Modeling biominerals formed by apatites and DNA
© Revilla-López et al.; licensee Springer. 2013
Received: 20 February 2013
Accepted: 19 March 2013
Published: 8 April 2013
Hydroxyapatite (HAp), a mineral with formula Ca10(PO4)6(OH)2 and hexagonal symmetry, is the most stable form of calcium phosphate at room temperature and in the pH range of 4–12 . This mineral, which is the main component of bones and teeth, is considered as an important biomaterial since several decades ago . Thus, due to both its outstanding biological responses to the physiological environment and its very close similarity to natural bone structure, HAp is currently applied in biomedicine. For example, it is used as a bioactive and osteoconductive bone substitute material in clinical surgery [3, 4], and as a system for the delivery of antitumor agents and antibodies in the treatment of cancer [5–7]. Furthermore, as HAp also has the advantage of absorbability and high binding affinity with a variety of molecules, it has been also used as a purification platform. For example, HAp is applied for the removal of heavy atoms from waste water , and for the separation, extraction and purification of proteins  and DNA .
DNA/HAp biominerals formed by the combination of DNA with a HAp matrix can be viewed from different perspectives. The first refers to the fact that therapeutic DNA is encapsulated in HAp nanoparticles for its subsequent transfection into living cells (e.g. liver cells, fibroblasts, osteoblasts and tumor cells) [5–7, 11, 12]. Specifically, HAp nanoparticles with embedded DNA chains can be obtained using different approaches, even though the more popular are those based on the in situ precipitation of the inorganic salt in presence of DNA [13, 14] and on the use of a HAp core that is coated using colloidal solutions to give a multi-shell particle . Nanostructured HAp has been shown to be superior for the transfection to other gene delivery methods in terms of immunogenicity and toxicity (i.e. safety) . Moreover, the transfection efficiency can be stabilized and enhanced by modulating properties such as extent of DNA binding and encapsulation, particle size, and dissolution behavior of the HAp phases [15, 16]. The interaction between the two entities of the biomineral has been proposed to occur because of the affinity between the calcium of HAp and the phosphate backbone of DNA [17–20]. It should be noted that this proposal makes the nucleotide sequence of DNA unimportant, whereas its length takes major importance.
Another perspective is the one reported by Kostetsky , who observed that the period of translation along the c-axis of the HAp lattice, 3.4 Å, is relatively similar to the period of the DNA double helix. This feature combined with the fact that the phosphate groups of HAp are able to catalyze the abiogenic synthesis of: D-riboses from ammonia, methane and water [22, 23]; nucleotides from nucleosides condensing agents and ammonium oxalate ; and polynucleotides with a 3′,5′-phosphodiether bond  under conditions similar to those of primeval Earth, led Kostetsky to propose a model for the synthesis of DNA through the interaction of its different elements with the lattice of HAp mineral . According to this model, the DNA double helix is embedded into the crystalline network of HAp forming a biomineral similar to that obtained by encapsulating therapeutic DNA into HAp nanoparticles.
On the other hand, in a very recent study Gerdon and co-workers  demonstrated the ability of DNA to template the mineralization of calcium phosphate. These authors developed a quartz crystal microbalance sensor for the quantification of HAp formation and the assessment of DNA as a template molecule. The results, which were also supported by optical density and dynamic light scattering measures, FTIR spectroscopy and scanning electron microscopy, suggested that DNA sequesters calcium and phosphate ions, thereby supersaturating the microenvironment and acting as a scaffold on which mineral forms . Moreover, small differences in DNA length, hybridization, and secondary structure were found to provoke differences in affinity for HAp and appear to influence mineralization.
In this work we have used molecular modeling tools to investigate the structure of DNA/HAp biominerals, in which single stranded (ss) and double stranded (ds) DNA are embedded into HAp nanopores. We have focused our analyses on the following aspects: (i) the smallest nanopore size required for the accommodation of ds DNA arranged in the typical B structure  (ds B-DNA) during the encapsulation process; (ii) the strain induced by the HAp crystalline field into the B-DNA structure; (iii) the importance of the chemical nature of the inorganic part of the biomineral in the DNA, which has been investigated by comparing DNA/HAp with the biomineral constructed by combining DNA with fluoroapatite [Ca10(PO4)6F2, abbreviated FAp], hereafter denoted DNA/FAp; (iv) the encapsulation of ss DNA in terms of molecular strain and relative stability with respect to ds DNA; and (v) the stability of HAp crystals formed around the ds B-DNA core. Furthermore, in order to contribute to a better understanding of the interaction of B-DNA with HAp at the atomic level, we have performed a simulation study of the nucleation and crystal growth of HAp at the ds B-DNA matrix. More specifically, we have used Molecular Dynamic (MD) simulations to provide detailed atomistic models for the initial stages of nucleation and cluster formation of calcium phosphate at a B-DNA molecule. The rest of the paper has been organized as follows. In the next section, we briefly summarize the main characteristics of the crystal structures of natural HAp and FAp, and the chemical structures of the three B-DNA duplexes studied in this work. After this, the strategy and computational details used for both the encapsulation of DNA in apatites and the early processes in the nucleation of HAp at a B-DNA template are described. The results have been organized in several sub-sections, which are devoted to the encapsulation of ds and ss DNA in both HAp and FAp, the validation of the force-field to reproduce organic···inorganic interactions in biominerals, and both the modeling and dynamics of HAp crystals growth around the ds B-DNA template. Finally, conclusions are summarized in the last section of the article.
1.1 Structures of apatites and DNA
Natural HAp has a hexagonal crystal structure with space group P63/m and periods a=b= 9.42 Å, and c= 6.87 Å. The total number of atoms in the unit cell is 44, even though it only contains seven symmetrically independent atoms: two calcium ions, one forming single atomic columns parallel to the c axis (CaI) and the other surrounding the hexagonal channel of hydroxyl in groups of the three calcium atoms at different heights (CaII); one phosphor and three oxygen atoms (P, OI, OII and OIII) forming PO4 tetrahedral units; and the O(H) ions disordered along c about the mirror plane at z= ¼. The occupancy of the OH- sites was 50%, as necessary in a P63/m. FAp shows a very similar crystal structure with 42 atoms in the P63/m hexagonal cell (a= b= 9.40 Å, c = 6.88 Å) . In this case, the OH- ions of HAp are replaced by F-, which are located on the c-axis. The Additional file 1: provides the positions of the non-equivalent atoms used to construct HAp and FAp for the modeling of the biominerals, and the projections of the HAp unit cells.
Three different ds dodecamers, which adopt a B-DNA double helix, have been examined. The chemical structures of the three duplexes, hereafter denoted I, II and III, are 5′-CGCGAATTCGCG-3′, 5′-GCGAGATCTGCG-3′ and 5′-CGCGAATTC*GCG-3′, respectively. Sequence I is known as the Dickerson’s dodecamer  and consists in a well-known sequence with three primary characteristic tracts: CG, AA and TT. Sequence II is a conventional sequence that becomes involved in different cellular processes, including carcinogenic ones . Finally, III involves methylation of the C5 position of cytidine base, identified as C*. This methylation is known to suppress hydrolysis by EcoRI restriction enzyme. The 3D structure of the three dodecamers was studied in solution and/or solid state [29–32], a B-DNA arrangement being observed in all cases. Details of the ds B-DNA structure are given in the The Additional file 1: On the other hand, ss DNAs were constructed by removing one of the strands from the three selected duplexes.
1.2 Encapsulation of DNA in apatites and nucleation of HAp
The atomic coordinates for the ds DNAs were generated using the NAB (Nucleic Acid Builder) program of the AMBER software , which constructed the double helix in the canonical B form. In order to maintain the electrical neutrality of the system, Ca2+ ions were put at the minor groove of the double helix, as is frequently observed by X-ray diffraction [34–36]. The positions of these ions were optimized by energy minimization while the coordinates of the rest of the atoms of the system were kept fixed. Models for encapsulated ss DNAs were constructed by removing one of the two strands from the ds B-DNAs embedded in HAp or FAp. In these cases, Ca2+ ions were put at random positions around the backbone phosphate groups and subsequently optimized by energy minimization.
The simulation system used to investigate the initial stages of nucleation and cluster formation of calcium phosphate at a B-DNA double helix consisted of the Dickerson’s dodecamer duplex (I), which was located at the center of the simulation box, 945 Ca2+ ions, 567 ions, 189 OH– ions, and 29560 water molecules (Figure 1c). In order to provide a comprehensive view of the templating role of the double helix, additional simulations of the same system but without B-DNA were carried out. Several factors are expected to affect the nucleation and growth of the HAp at the B-DNA, ionic concentration being among them. We are aware that the concentration of ions in the simulation systems is higher than in biological conditions. However, modeling much lower concentrations would require computationally prohibitively large simulation boxes. Furthermore, increasing the ion concentration is a practical way to accelerate the simulation of HAp nucleation and growth [37, 38].
2.1 Encapsulation of DNA
In order to relax and investigate the stability of the models constructed in the previous section, molecular mechanics calculations based on both energy minimization and MD simulations were applied using the NAMD 2.6 program . Initially, all the models were minimized by applying 5×103 steps of steepest descent to relax the more important conformational and structural tensions. Then, a MD run of 3.0 ns in the NVT ensemble (constant number of particles, volume and temperature) at 298 K was carried out to equilibrate the systems and eliminate small structural tensions. After such thermal relaxation, the saved coordinates were submitted to a new energy minimization by applying 5×103 steps of steepest descent. In both energy minimizations and MD simulation, atoms contained in ds and ss DNAs were the only ones allowed to move from their positions, the coordinates of the mineral being kept fixed at their crystallographic positions in all cases. It should be emphasized that all the systems were calculated in triplicate considering starting points that differ in the orientation of the DNA with respect to the apatite.
The potential energy was computed using the Amber force-field [40, 41]. All force-field parameters for DNA as well as the phosphate and hydroxyl groups of apatites were extracted from Amber ff03 . This is a variant of Amber ff99  in which charges and main chain torsion potentials have been re-derived from quantum mechanical calculations in solution. It should be noted that the ff03 parameters are identical to the ff99-SB  ones for nucleic acids, phosphate and hydroxyl groups. Force-field parameters of Ca2+ and F- were extracted from the works reported by Bradbrook et al. and Dang , respectively (see The Additional file 1).
where ΔE str , ΔE bnd and ΔE tor refer to the differences in the stretching, bending and torsional energies, respectively. It should be remarked that Δτ exclusively refers to the geometric stress of the double helix, the omission of non-bonding contributions in Eqn 1 allowing us to avoid masking effects associated with strong electrostatic interactions. These differences were calculated by subtracting the energy values associated with the relaxed structure (i.e. the structure obtained for the DNA embedded in apatite after relaxation by energy minimization and MD simulations) and canonical B-form of DNA (i.e. the structure directly provided by the NAB module). It should be noted that Δτ accounts for the structural stress induced by the apatite atoms in DNA.
2.2 Validation of the force-field
The reliability of the force-field parameters used in this work to reproduce apatite···DNA interactions in biominerals has been evaluated by comparing the interaction energies derived from molecular mechanics and quantum mechanics calculations. A total of 22 small model complexes containing a fragment of DNA and a fragment of apatite were taken from the modeled biominerals. These complexes, which involved a number of atoms ranging from 53 to 98, were selected to cover the modeling of both attractive and repulsive interactions. The interaction energies, which were estimated as the difference between the total energy of the complex and the energies of the isolated fragments, were calculated using both the AMBER force-field and the B3LYP/6-31G(d) [46–48] quantum mechanical method. The basis set superposition error (BSSE) of the interaction energies calculated at the B3LYP/6-31G(d) level was corrected using the counterpoise (CP) method . All quantum mechanical calculations were performed using the Gaussian 09 computer program .
2.3 Nucleation of HAp
MD simulations in NPT conditions (constant number of particles, temperature of 298 K and pressure of 1 atm) were performed using the NAMD 2.6  code to investigate the process of formation and growth of HAp around ds B-DNA molecule in a bath of water molecules. Before the incorporation of DNA, the density of the water in the simulation box was 1.00 g/cm3 at a temperature of 298 K. The force-field parameters for DNA, phosphate and hydroxyl groups, and Ca2+ were identical to those for the encapsulation study. The water molecules were represented using the TIP3P model . The initial simulation box (92.0×91.5×108.0 Å3) was equilibrated using the following strategy. Before any MD trajectory was run, 5×103 steps of energy minimization were performed in order to relax conformational and structural tensions. Next, different consecutive rounds of short MD runs were performed in order to equilibrate the density, temperature, and pressure. First, solvent and ions were thermally relaxed by three consecutives runs, while the B-DNA was kept frozen: 0.5 ns of NVT-MD at 500 K were used to homogeneously distribute the solvent and ions in the box. After this, 0.5 ns of isothermal (298 K) and 0.5 ns isobaric (1 atm and 298 K) relaxation were run. Finally, all the atoms of the system were submitted to 0.15 ns of steady heating until the target temperature was reached (298 K), 0.25 ns of NVT-MD at 298 K (thermal equilibration) followed by 0.5 ns of density relaxation (NPT-MD).
Atom pair distance cut-offs were applied at 16.0 Å to compute the van der Waals interactions. In order to avoid discontinuities in the Lennard-Jones potential, a switch function was applied to allow a continuous decay of the energy when the atom pair distances are larger than 14.0 Å. For electrostatic interactions, we computed the non-truncated electrostatic potential throughout Ewald Summations . The real space term was determined by the van der Waals cut-off (16 Å), while the reciprocal term was estimated by interpolation of the effective charge into a charge mesh with a grid thickness of 5 points per volume unit, i.e. Particle-Mesh Ewald (PME) method . Both temperature and pressure were controlled by the weak coupling method, the Berendsen thermobarostat . The relaxation times used for the coupling were 1 and 10 ps for temperature and pressure, respectively. Bond lengths were constrained using the SHAKE algorithm  with a numerical integration step of 1 fs. Periodic boundary conditions were applied using the nearest image convention, and the nonbonded pair list was updated every 1000 steps (1 ps). The end of the density relaxation simulation was the starting point of the 10 ns production simulations presented in this work. The coordinates of all the production runs were saved every 500 steps (1 ps intervals).
3 Results and discussion
3.1 Embedding double stranded B-DNA in hydroxyapatite
Stress induced by the minerals in the DNA molecules (Δτ; in kcal/mol), stretching, bending and torsional contributions to the stress (Δ E str , Δ E bnd and Δ E tor , respectively), inter-chain distance (IC; in Å) and root mean square deviations (RMSD; in Å) between the initial and the relaxed conformations of the biomolecule for different systems encapsulated in HAp and FAp
The overall of these results indicates that the cavity displayed in Figure 1b allows encapsulate B-DNA double helices without produce mineral-induced stress. Moreover, the dimensions of the pore combined with the crucial role played by the Ca2+ are appropriated to avoid any dependence on the nucleotide sequence. Accurate definition of the cavity is provided by the maximum distances between pairs of atoms of the mineral at the internal diagonals of the pore, which are 30.5 and 21.1 Å.
3.2 Embedding double stranded B-DNA in fluoroapatite
3.3 Embedding single stranded DNA in apatites
As expected, ss DNA molecules encapsulated in HAp and FAp underwent drastic conformational changes upon relaxation. Obviously, this should be attributed to the lack of inter-strand hydrogen bonding, which facilitates the distortions induced by the interactions with the mineral. Figure 3b reflects such important variations for ss-I. The RMSD obtained for the strand encapsulated in HAp and FAp after relaxation is 10.3 and 11.1 Å, respectively, suggesting that distortions are similar in both cases. The latter is corroborated by Δτ values (Table 1). Thus, the pore is large enough to minimize repulsive interactions, independently of the composition of the mineral, through the complete conformational reorganization of the biomolecule. The relaxed conformation displayed in Figure 3b should be simply considered as one of the many possible disordered conformational states of the ss DNA molecules (i.e. the pore allows multiple disordered conformational states for the DNA strand, as was observed during the MD simulation). Similar results were obtained for ss-II and ss-III (not shown).
3.4 Validation of the force-field
We are aware that the molecular mechanics calculations presented in the above sub-sections were carried out using force-field parameters that were not explicitly designed to investigate the inorganic···organic interactions found in biominerals. Specifically, the parameters used to simulate the phosphate and hydroxyl groups of apatites were extracted from Amber ff03 , which was explicitly developed to study the dynamics of proteins and nucleic acid in condensed phases, while those used for Ca2+ and F- were set to study the crystallographic structure of monosaccharides  and the solvation of LiF in polarizable water , respectively. Before to investigate the nucleation of HAp at a B-DNA double helix, we performed quantum mechanical calculations on model systems to demonstrate that such force-field parameters satisfactorily reproduce inorganic···organic interactions. A total of 22 model complexes, each containing a fragment of HAp and a fragment of B-DNA, were taken from the model obtained for I embedded in the mineral. These model complexes were selected to cover a wide range of interactions, both attractive and repulsive. The interaction between the HAp and B-DNA fragments was calculated for all the complexes using both the force-field potential (ΔEFF,i) and the B3LYP/6-31G(d) quantum mechanical method (ΔEQM,i), the CP procedure being applied in the latter to correct the BSSE.
3.5 Nucleation of apatites using B-DNA
3.6 Dynamics of the initial stages of nucleation of apatites at B-DNA
In order to simulate the early formation and growing of calcium phosphate clusters in the nucleation of HAp at B-DNA double helix template, MD simulations of two systems based on stoichiometric aqueous solutions of Ca2 +, and OH– ions were carried out. In the first system, hereafter denoted HAp/DNA, a double helix B-DNA molecule was immersed in the stoichiometric solution described in the Methods section. The second system, hereafter denoted HAp, no DNA was incorporated to the water box thus remaining the Ca2 +, and OH– ions. The analysis of the results was performed on the bases of a 10 ns production run (i.e. the trajectory after equilibration of the density, temperature, and pressure; see Methods section) in the NPT ensemble. It is worth noting that these simulations are two times larger than those used to examine the early stages of nucleation of HAp at a collagen template  and, therefore, the clustering process is expected to occur within such time scale.
In this study, biominerals made of apatite and DNA have been modeled at the atomistic level. The aims of the work were to provide understanding of the influence of the mineral on the conformation of the biomolecule and to determine the possible role of the latter as nucleating agent of the mineral. Encapsulation of the B-DNA double helix in rhombohedric pores (γ= 120°) of HAp does not induce significant structural distortions in the biomolecule. This observation has been found to be independent of the DNA sequence, which has been attributed to the strong stabilizing interactions between the Ca2+ atoms of HAp and the phosphate groups of DNA. The minimum dimensions of the pore needed to encapsulate B-DNA are defined by the maximum distances between atoms of the mineral at the internal diagonals, which are 30.5 and 21.1 Å. This result is fully consistent with experimental investigations devoted to encapsulate DNA into HAp nanoparticles, which show a relatively high loading capacity through their pores. The structural stability of the encapsulated double helix is an important finding that offers new possibilities for the design of efficient therapeutic biomedical applications. These results are particularly relevant considering recent findings like the mechanism used by carcinogenic cells to capture HAp nanoparticles .
On the other hand, the mechanism proposed for the growing of apatite crystals using the double helix of B-DNA as nucleating agent represents an alternative to classical encapsulation processes (i.e. loading of biomolecules at the nanopores and/or the surface). Thus, the controlled formation of biominerals (i.e. porous nanoparticles of mineral growing from biomolecules) combined with conventional encapsulation approaches may be used to design therapies with higher efficacy and durability. MD simulations have been used to investigate the initial stages of nucleation and cluster formation of calcium phosphate at a B-DNA double helix in aqueous solution. At room temperature, calcium ions interact with DNA phosphates to form ion complexes, but attracted by electrostatic forces, they coordinate to and other calcium ions starting the formation of clusters. Finally, it should be mentioned that this growing mechanism of the biomineral is compatible with the theory and models proposed by Kostetsky  to explain the origin of organic matter and life on the Earth.
This work was supported by B. Braun Surgical S.A. through a joint research agreement with UPC. Special thanks to Mr. M. Jiménez for believing in the idea and funding the project. Authors thank J.F. Julián, J. Navinés, J.R. Grifols, C. Colomer, L.F. del Castillo, S. Santos and J.M. Turon for their contributions to the conceptual framework of the work. This work is integrated within a wider research project supported by B. Braun Surgical S.A., UPC, Institut de Ciencies Fotòniques (ICFO), and the Institut Català de la Salut (ICS) through the H. A. Germans Trias i Pujol and H. U. Vall d’Hebron, MICINN-FEDER funds (MAT2012-34498), and by the Generalitat de Catalunya (2009SGR925 and XRQTC). Authors are indebted to the Centre de Supercomputació de Catalunya (CESCA) for computational facilities. Support for the research of C.A. was received through the “ICREA Academia”.
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