Multi-scale simulations of apatite–collagen composites: from molecules to materials

Abstract

We review scale-bridging simulation studies for the exploration of atomic-to-meso scale processes that account for the unique structure and mechanic properties of apatite–protein composites. As the atomic structure and composition of such complex biocomposites only partially is known, the first part (i) of our modelling studies is dedicated to realistic crystal nucleation scenarios of inorganic–organic composites. Starting from the association of single ions, recent insights range from the mechanisms of motif formation, ripening reactions and the self-organization of nanocrystals, including their interplay with growth-controlling molecular moieties. On this basis, (ii) reliable building rules for unprejudiced scale-up models can be derived to model bulk materials. This is exemplified for (enamel-like) apatite–protein composites, encompassing up to 10⁶ atom models to provide a realistic account of the 10 nm length scale, whilst model coarsening is used to reach µm length scales. On this basis, a series of deformation and fracture simulation studies were performed and helped to rationalize biocomposite hardness, plasticity, toughness, self-healing and fracture mechanisms. Complementing experimental work, these modelling studies provide particularly detailed insights into the relation of hierarchical composite structure and favorable mechanical properties.

Keywords

biocomposites / deformation / fracture / molecular simulation

References

[1] Fratzl P, Weinkamer R. Natures hierarchical materials. Progress in Materials Science, 2007, 52(8): 1263–1334

[2] Weiner S, Wagner H D. The material bone: structure‒mechanical function relations. Annual Review of Materials Science, 1998, 28(1): 271–298

[3] Fratzl P, Gupta H S, Paschalis E P, . Structure and mechanical quality of the collagen–mineral nano-composite in bone. Journal of Materials Chemistry, 2004, 14(14): 2115–2123

[4] Fratzl P, ed. Collagen: Structure and Mechanics. Springer, 2008

[5] He L H, Swain M V. Enamel — a “metallic-like” deformable biocomposite. Journal of Dentistry, 2007, 35(5): 431–437

[6] He L H, Swain M V. Contact induced deformation of enamel. Applied Physics Letters, 2007, 90(17): 171916 (3 pages)

[7] He L H, Swain M V. Nanoindentation creep behavior of human enamel. Journal of Biomedical Materials Research Part A, 2009, 91(2): 352–359

[8] Fantner G E, Hassenkam T, Kindt J H, . Sacrificial bonds and hidden length dissipate energy as mineralized fibrils separate during bone fracture. Nature Materials, 2005, 4(8): 612–616

[9] Buehler M J. Nature designs tough collagen: explaining the nanostructure of collagen fibrils. Proceedings of the National Academy of Sciences of the United States of America, 2006, 103(33): 12285–12290

[10] Kniep R, Simon P. Fluorapatite‒gelatine-nanocomposites: self-organized morphogenesis, real structure and relations to natural hard materials. Topics in Current Chemistry, 2006, 270: 73–125

[11] Simon P, Rosseeva E, Buder J, . Embryonic states of fluorapatite–gelatine nanocomposites and their intrinsic electric-field-driven morphogenesis: the missing link on the way from atomistic simulations to pattern formation on the mesoscale. Advanced Functional Materials, 2009, 19(22): 3596–3603

[12] Kawska A, Hochrein O, Brickmann J, . The nucleation mechanism of fluorapatite‒collagen composites: ion association and motif control by collagen proteins. Angewandte Chemie International Edition, 2008, 47(27): 4982–4985

[13] Zahn D, Hochrein O, Kawska A, . Towards an atomistic understanding of apatite‒collagen biomaterials: linking molecular simulation studies of complex-, crystal- and composite-formation to experimental findings. Journal of Materials Science, 2007, 42(21): 8966–8973

[14] Zahn D, Hochrein O. Computational study of interfaces between hydroxyapatite and water. Physical Chemistry Chemical Physics, 2003, 5(18): 4004–4007

[15] de Leeuw N H. Resisting the onset of hydroxyapatite dissolution through the incorporation of fluoride. The Journal of Physical Chemistry B, 2004, 108(6): 1809–1811

[16] Zahn D. A molecular rationale of shock absorption and self-healing in a biomimetic apatite‒collagen composite under mechanical load. Angewandte Chemie International Edition, 2010, 49(49): 9405–9407

[17] Duchstein P, Zahn D. Atomistic modeling of apatite‒collagen composites from molecular dynamics simulations extended to hyperspace. Journal of Molecular Modeling, 2011, 17(1): 73–79

[18] Zahn D, Bitzek E. Shearing in a biomimetic apatite‒protein composite: molecular dynamics of slip zone formation, plastic flow and backcreep mechanisms. PLoS One, 2014, 9(4): e93309

[19] Zahn D, Duchstein P. Multi-scale modelling of deformation and fracture in a biomimetic apatite‒protein composite: molecular-scale processes lead to resilience at the μm-scale. PLoS One, 2016, 11(6): e0157241

[20] Simon P, Zahn D, Lichte H, . Intrinsic electric dipole fields and the induction of hierarchical form developments in fluorapatite‒gelatine nanocomposites: a general principle for morphogenesis of biominerals? Angewandte Chemie International Edition, 2006, 45(12): 1911–1915

[21] Hauptmann S, Dufner H, Brickmann J, . Potential energy function for apatites. Physical Chemistry Chemical Physics, 2003, 5(3): 635–639

[22] de Leeuw N H. A computer modelling study of the uptake and segregation of fluoride ions at the hydrated hydroxyapatite (0001) surface: introducing a Ca₁₀(PO₄)₆(OH)₂ potential model. Physical Chemistry Chemical Physics, 2004, 6(8): 1860–1866

[23] Bhowmik R, Katti K S, Katti D. Molecular dynamics simulation of hydroxyapatite‒polyacrylic acid interface. Polymer, 2007, 48(2): 664–674

[24] Meißner R H, Wei G, Ciacchi L C. Estimation of the free energy of adsorption of a polypeptide on amorphous SiO₂ from molecular dynamics simulations and force spectroscopy experiments. Soft Matter, 2015, 11(31): 6254–6265

[25] Larrucea J, Lid S, Ciacchi L C. Parametrization of a classical force field for iron oxyhydroxide/water interfaces based on Density Functional Theory calculations. Computational Materials Science, 2014, 92: 343–352

[26] Almora-Barrios N, De Leeuw N H. Molecular dynamics simulation of the early stages of nucleation of hydroxyapatite at a collagen template. Crystal Growth & Design, 2012, 12(2): 756–763

[27] Milek T, Zahn D. Molecular modeling of (101‾0) and (0001‾) zinc oxide surface growth from solution: islands, ridges and growth-controlling additives. CrystEngComm, 2015, 17(36): 6890–6894

[28] Kawska A, Duchstein P, Hochrein O, . Atomistic mechanisms of ZnO aggregation from ethanolic solution: ion association, proton transfer, and self-organization. Nano Letters, 2008, 8(8): 2336–2340

[29] Helminger M, Wu B, Kollmann T, . Synthesis and characterization of gelatin-based magnetic hydrogels. Advanced Functional Materials, 2014, 24(21): 3187–3196

[30] Tommaso D D, de Leeuw N H. The onset of calcium carbonate nucleation: a density functional theory molecular dynamics and hybrid microsolvation/continuum study. The Journal of Physical Chemistry B, 2008, 112(23): 6965–6975

[31] Zahn D. Mechanisms of calcium and phosphate ion association in aqueous solution. Zeitschrift fur Anorganische und Allgemeine Chemie, 2004, 630(10): 1507–1511

[32] Wallace A F, Hedges L O, Fernandez-Martinez A, . Microscopic evidence for liquid‒liquid separation in supersaturated CaCO₃ solutions. Science, 2013, 341(6148): 885–889

[33] Duchstein P, Kniep R, Zahn D. On the function of saccharides during the nucleation of calcium carbonate‒protein biocomposites. Crystal Growth & Design, 2013, 13(11): 4885–4889

[34] Hochrein O, Zahn D. On the molecular mechanisms of the acid-induced dissociation of hydroxy-apatite in water. Journal of Molecular Modeling, 2011, 17(6): 1525–1528

[35] Damkier H H, Josephsen K, Takano Y, . Fluctuations in surface pH of maturing rat incisor enamel are a result of cycles of H⁺-secretion by ameloblasts and variations in enamel buffer characteristics. Bone, 2014, 60(3): 227–234

[36] Anwar J, Zahn D. Uncovering molecular processes in crystal nucleation and growth by using molecular simulation. Angewandte Chemie International Edition, 2011, 50(9): 1996–2013

[37] Rosseeva E V, Buder J, Simon P, . Synthesis, characterization, and morphogenesis of carbonated fluorapatite‒gelatine nanocomposites: A complex biomimetic approach toward the mineralization of hard tissues. Chemistry of Materials, 2008, 20(19): 6003–6013

[38] Bos K J, Rucklidge G J, Dunbar B, . Primary structure of the helical domain of porcine collagen X. Matrix Biology, 1999, 18(2): 149–153

[39] Nair A K, Gautieri A, Chang S W, . Molecular mechanics of mineralized collagen fibrils in bone. Nature Communications, 2013, 4: 1724

[40] Grenoble D E, Katz J L, Dunn K L, . The elastic properties of hard tissues and apatites. Journal of Biomedical Materials Research, 1972, 6(3): 221–233

[41] Maas M C, Dumont E R. Built to last: The structure, function, and evolution of primate dental enamel. Evolutionary Anthropology: Issues, News and Reviews, 1999, 8(4): 133–152

[42] Pomes R, Eisenmesser E, Post C B, . Calculating excess chemical potentials using dynamic simulations in the fourth dimension. The Journal of Chemical Physics, 1999, 111(8): 3387–3395

Acknowledgements

The author thanks P. Duchstein and R. Kniep for many fruitful discussions. This work was supported by the Deutsche Forschungsgemeinschaft via grants ZA 420/7, 420/8 and EXC315.

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2017 Higher Education Press and Springer-Verlag Berlin Heidelberg