Multiscale Model of Collagen Fibril in Bone: Elastic Response
Publication: Journal of Engineering Mechanics
Volume 140, Issue 3
Abstract
In this paper, the development of a multiscale model of collagen fibril is described using a hierarchical approach by combining molecular dynamics simulations and FEM. Steered molecular dynamics was used to investigate the mechanical response of collagen under various conditions that mimic the organization of collagen molecules and mineral inside the collagen fibril. The steered molecular dynamics simulations showed that the elastic properties of collagen molecules are significantly higher in the proximity of mineral. The properties of collagen and interfaces at the molecular scale were carried over to the continuum model of collagen fibril. The model of collagen fibril (measuring approximately in length and 50 nm in diameter) was constructed using FEM. Results showed that the deformation properties of collagen fibril are significantly influenced by interactions between collagen and mineral at the molecular scale, significantly affecting the elastic properties of fibril. Here, a model of fibril is presented that, for the first time, incorporates the effects of interactions occurring between the mineral and the collagen at the molecular scale.
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Acknowledgments
The authors acknowledge TeraGrid for computational resources at the National Center for Supercomputing Applications (NCSA). The computational resources at North Dakota State University (NDSU) Center for Computationally Assisted Science & Technology (CCAST) are acknowledged. The authors thank Dr. Greg Wettstein for hardware and software support. S. M. P. acknowledges support from North Dakota Experimental Program to Stimulate Competitive Research (NDEPSCoR).
References
Almora-Barrios, N., and de Leeuw, N. H. (2010). “A density functional theory study of the interaction of collagen peptides with hydroxyapatite surfaces.” Langmuir, 26(18), 14535–14542.
Arsenault, A. L. (1991). “Image-analysis of collagen-associated mineral distribution in cryogenically prepared turkey leg tendons.” Calcif. Tissue Int., 48(1), 56–62.
Bhowmik, R., Katti, K. S., and Katti, D. R. (2007a). “Molecular dynamics simulation of hydroxyapatite-polyacrylic acid interfaces.” Polymer (Guildf.), 48(2), 664–674.
Bhowmik, R., Katti, K. S., and Katti, D. R. (2007b). “Mechanics of molecular collagen is influenced by hydroxyapatite in natural bone.” J. Mater. Sci., 42(21), 8795–8803.
Bhowmik, R., Katti, K. S., and Katti, D. R. (2008). “Influence of mineral on the load deformation behavior of polymer in hydroxyapatite-polyacrylic acid nanocomposite biomaterials: A steered molecular dynamics study.” J. Nanosci. Nanotechnol., 8(4), 2075–2084.
Bhowmik, R., Katti, K. S., and Katti, D. R. (2009). “Mechanisms of load-deformation behavior of molecular collagen in hydroxyapatite-tropocollagen molecular system: Steered molecular dynamics study.” J. Eng. Mech., 413–421.
Bonar, L. C., Lees, S., and Mook, H. A. (1985). “Neutron diffraction studies of collagen in fully mineralized bone.” J. Mol. Biol., 181(2), 265–270.
Brooks, B. R., Bruccoleri, R. E., Olafson, B. D., States, D. J., Swaminathan, S., and Karplus, M. (1983). “CHARMM: A program for macromolecular energy, minimization, and dynamics calculations.” J. Comput. Chem., 4(2), 187–217.
Buehler, M. J. (2006). “Nature designs tough collagen: Explaining the nanostructure of collagen fibrils.” Proc. Natl. Acad. Sci. USA, 103(33), 12285–12290.
Buehler, M. J. (2007). “Molecular nanomechanics of nascent bone: Fibrillar toughening by mineralization.” Nanotechnology, 18(29), 295102.
Buehler, M. J. (2008). “Nanomechanics of collagen fibrils under varying cross-link densities: Atomistic and continuum studies.” J. Mech. Behav. Biomed. Mater., 1(1), 59–67.
Currey, J. D. (1990). “Biomechanics of mineralized skeletons.” Skeletal biomineralization: Patterns, processes, and evolutionary trends, J. G. Carter, ed., Van Nostrand, New York, 11–25.
Currey, J. D., Zioupos, P., Davies, P., and Casinos, A. (2001). “Mechanical properties of nacre and highly mineralized bone.” Proc. R. Soc. London, Ser. B, 268(1462), 107–111.
Dorozhkin, S. V., and Epple, M. (2002). “Biological and medical significance of calcium phosphates.” Angew. Chem. Int. Ed., 41(17), 3130–3146.
Dubey, D. K., and Tomar, V. (2009). “Role of the nanoscale interfacial arrangement in mechanical strength of tropocollagen-hydroxyapatite-based hard biomaterials.” Acta Biomater., 5(7), 2704–2716.
Dubey, D. K., and Tomar, V. (2010). “Effect of changes in tropocollagen residue sequence and hydroxyapatite mineral texture on the strength of ideal nanoscale tropocollagen-hydroxyapatite biomaterials.” J. Mater. Sci. Mater. Med., 21(1), 161–171.
Eastoe, J. E., and Eastoe, B. (1954). “The organic constituents of mammalian compact bone.” Biochem. J., 57(3), 453–459.
Fisher, L. W., and Termine, J. D. (1985). “Noncollagenous proteins influencing the local mechanisms of calcification.” Clin. Orthop. Relat. Res., November(200), 362–385.
Fratzl, P., and Weinkamer, R. (2007). “Nature’s hierarchical materials.” Prog. Mater. Sci., 52(8), 1263–1334.
Fritsch, A., Hellmich, C., and Dormieux, L. (2009). “Ductile sliding between mineral crystals followed by rupture of collagen crosslinks: Experimentally supported micromechanical explanation of bone strength.” J. Theor. Biol., 260(2), 230–252.
Gautieri, A., Buehler, M. J., and Redaelli, A. (2009a). “Deformation rate controls elasticity and unfolding pathway of single tropocollagen molecules.” J. Mech. Behav. Biomed. Mater., 2(2), 130–137.
Gautieri, A., Vesentini, S., Redaelli, A., and Buehler, M. J. (2009b). “Intermolecular slip mechanism in tropocollagen nanofibrils.” Int. J. Mater. Res., 100(07), 921–925.
Gautieri, A., Vesentini, S., Redaelli, A., and Buehler, M. J. (2011). “Hierarchical structure and nanomechanics of collagen microfibrils from the atomistic scale up.” Nano Lett., 11(2), 757–766.
Ghosh, P., Katti, D. R., and Katti, K. S. (2007). “Mineral proximity influences mechanical response of proteins in biological mineral-protein hybrid systems.” Biomacromolecules, 8(3), 851–856.
Ghosh, P., Katti, D. R., and Katti, K. S. (2008). “Mineral and protein-bound water and latching action control mechanical behavior at protein-mineral interfaces in biological nanocomposites.” J. Nanomater., 2008, 582973.
Gupta, H. S., et al. (2006). “Fibrillar level fracture in bone beyond the yield point.” Int. J. Fract., 139(3–4), 425–436.
Gupta, H. S., Messmer, P., Roschger, P., Bernstorff, S., Klaushofer, K., and Fratzl, P. (2004). “Synchrotron diffraction study of deformation mechanisms in mineralized tendon.” Phys. Rev. Lett., 93(15), 15801.
Hellmich, C., Barthelemy, J. F., and Dormieux, L. (2004). “Mineral-collagen interactions in elasticity of bone ultrastructure - a continuum micromechanics approach.” Eur. J. Mech. A, Solids, 23(5), 783–810.
Hodge, A. J., and Petruska, J. A. (1963). “Recent studies with the electron microscope on ordered aggregates of the tropocollagen molecule.” Aspects of protein structure, G. N. Ramachandran, ed., Academic Press, London, 289–300.
Katti, D. R., and Katti, K. S. (2001). “Modeling microarchitecture and mechanical behavior of nacre using 3D finite element techniques. Part I: Elastic properties.” J. Mater. Sci., 36(6), 1411–1417.
Katti, D. R., Pradhan, S. M., and Katti, K. S. (2010). “Directional dependence of hydroxyapatite-collagen interactions on mechanics of collagen.” J. Biomech., 43(9), 1723–1730.
Katti, K. S., Katti, D. R., Pradhan, S. M., and Bhosle, A. (2005). “Platelet interlocks are the key to toughness and strength in nacre.” J. Mater. Res., 20(05), 1097–1100.
Landis, W. J. (1995). “The strength of a calcified tissue depends in part on the molecular structure and organization of its constituent mineral crystals in their organic matrix.” Bone, 16(5), 533–544.
Landis, W. J., et al. (1996a). “Mineralization of collagen may occur on fibril surfaces: evidence from conventional and high-voltage electron microscopy and three-dimensional imaging.” J. Struct. Biol., 117(1), 24–35.
Landis, W. J., Hodgens, K. J., Arena, J., Song, M. J., and McEwen, B. F. (1996b). “Structural relations between collagen and mineral in bone as determined by high voltage electron microscopic tomography.” Microsc. Res. Tech., 33(2), 192–202.
Landis, W. J., Song, M. J., Leith, A., McEwen, L., and McEwen, B. F. (1993). “Mineral and organic matrix interaction in normally calcifying tendon visualized in three dimensions by high-voltage electron microscopic tomography and graphic image reconstruction.” J. Struct. Biol., 110(1), 39–54.
Lorenzo, A. C., and Caffarena, E. R. (2005). “Elastic properties, Young’s modulus determination and structural stability of the tropocollagen molecule: A computational study by steered molecular dynamics.” J. Biomech., 38(7), 1527–1533.
Marc 2010 [Computer software]. Santa Ana, CA, MSC Software.
Mentat 2010 [Computer software]. Santa Ana, CA, MSC Software.
Nanci, A. (1999). “Content and distribution of noncollagenous matrix proteins in bone and cementum: Relationship to speed of formation and collagen packing density.” J. Struct. Biol., 126(3), 256–269.
Nylen, M. U., Scott, D. B., and Mosley, V. M. (1960). “Mineralization of turkey leg tendon. II. Collagen-mineral relations revealed by electron and x-ray microscopy.” Calcification in biological systems, R. F. Sognnaes, ed., American Association for the Advancement of Science, Washington, DC, 129–142.
Olszta, M. J., Odom, D. J., Douglas, E. P., and Gower, L. B. (2003). “A new paradigm for biomineral formation: Mineralization via an amorphous liquid-phase precursor.” Connect. Tissue Res., 44(Suppl. 1), 326–334.
Orgel, J. P., Miller, A., Irving, T. C., Fischetti, R. F., Hammersley, A. P., and Wess, T. J. (2001). “The in situ supermolecular structure of type I collagen.” 9(11), 1061–1069.
Pradhan, S. M., Katti, D. R., and Katti, K. S. (2011). “Steered molecular dynamics study of mechanical response of full length and short collagen molecules.” J. Nanomech. Micromech., 104–110.
Rubin, M. A., Rubin, J., and Jasiuk, W. (2004). “SEM and TEM study of the hierarchical structure of C57BL/6J and C3H/HeJ mice trabecular bone.” Bone, 35(1), 11–20.
Saber-Samandari, S., and Gross, K. A. (2009). “Micromechanical properties of single crystal hydroxyapatite by nanoindentation.” Acta Biomater., 5(6), 2206–2212.
Shen, Z. L., Dodge, M. R., Kahn, H., Ballarini, R., and Eppell, S. J. (2008). “Stress-strain experiments on individual collagen fibrils.” Biophys. J., 95(8), 3956–3963.
Sikdar, D., Pradhan, S. M., Katti, D. R., Katti, K. S., and Mohanty, B. (2008). “Altered phase model for polymer clay nanocomposites.” Langmuir, 24(10), 5599–5607.
Streeter, I., and de Leeuw, N. H. (2010). “Atomistic modeling of collagen proteins in their fibrillar environment.” J. Phys. Chem. B, 114(41), 13263–13270.
Streeter, I., and de Leeuw, N. H. (2011). “A molecular dynamics study of the interprotein interactions in collagen fibrils.” Soft Matter, 7(7), 3373–3382.
Sudarsanan, K., and Young, R. A. (1969). “Significant precision in crystal structural details: Holly Springs hydroxyapatite.” Acta Crystallogr., Sect. B: Struct. Crystallogr. Crystal Chem., 25(Part 8), 1534–1543.
Tang, Y., Ballarini, R., Buehler, M. J., and Eppell, S. J. (2010). “Deformation micromechanisms of collagen fibrils under uniaxial tension.” J. R. Soc. Interface, 7(46), 839–850.
Tasker, P. W. (1979). “The stability of ionic crystal surfaces.” J. Phys. C Solid State Phys., 12(22), 4977–4984.
Termine, J. D., and Robey, P. G. (1996). “Bone matrix proteins and the mineralization process.” Primer on the metabolic bone diseases and disorders of mineral metabolism, M. J. Favus, ed., The American Society for Bone and Mineral Research, Lippincott Williams & Wilkins, New York.
Traub, W., Arad, T., and Weiner, S. (1989). “Three-dimensional ordered distribution of crystals in turkey tendon collagen fibers.” Proc. Natl. Acad. Sci. USA, 86(24), 9822–9826.
van der Rijt, J. A. J., van der Werf, K. O., Bennink, M. L., Dijkstra, P. J., and Feijen, J. (2006). “Micromechanical testing of individual collagen fibrils.” Macromol. Biosci., 6(9), 697–702.
Weiner, S., and Wagner, H. D. (1998). “The material bone: Structure-mechanical function relations.” Annu. Rev. Mater. Sci., 28(August), 271–298.
Wenger, M. P. E., Bozec, L., Horton, M. A., and Mesquida, P. (2007). “Mechanical properties of collagen fibrils.” Biophys. J., 93(4), 1255–1263.
Wenk, H. R., and Heidelbach, F. (1999). “Crystal alignment of carbonated apatite in bone and calcified tendon: Results from quantitative texture analysis.” Bone, 24(4), 361–369.
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Published In
Journal of Engineering Mechanics
Volume 140 • Issue 3 • March 2014
Pages: 454 - 461
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Nov 8, 2011
Accepted: May 29, 2012
Published online: Jul 30, 2012
Published in print: Mar 1, 2014
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