Molecular Dynamics Simulation of the Early Stages of Nucleation of

Article pubs.acs.org/crystal

Molecular Dynamics Simulation of the Early Stages of Nucleation of Hydroxyapatite at a Collagen Template Neyvis Almora-Barrios*,†,§ and Nora H. De Leeuw*,†,‡ †

Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, United Kingdom Institute of Orthopaedics and Musculoskeletal Science, University College London, Brockley Hill, Stanmore HA7 4LP, Middlesex, United Kingdom

‡

S Supporting Information *

ABSTRACT: We have used molecular dynamics simulations to investigate the early processes in the nucleation of hydroxyapatite at a collagen template, by immersing a triplehelical collagen molecule in a stoichiometric solution of Ca2+, PO43−, and OH− ions, where we have observed the formation of calcium phosphate clusters at the collagen template. Electrostatic attractions were prevalent between calcium ions and oxygen atoms of the glycine and hydroxyproline residues, which were the starting point for the formation of the calcium phosphate clusters. Some phosphate ions form hydrogen-bonds with the hydroxy groups of hydroxyproline residues, whereas most of the hydroxy ions stay in solution, although some become attached to calcium phosphate clusters. The observed nucleation and clustering is too early in the hydroxyapatite formation process to show differentiation between distinct hydroxyapatite surfaces. However, calculations of the interaction of a collagen peptide with the (0001) and (011̅0) surfaces of hydroxyapatite show a clear energetic preference by the peptide for adsorption at the (0110̅ ) surface, which suggests that in the presence of the collagen matrix the hydroxyapatite crystal would grow more rapidly in the (0001) direction and express the (011̅0) surface in the particle shape, in agreement with the observed morphology of biological hydroxyapatite.

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INTRODUCTION A number of composite materials have been investigated as possible bioactive implant materials for biomedical applications, for example polymer/apatite and polymer/bioglass composites.1 Bioactive implant materials, such as Bioglass, first discovered by Hench and co-workers, have the tendency to dissolve in the body and be resorbed into hard tissue.2 As such, these materials do not work themselves loose, as the older, bioinert implants eventually do, and hence, they need not be replaced regularly, thus eliminating the need for invasive repeat surgery. Since the discovery of the biocompatible properties of Bioglass have revolutionized the field of biomaterials research, most investigations have concentrated on designing bioactive implant materials for hard tissue replacement, which resemble as closely as possible the structure and properties of natural bone, including its composite nature. Although polyethylene and polyethylene-glycol foams are widely used in composite materials for clinical and pharmaceutical applications,3,4 collagen itself has also been investigated as a biomaterial candidate.5−8 In this case, the collagen triple helices are limited to the length of a synthetic peptide (∼10 nm), which is much shorter than the natural collagen (∼300 nm).9 Collagen-based biomedical devices have been developed in a variety of physical forms, including nanoparticles, fibers, films, hydrogels, and pellets, where they have been used as drug carriers, wound dressings, skin replacements, and bone substitutes.10 However, in the most © 2011 American Chemical Society

recent biomaterials applications, the collagen matrix is usually combined with a reinforcing phase such as hydroxyapatite, which should improve both the mechanical properties and the bioactivity of the material.11 Apatite−collagen composites are biodegradable and good matrices for bone cell attachment and proliferation, as well as new bone formation.12 Experimental studies have demonstrated that the growth process of apatite is controlled by the interaction between the organic matrix and the apatite crystal,13−17 which determines the eventual morphology of the HA platelets in the bone. An important but largely unresolved issue is the way in which nature controls the nucleation, growth and morphology of inorganic crystallites and the function of biomolecules (such as amino acids and proteins) in these reactions. However, it is not yet possible to study directly, by experiment alone, the molecular mechanisms of fast processes, such as the binding sites and adsorption modes of these biomolecules on the HA surfaces. A wide variety of simulation techniques have been developed, applicable to a range of different problems in biomolecular science.18−21 Simulations are an excellent tool for modeling and probing the structure and interfacial processes of organic molecules and Received: August 20, 2011 Revised: December 12, 2011 Published: December 16, 2011 756

dx.doi.org/10.1021/cg201092s | Cryst. Growth Des. 2012, 12, 756−763

Crystal Growth & Design

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inorganic crystals at the atomic level.22−28 Useful information, such as the interfacial energy,29 adsorption energy,22,23,30 and interaction sites,24,31,32 can be obtained from molecular dynamics simulations to gain insight into organic−inorganic interfaces. More recently, ab initio methods have been applied successfully to simulate the adsorption of protein residues at inorganic materials,25,33−35 but this method cannot generally be taken beyond a few hundred atoms for a few tens of picoseconds. Alternatively, ab initio methods have often been employed to derive reliable interatomic potential models for the less compute-intensive interatomic potential-based techniques, which allow for the simulation of larger and more complex systems, such as the collagen−apatite system. This paper aims to contribute to a better understanding of the interaction of collagen with hydroxyapatite at the atomic level, by carrying out a computational study of the nucleation and directed growth of hydroxyapatite at the collagen matrix. We have used molecular dynamics simulations to provide detailed atomistic models for the initial stages of nucleation and cluster formation of calcium phosphate at a collagen molecule. As this nucleation/growth process in vivo obviously occurs in body fluid, we have included an aqueous solution in the calculations. We also study the interaction of a small collagen peptide with different surfaces of hydroxyapatite, where we are particulary interested in investigating whether this peptide might infer a preferential crystal growth direction.

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METHODOLOGY Structural Models. Natural bone tissue is built up of many distinct structural levels with highly specific chemical interactions between a collagen matrix and the apatite mineral.36 The protein in bone is predominantly type I collagen, whose structure is complex and which is selfassembled in a multistep process.37 In summary, the collagen contains the complete sequence of amino acids along each of three polypeptide chains that are coiled into a left-handed helix, where hydrogen-bonding plays a structure-directing role. The three chains are then wrapped around each other into a righthanded superhelix so that the final structure is a rope-like rod. The presence of glycine as the third amino acid in the repeating GLY−X−Y− sequence of each chain is essential, because a larger amino acid will not fit in the center of the triple helix, where the three chains come together. Proline is frequently in the X-position of the GLY−X−Y− sequence and 4-hydroxyproline is frequently in the Y-position. Biological apatite is essentially the calcium phosphate mineral hydroxyapatite,38 Ca10(PO4)6(OH)2, but with crystal defects, such as substitutions by carbonate, water, and various metal cations.39 A hydrated crystal structure of collagen was obtained from the RSCB protein database (PDB ID 1CGD). The structure was modified with the Materials Studio version 4.0 package, to contain three chains of [−OOC−(GLY−PRO− HYP)10−NH2+]3 folded into a triple helix collagen molecule. The final simulation system consisted of the [−OOC−(GLY− PRO−HYP)10−NH2+]3 collagen molecule, 120 Ca2+ ions, 72 PO43− ions, 24 OH− ions, and 5225 water molecules placed in a box of 100 × 35 × 35 Å3 size (Figure 1). Several factors affect the nucleation and growth of the HA at the collagen, including ionic concentration, pH and growth inhibiting impurities. The concentration of ions in our simulation system is higher than is found in blood, but modeling much lower concentrations would require computationally prohibitively large simulation boxes. Furthermore,

Figure 1. Graphical representation of the system: collagen-like triple helix peptide shown in the center of the simulation box by CPK model (chain A red, chain B gray, and chain C blue). Ca2+ ions as light blue, PO43−, and OH− as ball and stick model, and water molecules as stick model .

increasing the ion concentration is a practical way to accelerate the simulation of apatite nucleation and growth.40 The pH of the simulation system is approximately pH = 7.7, which is similar to the average pH found in the body and experimental studies suggest this to be a suitable pH for HA particle growth. Molecular Dynamics Simulations. We have used molecular dynamics simulations (MD), employing the DL_POLY41 code to investigate the processes of formation and growth of apatite clusters at the collagen molecule in a bath of water molecules. The density of the water in the simulation box was 0.9922 g cm−3 at a temperature of 310 K. The equilibration period was 500 ps, in which all the atoms were free to move in the NVT ensemble (constant number of particles, volume and temperature). The temperature was fixed using the Nosé−Hoover thermostat, and the Verlet leapfrog algorithm was used to integrate the equations of motion with a time step of 0.1 fs. The analysis of the results was performed on 757



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Figure 2. Radial distribution functions (RDF) obtained by time-averaging of interatomic distances in molecular dynamics simulations during the equilibration period. (a) Distances from Ca2+ ions to oxygen atoms in water molecules (Ow). (b) Distances from oxygen ions in PO43− to hydrogen atoms in water molecules (Hw).

calculations.51,52 The complete potential model is listed in the Supporting Information (SI).

the basis of a 5 ns run in the NPT ensemble (constant number of particles, pressure, and temperature), where the Nosé− Hoover algorithm is used for both the thermostat (0.1 ps) and the barostat (0.5 ps) relaxation times to maintain the system at room temperature and pressure. We have used a combination of compatible interatomic potential models for the description of the interactions of the various atoms in the systems, namely the Generalized AMBER force field42,43 for the collagen molecule, whereas water was described by the TIP3P water model,44 commonly used in simulations of biological systems.45 The interatomic potential model for hydroxyapatite was taken from De Leeuw,26 which includes electronic polarizability via the shell model of Dick and Overhauser,46 where each polarizable ion, here oxygen, is represented by a core and a massless shell, connected by a spring. The polarizability of the oxygen ions is then determined by the spring constant and the charges of the core and shell. When necessary, angle-dependent forces are included to allow directionality of bonding, for example in the covalent phosphate anion. In addition to the interatomic potential parameters for the HA crystal, water and collagen individually, we also need parameters describing the cross-interactions between the HA, the collagen and water. We have made use of the Lorentz− Berthelot mixing rules47 for the collagen/hydroxyapatite/water interactions. These types of scaled parameters have been used extensively to calculate the intermolecular potential between pairs of nonidentical atoms.22,48−50 The same interactions have been used in previous work on the adsorption of biomolecules, including collagen peptides, at HA surfaces,23,24,26,27 which showed good agreement with experiment and ab initio

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RESULTS AND DISCUSSION NVT Simulations at 310 K. During the equilibration period, hydration spheres are formed around the Ca2+ and PO43− ions. The snapshot in Figure 2a shows how a number of water molecules have moved close to the calcium ion. For Ca2+ the first maximum in the Ca−Owater radial distribution function (RDF) is at 2.38 Å (Figure 2a), which corresponds to the positions of the oxygen atoms in the first coordination shell. The second coordination shell is less clearly defined since its associated peak is smaller and it spreads over a broader region, from 4.1 to 4.7 Å. The average number of the water molecules in the first hydration shell is between 6 and 8, which is in very good agreement with the values obtained from ab initio MD simulations of calcium in water.53 Phosphate ions also form stable complexes with the water molecules. Figure 2b shows the RDF of the oxygen atoms of the phosphate with the hydrogen atoms of the surrounding water, which has its first maximum located at 1.88 Å and the integration of the numbers of all four (PO4Hwater) RDF functions show an average value of about 12 water molecules in the first hydration shell. These results are all in complete agreement with a neutron diffraction study of a K3PO4 aqueous solution (15 ± 3 water molecules),54 and with ab initio MD simulations of a single PO43− ion in water.55 Although the calcium and phosphate ions are stable in water, there is a strong electrostatic attraction between them, and after 0.5 ns calcium has became coordinated to the oxygen atoms of phosphate. The ions diffuse through the liquid water and form a variety of types of ion pairs. The calcium ions mainly adopt a distorted pentagonal-based bipyramid, where Ca2+ is hepta758



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the structures of model collagen peptides.56−63 We can see a representation of the solvation shell of the collagen in Figure 4,

coordinated (Figure 3a). However, there are other configurations where the Ca2+ ions interact with two and three PO43−

Figure 4. Snapshot showing the aqueous environment surrounding a collagen strand. The triple helix peptide backbone is in stick, −OH of hydroxyproline residues and O of the carbonyl groups as ball and stick model, and stick model for the water.

where the water molecules at a distance greater than 3 Å have been removed. After 1 ns of simulation, the phosphate ions and hydroxy ions (OH−) prefer to be in solution rather than interact with the collagen molecule. However, the collagen peptide begins to attract the Ca2+ ions from solution at a distance of ∼3 Å. The strong interaction between the hydroxy ions and the water molecules is reflected by the peak shifts of the OH−Hwater and OH−Owater RDF (Figure 5). In fact, the

Figure 3. Structure of the five clusters formed in solution, (a) Ca(H2O)5PO4, (b) Ca(H2O)4(PO4)2, (c) Ca(H2O)(PO4)3, and (d) Ca2(H2O)10PO4.

anions within the cluster. In these cases, the Ca2+ ion interacts with fewer water molecules (Figure 3b, c), and the distances to the Ca−OPO33− are slightly shorter than in the first configuration. A phosphate ion can be part of more than one ion pair since two pairs of oxygen per PO43− can interact to form a larger entity in which the Ca2+ cations stay in their penta-aquo complexes and the Ca−OPO33− distances oscillate between 2.43 and 2.22 Å (Figure 3d). All ion pairs are stable units at body temperature, and they move through the liquid water without dissociation for hundreds of picoseconds. At the beginning of the simulation, the presence of the collagen molecule in the system offers a variety of favorable sites for Ca2+ association. This particularly applies to the carboxylate terminal groups of glycine, but the carbonyl oxygen atoms and hydroxy oxygen atoms also interact with Ca2+ ions, although not very strongly (average distance is 4.24 Å). The water molecules form strong hydrogen-bonds with the hydroxy group of hydroxyproline residues (1.94 Å), which interaction is more pronounced than with hydrogen atoms of the amine group of the glycine residues or oxygen atoms of any of the residues (2.24 Å). The carbonyl oxygen of the proline is directed toward the center of the triple helix and forms hydrogen bonds with the amine hydrogen of the glycine in the neighboring chain, leaving no space for water molecules or other ions. Some of these characteristic hydrogen-bonding patterns of the water molecules have already been reported for

Figure 5. OH−Hwater and OH−Owater radial distribution functions from NVT simulation.

hydrogen of OH− is only weakly hydrogen-bonded to other oxygen ions, whereas the oxygen of OH− forms several hydrogen-bonded interactions with water. NPT Simulation at 310 K. The NVT simulations described in the previous section were used as an equilibration period. We considered, however, that there could be significant variation in volume because of the changes in the hydration spheres when the clusters were growing, which would be better modeled in an 759



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NPT ensemble. We therefore simulated the system for 5 ns, to gain further insight into the nucleation process. Figure 6a shows the change with time of the hydration spheres around the Ca2+ ions. The number of water molecules

oxygen atoms of phosphate ions or oxygen atoms of the carboxylate, carbonyl and hydroxy groups in the collagen, as shown in Figure 6b and c. Electrostatic attractions are likely to be important between the calcium ions and oxygen atoms of the glycine and hydroxyproline residues, as well as between the positively charged −NH2+ of the hydroxyproline terminal molecule and the oxygen of phosphate ions (see Figure 7). In

Figure 7. Snapshot of the system at 5 ns. Water molecules have been removed to allow a clear view of the growing clusters at the collagen sites. The triple helix collagen peptide shown in the center of the simulation box as a stick model, Ca2+ ions as green balls, PO43‑ and OH− as stick models (Ca = green, P = pink, O = red, C = gray, N = blue, H = white).

addition, some hydroxy groups of hydroxyproline residues form hydrogen-bonded interactions to phosphate and hydroxy oxygen atoms. During the first nanosecond, the embryonic clusters begin to grow; they attract additional calcium and phosphate ions. As a result, PO4 groups become surrounded by three Ca atoms, placed at the vertices of a triangle, and at least

Figure 6. Calcium−oxygen radial distribution functions (RDF) during the simulation.

coordinating to the calcium ions become fewer as time advances, as shown by the height of the peak in the graph of the radial distribution function. They are being replaced by 760



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Figure 8. Final structures of the (GLY-PRO-HYP) peptide adsorbed at the hydroxyapatite surfaces in an aqueous environment (a) at the (0001) surface and (b) at the (011̅0) (Ca = green, O = red, P = purple, H = white, C = gray, N = blue).

larger concentration of OH− in solution than F− which will form stable ion complexes with Ca2+ (we are ignoring here any possible effect of the autodissociation of water). In our study of hydroxyapatite, we found that calcium phosphates were the most stable ion complexes. This initial formation of clusters of calcium phosphate is in agreement with experimental studies, which report the initial formation of the more soluble octacalcium phosphate precursor phase for hydroxyapatite,64 which does not as yet incorporate OH− groups. Surface Studies. In crystal growth processes, some degree of saturation is required for rapid growth to occur, but much less than is required for nucleation. The growth reaction continues to the solubility limit and growth can therefore be made to dominate and even prevent further nucleation once initial nucleation has occurred. Whereas nucleation and early growth processes often favor the formation of metastable precursor phases, as is seen in our simulations, ultimately growth of the most stable phase is favored.65 However, it is clearly a long way to go from the association of single ions into clusters to the formation of HA crystallites. Similar to studies of Yang et al.32 our simulations do not reveal the formation of semicrystalline structures, or indeed any structures that may resemble HA surface features. Therefore, in order to evaluate whether the collagen is likely to have a structure-directing or growth-modifying effect, we have investigated the strength of binding of a small collagen strand to the (0001) and (011̅0) surfaces of hydroxyapatite in an aqueous environment. Figure 8a and b shows the final configurations after 1 ns of MD simulations of the collagen strand adsorbed at the HA (0001) and (011̅0) surfaces, respectively. On the (0001) surface, the peptide forms a number of close interactions between the molecule’s oxygen atoms of the carboxylate groups and two surface calcium ions. In addition, hydrogen-bonding takes place between oxygen atoms of a surface phosphate group and the hydrogen atoms of the molecule’s −OH and −NH2+ groups (−OH−OPO3 = 1.54−1.79 Å, −NH2+−OPO3 = 1.75

one of the calcium ions of the cluster is linked to the oxygen atoms of collagen. Some clusters, however, do not form close to the organic matrix (see Figure 7). In this case, the process of cluster growth is much slower than occurs near the collagen. Most of the hydroxy groups stay in solution, although some become attached to calcium-phosphate clusters. In contrast to Kawska et al.,21,31 we have not found that calcium ions become incorporated between the strands of the triple helix or have observed the formation of Ca3F motifs, as no F− is present. The difference in behavior between solvated F− and OH− ions may be the cause of the different types of clusters formed in the two studies. We can consider the equilibria between the solid phases and the ions in solution for hydroxyapatite and fluorapatite:

Ca10(PO4 )6 (OH)2(s) ⇄ 10Ca 2 +(aq) + 6(PO4 3 −)(aq) + 2(OH−)(aq) Ca10(PO4 )6 (F)2(s) ⇄ 10Ca 2 +(aq) + 6(PO4 3 −)(aq) + 2(F−)(aq) The Ca2+ released may be involved in multiple equilibria:

Ca3(PO4 )2(s) ⇄ 3Ca 2 +(aq) + 2(PO4 3 −)(aq) , K ps = 2.1 × 10−33 Ca(OH)2(s) ⇄ 3Ca 2 +(aq) + 2(OH−)(aq) , K ps = 4.7 × 10−6 Ca(F)2(s) ⇄ Ca 2 +(aq) + 2F−(aq), K ps = 3.9 × 10−11 The equilibrium of hydroxyapatite and fluorapatite is rather similar. However, it is clear that the CaF2/water system is more stable than the Ca(OH)2/water combination, with a much 761



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Å). On the (0110̅ ) surface, interfacial water molecules replace surface hydroxy groups, similarly to previous simulations of another hydrated HA surface using a different water model.26,66 The average adsorption mode for the peptide is through coordination by both carbonyl oxygen atoms to two surface calcium atoms. One of the carbonyl oxygens is coordinated to a calcium at a distance of 2.77 Å, while the other interacts with another calcium at a distance of 2.46 Å, whereas a number of hydrogen-bonded interactions between its −OH and −NH2+ groups and oxygen atoms of the surface hydroxy groups further enhance the binding between the peptide molecule and the (011̅0) surface. Further hydrogen-bonding occurs between the oxygen atoms of the carboxylate and carbonyl groups and the hydrogen atoms of the two topmost hydroxy groups (−COO−−HO− = 2.66 Å, CO−HO− = 1.81 Å). The calculated adsorption energies of 157 and 677 kJ mol−1 for the (0001) and (011̅0) surfaces, respectively, show that the collagen peptide binds far more strongly to the HA (011̅0) surface than to the (0001) surface, which supports the notion that the collagen would direct growth of the HA crystal toward expression of the (011̅0) surface, which can form a strong interface with the collagen matrix.

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ASSOCIATED CONTENT

S Supporting Information *

Interatomic potential model and details of simulation models. This information is available free of charge via the Internet at http://pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (N.A.-B.); [email protected] (N.H.D.L.). Present Address

Institute of Research of Catalonia, ICIQ, Avgda Pais̈ os Catalans 16, 43007 Tarragona, Spain §

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ACKNOWLEDGMENTS We acknowledge the U.K. Medical Research Council (Grant No. 82407) and the U.K. Engineering and Physical Sciences Research Council for funding.

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REFERENCES

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CONCLUSIONS

We have presented a computational investigation of the initial stages of nucleation and cluster formation of calcium phosphate at a collagen molecule in aqueous solution. At body temperature, calcium ions interact with water molecules to form stable complexes, but attracted by electrostatic forces, they coordinate to PO4 ions and start forming clusters. For the association of the calcium ions at the collagen molecule, the carboxylate groups in the ends of the peptide strands were found to be freely accessible to the ions. More importantly, however, the hydroxy and carbonyl oxygen atoms within the collagen strands also support calcium-collagen bonds, where we found that the collagen molecule can interact with the ions before and/or after they form clusters. Phosphate ions interact less strongly with the collagen, although relatively stable hydrogen-bonding interactions were found between oxygen atoms of the phosphate groups and hydrogen atoms of the OH group of the hydroxyproline residues. Our simulations of collagen−surface interactions finds that only the (011̅0) surface interacts strongly with a collagen peptide, which helps to explain the biological morphology of the hydroxyapatite mineral, where this surface is expressed preferentially as a result of the growth-directing effect of the protein matrix. As such, this peptide should be a good growth modifier for synthetic hydroxyapatite, leading to morphologies closer to the natural materials. Nucleation processes can be affected by the interaction of the mineral phases with impurities that inhibit crystal nucleation and growth (such as magnesium, carbonate, fluoride and glycoproteins). Comparison of our results with those of Kawska et al.21,31 have shown that fluoride ions inhibit calcium phosphate formation by competitively binding the Ca ions into calcium fluoride clusters. The effects of Mg, CO3, and other species present in the aqueous solution on the nucleation and cluster formation processes will be the focus of future simulations. 762



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Molecular Dynamics Simulation of the Early Stages of Nucleation of

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