Elsevier Academic Press, Amsterdam, 2005), p. 437.

    CAS  Google Scholar 

  11. B. Li, V. Daggett: Molecular basis for the extensibility of elastin. J. Muscle Res. Cell Motil. 23, 561 (2002).

    Google Scholar 

  12. C. Hellmich, F.J. Ulm: Are mineralized tissues open crystal foams reinforced by crosslinked collagen? Some energy arguments. J. Biomech. 35, 1199 (2002).

    Google Scholar 

  13. R.Z. Kramer, M.G. Venugopal, J. Bella, P. Mayville, B. Brodsky, H.M. Berman: Staggered molecular packing in crystals of a collagen-like peptide with a single charged pair. J. Mol. Biol. 301, 1191 (2000).

    CAS  Google Scholar 

  14. M. Zervakis, V. Gkoumplias, M. Tzaphlidou: Analysis of fibrous proteins from electron microscopy images. Med. Eng. Phys. 27, 655 (2005).

    CAS  Google Scholar 

  15. B.E. Layton, S.M. Sullivan, J.J. Palermo, G.J. Buzby, R. Gupta, R.E. Stallcup: Nanomanipulation and aggregation limitations of self-assembling structural proteins. Microelectron. J. 36, 644 (2005).

    CAS  Google Scholar 

  16. K.N. An, Y.L. Sun, Z.P. Luo: Flexibility of type I collagen and mechanical property of connective tissue. Biorheology 41, 239 (2004).

    CAS  Google Scholar 

  17. Y.L. Sun, Z.P. Luo, A. Fertala, K.N. An: Stretching type II collagen with optical tweezers. J. Biomech. 37, 1665 (2004).

    Google Scholar 

  18. Y.L. Sun, Z.P. Luo, A. Fertala, K.N. An: Direct quantification of the flexibility of type I collagen monomer. Biochem. Biophys. Res. Commun. 295, 382 (2002).

    CAS  Google Scholar 

  19. P.J. Arnoux, J. Bonnoit, P. Chabrand, M. Jean, M. Pithioux: Numerical damage models using a structural approach: Application in bones and ligaments. Eur. Phys. J. Appl. Phys. 17, 65 (2002).

    Google Scholar 

  20. J.H. Waite, X.X. Qin, K.J. Coyne: The peculiar collagens of mussel byssus. Matrix Biol. 17, 93 (1998).

    CAS  Google Scholar 

  21. A.C. Lorenzo, E.R. Caffarena: 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).

    Google Scholar 

  22. A.V. Persikov, J.A.M Ramshaw, A. Kirkpatrick, B. Brodsky: Electrostatic interactions involving lysine make major contributions to collagen triple-helix stability. Biochemistry 44, 1414 (2005).

    CAS  Google Scholar 

  23. M. Israelowitz, S.W.H Rizvi, J. Kramer, H.P. von Schroeder: Computational modeling of type I collagen fibers to determine the extracellular matrix structure of connective tissues. Protein Eng. Des. Sel. 18, 329 (2005).

    CAS  Google Scholar 

  24. S.D. Mooney, T.E. Klein: Structural models of osteogenesis imperfecta-associated variants in the COL1A1 gene. Mol. Cell. Proteomics 1, 868 (2002).

    CAS  Google Scholar 

  25. S.D. Mooney, P.A. Kollman, T.E. Klein: Conformational preferences of substituted prolines in the collagen triple helix. Biopolymers 64, 63 (2002).

    CAS  Google Scholar 

  26. S.D. Mooney, C.C. Huang, P.A. Kollman, T.E. Klein: Computed free energy differences between point mutations in a collagen-like peptide. Biopolymers 58, 347 (2001).

    CAS  Google Scholar 

  27. J.E. Bischoff, E.M. Arruda, K. Grosh: Finite element modeling of human skin using an isotropic, nonlinear elastic constitutive model. J. Biomech. 33, 645 (2000).

    CAS  Google Scholar 

  28. J.W. Freeman, F.H. Silver: Elastic energy storage in unmineralized and mineralized extracellular matrices (ECMs): A comparison between molecular modeling and experimental measurements. J. Theor. Biol. 229, 371 (2004).

    CAS  Google Scholar 

  29. M.J. Buehler, F.F. Abraham, H. Gao: Hyperelasticity governs dynamic fracture at a critical length scale. Nature 426, 141 (2003).

    CAS  Google Scholar 

  30. M.J. Buehler, H. Gao: Dynamical fracture instabilities due to local hyperelasticity at crack tips. Nature 439, 307 (2006).

    CAS  Google Scholar 

  31. A.D. MacKerell, D. Bashford, M. Bellott, R.L. Dunbrack, J.D. Evanseck, M.J. Field, S. Fischer, J. Gao, H. Guo, S. Ha, et al.: All-atom empirical potential for molecular modeling and dynamics studies of proteins. J. Phys. Chem. B 102, 3586 (1998).

    CAS  Google Scholar 

  32. J.C. Phillips, R. Braun, W. Wang, J. Gumbart, E. Tajkhorshid, E. Villa, C. Chipot, R.D. Skeel, L. Kale, K. Schulten: Scalable molecular dynamics with NAMD. J. Comput. Chem. 26, 1781 (2005).

    CAS  Google Scholar 

  33. M.T. Nelson, W. Humphrey, A. Gursoy, A. Dalke, L.V. Kale, R.D. Skeel, K. Schulten: NAMD: A parallel, object oriented molecular dynamics program. Int. J. Supercomp. Appl. High Perf. Comput. 10, 251 (1996).

    Google Scholar 

  34. D. Anderson: Collagen self-assembly: A complementary experimental and theoretical perspective. University of Toronto, 2005.

    Google Scholar 

  35. D.W. Brenner, O.A. Shenderova, J.A. Harrison, S.J. Stuart, B. Ni, S.B. Sinnott: A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys.: Condens. Matter 14, 783 (2002).

    CAS  Google Scholar 

  36. S.J. Stuart, A.B. Tutein, J.A. Harrison: A reactive potential for hydrocarbons with intermolecular interactions. J. Chem. Phys. 112, 6472 (2000).

    CAS  Google Scholar 

  37. A.C.T.v. Duin, A. Strachan, S. Stewman, Q. Zhang, X. Xu, W.A. Goddard: ReaxFF SiO: Reactive force field for silicon and silicon oxide systems. J. Phys. Chem. A 107, 3803 (2003).

    Google Scholar 

  38. A.C.T.v. Duin, S. Dasgupta, F. Lorant, W.A. Goddard: ReaxFF: A reactive force field for hydrocarbons. J. Phys. Chem. A 105, 9396 (2001).

    Google Scholar 

  39. M.J. Buehler, A.C.T.v. Duin, W.A. Goddard: Multi-paradigm modeling of dynamical crack propagation in silicon using a reactive force field. Phys. Rev. Lett. 96, 09505 (2006).

    Google Scholar 

  40. A. Strachan, A.C.T. van Duin, D. Chakraborty, S. Dasgupta, W.A. Goddard: Shock waves in high-energy materials: The initial chemical events in nitramine RDX. Phys. Rev. Lett. 91, 098301 (2003).

    Google Scholar 

  41. K.D. Nielson, A.C.T.v. Duin, J. Oxgaard, W. Deng, W.A. Goddard: 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).

    Google Scholar 

  42. S.S. Han, A.C.T. van Duin, W.A. Goddard, H.M. Lee: Optimization and application of lithium parameters for the reactive force field, ReaxFF. J. Phys. Chem. A. 109, 4575 (2005).

    CAS  Google Scholar 

  43. K. Chenoweth, S. Cheung, A.C.T. van Duin, W.A. Goddard, E.M. Kober: Simulations on the thermal decomposition of a poly(dimethylsiloxane) polymer using the ReaxFF reactive force field. J. Am. Chem. Soc. 127, 7192 (2005).

    CAS  Google Scholar 

  44. A. Strachan, E.M. Kober, A.C.T. van Duin, J. Oxgaard, W.A. Goddard: Thermal decomposition of RDX from reactive molecular dynamics. J. Chem. Phys. 107, 3803 (2005).

    Google Scholar 

  45. S. Cheung, W.Q. Deng, A.C.T. van Duin, W.A. Goddard: ReaxFF(MgH) reactive force field for magnesium hydride systems. J. Phys. Chem. A 109, 851 (2005).

    CAS  Google Scholar 

  46. K.D. Nielson, A.C.T. van Duin, J. Oxgaard, W. Deng, W.A. Goddard: 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).

    CAS  Google Scholar 

  47. L. Tao, M.J. Buehler, A.C.T.v. Duin, W.A. Goddard: Mixed hybrid Dreiding-ReaxFF calculations for modeling enzymatic reactions in proteins. (2005, unpublished).

    Google Scholar 

  48. D. Datta, A.C.T.V Duin, and W.A. Goddard: Extending ReaxFF to biomacromolecules. (2005, unpublished).

    Google Scholar 

  49. A.K. Rappé, W.A. Goddard: Charge eqilibration for molecular-dynamics simulations. J. Phys. Chem. 95, 3358 (1991).

    Google Scholar 

  50. M.J. Buehler, J. Dodson, P. Meulbroek, A. Duin, and W.A. Goddard: The computational materials design facility (CMDF): A powerful framework for multiparadigm multi-scale simulations, in Combinatorial Methods and Informatics in Materials Science edited by M.J. Fasolka, Q. Wang, R.A. Potyrailo, T. Chikyow, U.S. Schubert, and A. Korkin (Mater. Res. Soc. Symp. Proc.894, Warrendale, PA, 2006), p. 327.

    Google Scholar 

  51. J. Stone, J. Gullingsrud, P. Grayson, and K. Schulten: A system for interactive molecular dynamics simulation, in 2001 ACM Symposium on Interactive 3D Graphics edited by J.F. Hughes and C.H. Sequin (ACM Press, New York, 2001), pp. 191–194.

  52. W. Humphrey, A. Dalke, K. Schulten: VMD: Visual molecular dynamics. J. Mol. Graphics 14, 33 (1996).

    CAS  Google Scholar 

  53. M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids (Oxford University Press, New York, 1989).

    Google Scholar 

  54. F. Ercolessi, J.B. Adams: Interatomic potentials from 1st principle-calculations—the force matching method. Europhys. Lett. 28, 583 (1994).

    Google Scholar 

  55. S. Plimpton: Fast parallel algorithms for short-range molecular-dynamics. J. Comput. Phys. 117, 1 (1995).

    CAS  Google Scholar 

  56. R.O. Ritchie, J.J. Kruzic, C.L. Muhlstein, R.K. Nalla, E.A. Stach: Characteristic dimensions and the micro-mechanisms of fracture and fatigue in “nano” and “bio” materials. Int. J. Fract. 128, 1 (2004).

    CAS  Google Scholar 

  57. R.K. Nalla, J.J. Kruzic, J.H. Kinney, R.O. Ritchie: Mechanistic aspects of fracture and R-curve behavior in human cortical bone. Biomaterials 26, 217 (2005).

    CAS  Google Scholar 

  58. R.K. Nalla, J.H. Kinney, R.O. Ritchie: Effect of orientation on the in vitro fracture toughness of dentin: The role of toughening mechanisms. Biomaterials 24, 3955 (2003).

    CAS  Google Scholar 

  59. D.A. Pearlman, D.A. Case, J.W. Caldwell, W.S. Ross, T.E. Cheatham, S. Debolt, D. Ferguson, G. Seibel, P. Kollman: 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).

    CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Markus J. Buehler.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Buehler, M.J. Atomistic and continuum modeling of mechanical properties of collagen: Elasticity, fracture, and self-assembly. Journal of Materials Research 21, 1947–1961 (2006). https://doi.org/10.1557/jmr.2006.0236

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/jmr.2006.0236

Navigation