Ion-association complexes unite classical and non-classical theories for the biomimetic nucleation of calcium phosphate

Volmer M. & Weber A. . Keimbildung in übersättigten Gebilden (Nucleation of supersaturated structures). Z. Phys. Chem. 119, 277–301 (1926).

Becker R. & Döring W. . Kinetische Behandlung der Keimbildung in übersättigten Dämpfen. Ann. Phys. Berlin 24, 719–752 (1935).

Navrotsky A. . Energetic clues to pathways to biomineralization: precursors, clusters, and nanoparticles. Proc. Natl Acad. Sci. USA 101, 12096–12101 (2004).

Ostwald W. Z. . Studien über die Bildung und Umwandlung fester Körper. Z. Phys. Chem. 22, 289–330 (1897).

ten Wolde P. R. & Frenkel D. . Homogeneous nucleation and the Ostwald step rule. Phys. Chem. Chem. Phys. 1, 2191–2196 (1999).

Legeros R. Z. . Calcium-phosphate based osteoinductive materials. Chem. Rev. 108, 4742–4753 (2008).

Omelon S. J. & Grynpas M. D. . Relationships between polyphosphate chemistry, biochemistry and apatite biomineralization. Chem. Rev. 108, 4694–4715 (2008).

Mahamid J., Sharir A., Addadi L. & Weiner S. . Amorphous calcium phosphate is a major component of the forming fin bones of zebrafish: indications for an amorphous precursor phase. Proc. Natl Acad. Sci. USA 105, 12748–12753 (2008).

Crane N. J., Popescu V., Morris M. D., Steenhuis P. & Ignelzi M. A. Jr . Raman spectroscopic evidence for octacalcium phosphate and other transient mineral species deposited during intramembranous mineralization. Bone 39, 434–442 (2006).

Mahamid J. et al. Mapping amorphous calcium phosphate transformation into crystalline mineral from the cell to the bone in zebrafish fin rays. Proc. Natl Acad. Sci. USA 107, 6316–6321 (2010).

Eanes E. D., Gillessen I. H. & Posner A. S. . Intermediate states in the precipitation of hydroxyapatite. Nature 208, 365–367 (1965).

Posner A. S. & Betts F. . Synthetic amorphous calcium phosphate and its relation to bone mineral structure. Acc. Chem. Res. 8, 273–281 (1975).

Bonar L. C., Roufosse A. H., Sabine W. K., Grynpas M. D. & Glimcher M. J. . X-ray diffraction studies of the crystallinity of bone mineral in newly synthesized and density fractionated bone. Calcif. Tissue Int. 35, 202–209 (1983).

Dey A. et al. The role of prenucleation clusters in surface-induced calcium phosphate crystallization. Nat. Mater. 9, 1010–1014 (2010).

Nudelman F. et al. The role of collagen in bone apatite formation in the presence of hydroxyapatite nucleation inhibitors. Nat. Mater. 9, 1004–1009 (2010).

Onuma K. & Ito A. . Cluster growth model for hydroxyapatite. Chem. Mater. 10, 3346–3351 (1998).

Wang L. & Nancollas G. H. . Calcium orthophosphates: crystallization and dissolution. Chem. Rev. 108, 4628–4669 (2008).

Gebauer D., Völkel A. & Cölfen H. . Stable prenucleation calcium carbonate clusters. Science 322, 1819–1822 (2008).

Vekilov P. G. . Nucleation. Cryst. Growth Des. 10, 5008–5019 (2010).

Erdemir D., Lee A. Y. & Myerson A. S. . Nucleation of crystals from solution: classical and two-step models. Acc. Chem. Res. 42, 621–629 (2009).

Pouget E. M. et al. The initial stages of template-controlled CaCO3 formation revealed by Cryo-TEM. Science 323, 1455–1458 (2009).

Hu Q. et al. The thermodynamics of calcite nucleation at organic interfaces: classical versus non-classical pathways. Faraday Discuss. 159, 509–523 (2012).

Brecevic L. J. & Füredi-Milhofer H. . Precipitation of calcium phosphates from electrolyte solutions. II. The formation and transformation of the precipitates. Calcif. Tissue Res. 10, 82–90 (1972).

Christoffersen J., Christoffersen M. R., Kibalczyc W. & Andersen F. A. . A contribution to the understanding of the formation of calcium phosphates. J. Cryst. Growth 94, 767–777 (1989).

Posner A. S., Betts F. & Blumenthal N. C. . Role of ATP and Mg in the stabilization of biological and synthetic amorphous calcium phosphates. Calcif. Tissue Int. 22, 208–212 (1976).

Kokubo T., Kim H. M. & Kawashita M. . Novel bioactive materials with different mechanical properties. Biomaterials 24, 2161–2175 (2003).

Terpstra R. A. & Bennema P. . Crystal morphology of octacalcium phosphate: theory and observation. J. Cryst. Growth 82, 416–426 (1987).

Kibalzyc W., Christoffersen J., Christoffersen M. R., Zielenkiewicz A. & Zielenkiewicz W. . The effect of magnesium ions on the precipitation of calcium phosphates. J. Cryst. Growth 106, 355–366 (1990).

Tung M. S. & Brown W. E. . An intermediate state in hydrolysis of amorphous calcium phosphate. Calcif. Tissue Int. 35, 783–790 (1983).

Kazanci M., Fratzl P., Klaushofer K. & Paschalis E. P. . Complementary information on in vitro conversion of amorphous calcium phosphate to HA from Raman microspectroscopy and wide angle scattering. Calcif. Tissue Int. 79, 354–359 (2006).

Sauer G. R. & Wuthier R. E. . Fourier transform infrared characterization of mineral phases formed during induction of mineralization by collagenase-released matrix vesicles in vitro. J. Biol. Chem. 263, 13718–13724 (1988).

Tanford C. . The Hydrophobic Effect Wiley Interscience: New York, (1973).

Besenius P. et al. Controlling the growth and shape of chiral supramolecular polymers in water. Proc. Natl Acad. Sci. USA 107, 17888–17893 (2010).

Weitz D. A., Huang J. S., Lin M. Y. & Sung J. . Limits of the fractal dimension for irreversible kinetic aggregation of colloids. Phys. Rev. Lett. 54, 1416–1419 (1985).

Cerreta M. K. & Berglund K. A. . The structure of aqueous solutions of some dihydrogen orthophosphates by laser Raman spectroscopy. J. Cryst. Growth 84, 577–588 (1987).

Dorozhkin S. V. . Amorphous calcium (ortho)phosphates. Acta Biomater. 6, 4457–4475 (2010).

Friddle R. W. et al. Subnanometer atomic force microscopy of peptide–mineral interactions links clustering and competition to acceleration and catastrophe. Proc. Natl. Acad. Sci. USA 107, 11–15 (2010).

Nielsen A. E. & Söhnel O. . Interfacial tensions electrolyte crystal-aqueous solution, from nucleation data. J. Cryst. Growth 11, 233–242 (1971).

Zhang H., Chen B. & Banfield J. F. . The size dependence of the surface free energy of titania nanocrystals. Phys. Chem. Chem. Phys. 11, 2553–2558 (2009).

Cheng X., Xu L., Patterson A., Jaeger H. M. & Nagel S. R. . Towards the zero-surface-tension limit in granular fingering instability. Nat. Phys. 4, 234–237 (2008).

Betts F. & Posner A. S. . An X-ray radial distribution study of amorphous calcium phosphate. Mater. Res. Bull. 9, 353–360 (1974).

Urch H., Vallet-Regi M., Ruiz L., Gonzalez-Calbet J. M. & Epple M. . Calcium phosphate nanoparticles with adjustable dispersability and crystallinity. J. Mater. Chem. 19, 2166–2171 (2009).

Wu Y., Glimcher M. J., Rey C. & Ackerman J. L. . A unique protonated phosphate group in bone mineral not present in synthetic calcium phosphates. Identification by phosphorus-31 solid state NMR spectroscopy. J. Mol. Biol. 244, 423–435 (1994).

Demichelis R., Raiteri P., Gale J. D., Quigley D. & Gebauer. D. . Stable prenucleation mineral clusters are liquid-like ionic polymers. Nat. Commun. 2, 590 (2011).

Termine J. D. & Posner A. S. . Calcium phosphate formation in vitro. I. Factors affecting initial phase separation. Arch. Biochem. Biophys. 140, 307–317 (1970).

Mitchell D. R. G. . DiffTools: electron diffraction software tools for DigitalMicrograph™. Microsc. Res. Tech. 71, 588–593 (2008).

Paris O. et al. A new experimental station for simultaneous X-ray microbeam scanning for small- and wide-angle scattering and fluorescence at BESSY II. J. Appl. Cryst. 40, s466–s470 (2007).

Davies C. W. . Ion Association 37Butterworths: London, (1962).

Shyu L. J., Perez L., Zawacki S. J., Heughebaert J. C. & Nancollas G. H. . The solubility of octacalcium phosphate at 37°C in the system Ca(OH)2-H 3PO4-KNO3-H2O. J. Dent. Res. 62, 398–400 (1983).

Meyer J. L. & Eanes E. D. . A thermodynamic analysis of the secondary transition in the spontaneous precipitation of calcium phosphate. Calcif. Tissue Res. 25, 209–216 (1978).

Fowler B. O., Markovic M. & Brown W. E. . Octacalcium phosphate. 3. Infrared and Raman vibrational spectra. Chem. Mater. 5, 1417–1423 (1993).

Gadaleta S. J., Paschalis E. P., Betts F., Mendelsohn R. & Boskey A. L. . Fourier transform infrared spectroscopy of the solution-mediated conversion of amorphous calcium phosphate to hydroxyapatite: new correlations between X-ray diffraction and infrared data. Calcif. Tissue Int. 58, 9–16 (1996).

Fratzl P. . Small-angle scattering in materials science—a short review of applications in alloys, ceramics and composite materials. J. Appl. Cryst. 36, 397–404 (2003).

Fratzl P. . Small-angle neutron scattering in materials science. PSI Proceed. 97, 113–128 (1997).

von Smoluchowski M. . Contribution to the theory of electro-osmosis and related phenomena. Bull. Int. Acad. Sci. Cracovie 184–199 (1903).

Dahirel V. & Jardat M. . Effective interactions between charged nanoparticles in water: what is left from the DLVO theory? Curr. Opin. Colloid Interface Sci. 15, 2–7 (2010).

Groenewold J. & Kegel W. K. . Anomalously large equilibrium clusters of colloids. J. Phys. Chem. B 105, 11702–11709 (2001).

Stradner A. et al. Equilibrium cluster formation in concentrated protein solutions and colloids. Nature 432, 492–495 (2004).

Denton A. R. . Charge renormalization, effective interactions, and thermodynamics of deionized colloidal suspensions. J. Phys.:Condens. Matter 20, 494230 (2008).

Manning G. S. . Counterion condensation theory of attraction between like charges in the absence of multivalent counterions. Eur. Phys. J. E. 34, 132 (2011).