Energetic basis for the molecular-scale organization of bone

Significance

The remarkable mechanical properties of bone are determined by the organization and strength of binding at the mineral–collagen interface. Although the process through which collagen becomes mineralized has been extensively studied, little is known about the mechanisms or energetics that underlie the organization of this mineral–matrix composite. Combining molecular-scale imaging and analyses of collagen adsorption on four bone-related calcium phosphate phases, single-molecule force measurements and molecular simulations of collagen binding to hydroxyapatite, and electron microscopy analyses of bone and dentine, we determine the magnitude and chemistry of collagen–hydroxyapatite binding and show that calcium-deficient apatite is the only phase consistent with observed structural relationships.

Abstract

The remarkable properties of bone derive from a highly organized arrangement of coaligned nanometer-scale apatite platelets within a fibrillar collagen matrix. The origin of this arrangement is poorly understood and the crystal structures of hydroxyapatite (HAP) and the nonmineralized collagen fibrils alone do not provide an explanation. Moreover, little is known about collagen–apatite interaction energies, which should strongly influence both the molecular-scale organization and the resulting mechanical properties of the composite. We investigated collagen–mineral interactions by combining dynamic force spectroscopy (DFS) measurements of binding energies with molecular dynamics (MD) simulations of binding and atomic force microscopy (AFM) observations of collagen adsorption on single crystals of calcium phosphate for four mineral phases of potential importance in bone formation. In all cases, we observe a strong preferential orientation of collagen binding, but comparison between the observed orientations and transmission electron microscopy (TEM) analyses of native tissues shows that only calcium-deficient apatite (CDAP) provides an interface with collagen that is consistent with both. MD simulations predict preferred collagen orientations that agree with observations, and results from both MD and DFS reveal large values for the binding energy due to multiple binding sites. These findings reconcile apparent contradictions inherent in a hydroxyapatite or carbonated apatite (CAP) model of bone mineral and provide an energetic rationale for the molecular-scale organization of bone.

Bone is a natural protein–mineral composite consisting of nonstoichiometric nanometer-scale carbonated apatite crystallites inside a fibrillar protein matrix. The matrix is mainly composed of type I collagen and is organized on multiple length scales (1, 2). At the shortest scale, three polypeptide chains form a triple helix referred to as a tropocollagen molecule that is ∼300 nm in length and 1.5 nm in diameter. These helices are arranged in a quasi-hexagonal bundle in which they overlap and intertwine to form microfibrils containing “hole zones,” where there is a gap between the N termini of one helix and the C termini of another (3–5). These microfibrils are further bundled both laterally and longitudinally to form native collagen (3, 4).

Within this highly organized scaffold, apatite crystallites form nanometer-scale platelets (6–9) with their [001] axes preferentially aligned parallel to the fibril axis (10–15) and the platelet faces defined by {100} crystal planes (16). Recent in vitro investigations of hydroxyapatite (HAP) formation within collagen fibrils revealed a multistage process in which amorphous calcium phosphate (ACP) first infiltrated through the hole zones and then converted into HAP platelets with initial mineral deposition occurring near the hole zones (11, 13). In vitro transmission electron microscopy (TEM) and atomic force microscopy (AFM) studies found that conversion of ACP to HAP involved an intermediate octacalcium phosphate (OCP) phase (17). In accord with these results, ACP was observed in vivo in developing zebrafish fin bone (18). Micro-Raman spectra of forming murine calvarial sutures also revealed an OCP-like phase deposited before the formation of apatite (19).

From these studies and others, the basic steps in apatite formation within collagen are becoming relatively clear, even if important questions remain (11, 13). In contrast, reasons for the topological organization of apatite within collagen that is key to the remarkable mechanical properties of bone remain unclear. Why, for example, does apatite, which has a nominal hexagonal symmetry, form platelets with the c axis in the plane of the platelets in violation of the underlying HAP crystallographic symmetry, and why do the platelets grow with their c axes parallel to the fibril axis?

The details of collagen fibril structure add to the mystery. Until recently, collagen was viewed as a pack of parallel rods between which laterally confined nuclei of apatite naturally grow with the fast-growth direction along the fibrils, giving the observed elongated plate-like morphology (20). This led to a model in which c-axis alignment is due to confined growth, which naturally selects for the fast-growth axis along the channels between the collagen helices (11, 21). However, structural studies have shown collagen helices are actually twisted and interwoven (5). Moreover, electron diffraction shows that apatite platelets exhibit significant rotational and tilting disorder (11), with a c-axis spread of ∼15–20° (22). X-ray diffraction studies have even documented a secondary orientation with the c axis perpendicular to the collagen axis (23). Thus, collagen alignment along the apatite [001] vector represents a statistical average of the molecular-scale organization and the local relationship between collagen and apatite is far more diverse, implying a complex collagen–apatite interaction.

Insights regarding this interaction have come from simulations in which HAP served as the mineral prototype (24, 25). The results suggest collagen peptides can induce solvated ions to form an apatite-like structure aligned along the collagen axis and that terminal carboxyl groups and amine groups exhibit stronger affinity to HAP (100) than to HAP (001). Subsequent 2D and 3D models of the supramolecular structure of collagen fibrils have been developed in an attempt to reproduce the relationship between collagen and HAP and understand the mechanical behavior (25–27). However, until now, experimental data that shed light on the face- and orientation-dependent collagen–mineral interaction energies that ultimately must underlie bone architecture have been nonexistent. Filling this gap has important implications beyond providing an accurate description of bone formation. The interactions at the collagen–bone apatite interface are a determining factor in the properties of bone (28), such as its fracture modes and toughness, compressive strength, and shear strength (1). These interactions must be approximated to engineer mineralized tissues or synthesize biomimetic materials that exhibit similar properties.

The purpose of this study is to define the energetics of the collagen–apatite interface. We use AFM to measure the equilibrium collagen binding orientations and binding free energies on various calcium phosphate mineral surfaces thought to play a role in bone formation, including OCP, HAP, carbonated apatite (CAP), and calcium-deficient apatite (CDAP). We compare the results to TEM analyses of collagen–apatite relationships in bone and dentine and then use molecular dynamics (MD) to explore the nature of the interactions, as well as the structural factors controlling collagen orientation on apatite. In doing so, we develop an energetic and structural rationale for the molecular-scale organization of this unique mineral–matrix composite.

Preparation and Characterization of Mineral Surfaces

Single-crystal surfaces of HAP hexagonal prisms expressing (100) and (001) faces, HAP platelets exhibiting (100) and (110) faces, CAP plates expressing the (100) face, and OCP and CDAP expressing (100) faces were prepared as described in SI Materials and Methods. HAP, OCP, and CAP were crystallized directly either from molten salts or hydrothermal solutions, and CDAP was prepared through hydrolysis of initially formed metastable OCP. The crystal phases were determined by Raman spectroscopy (Fig. 1A) and X-ray diffraction (XRD) (SI Appendix, Figs. S1 and S2).

Fig. 1.

Collagen orientation on HAP (100), HAP (110), CAP (100), OCP (100), and CDAP (100) faces. (A) Raman spectra of HAP hexagonal prism with (100) face, HAP platelet with (110) face, and HAP platelet with (100) face, CAP, OCP, and CDAP. (B–G) AFM images of collagen adsorption on faces of (B) HAP hexagonal prism (100) where Inset shows optical micrograph of whole crystal with AFM imaged region highlighted by white square, (C) HAP (110) where Inset shows magnified image taken from region shown by dashed square, (D) HAP platelet (100), (E) CAP (100), (F) OCP (100), (G) CDAP (100). White lines in B–G indicate steps of heights 0.816, 0.475, 0.817, 0.822, 1.863, and 0.660 nm, respectively. Note the 126.4° angle defined by two adjacent CDAP edges (G) matches that seen in TEM (SI Appendix, Fig. S4). (H) Histograms of collagen alignment angles with respect to [001] on HAP hexagonal prism (100) face, HAP (110) face, HAP platelet (100) face, CAP (100), OCP (100), and CDAP (100) showing most probable angles of 72.5°, −0.01°, 70°, 72.5°, 35.3°, and 0° and 90°, respectively.

The Raman spectra of all of the HAP crystals (Fig. 1A) exhibited the expected peaks (29), and XRD patterns of both hexagonal prisms (SI Appendix, Fig. S1A, red curve) and platelets (SI Appendix, Fig. S1A, blue curve) corresponded to phase-pure HAP. The Raman spectrum of CAP (Fig. 1A) matched that previously published; two distinct frequencies for the symmetric carbonate stretching mode (ν₁) have been suggested depending on whether substitution is of hydroxyl (type A substitution) or phosphate (type B substitution) at 1,107 and 1,070 cm⁻¹, respectively (30). The presence of only the characteristic peak at 1,070 cm⁻¹ indicates only carbonate replaced the phosphate of HAP. Based on the carbonate dependence of the Raman intensity (SI Appendix, Fig. S2) (31), we obtained a carbonate content of 5%, which is within the range of carbonate concentration in bone (4–7%) (32). The Raman spectrum of OCP (Fig. 1A) matched the accepted spectrum, with differences from that of HAP reflecting alternating apatitic and hydrated layers (SI Appendix, Fig. S3) (33).The hydrolysis of OCP to CDAP is evident by the decreased intensity of numerous Raman peaks (Fig. 1A) (33).

The HAP hexagonal prisms have six equivalent (100) faces (Fig. 1B, Inset and SI Appendix, Fig. S1B) dominated by atomically flat terraces separated by steps (SI Appendix, Fig. S1C) with height of 0.815 ± 0.021 nm. This matches the 0.817-nm d-spacing of (100) (34) and indicates only one kind of surface termination was present (35). The HAP platelets expressed (110) faces, as shown by the step height of 0.475 nm, in good agreement with the HAP (110) d-spacing of 0.472 nm (SI Appendix, Fig. S1D) (34). CAP, OCP, and CDAP also exhibited plate-like habits, with step heights of 0.822 ± 0.025 (Fig. 1E), 1.863 ± 0.039 (Fig. 1F), and 0.660 ± 0.075 nm (Fig. 1G), respectively. The exposed surfaces for CAP and OCP are assigned to CAP (100) and OCP (100), due to the match of these step heights with the d-spacing of 0.817 and 1.899 nm of these faces (34, 36). The surface step height of CDAP matched half the thickness of the apatitic layer in the OCP precursor (1.35 nm) (36). We determined the face to be (100) by TEM selected area electron diffraction, and measured angles between adjacent facets (Fig. 1G and SI Appendix, Fig. S4).

Results and Analysis

Collagen Alignment on Crystal Faces.

The dominant alignment directions for collagen on the various mineral faces were investigated in PBS solution. Typical fibrils heights were 1.5 nm, which agrees with the diameter of the collagen triple helix (3). In situ AFM images of the HAP hexagonal prism (100) face showed the most probable angle between collagen and the HAP [001] vector (c axis) was 72.5° (Fig. 1 B and H). Based on the HAP crystal structure (34), this corresponds to HAP [0-21], which has a theoretical angle of 69.9° from HAP [001]. On the (110) face of the HAP platelets, collagen adsorbed with a most probable alignment nearly along HAP [001] (Fig. 1 C and H). However, individual collagen triple helices often exhibited “cross-overs” from one c-axis–oriented track to another. These patterns were continuous over the entire face of the crystal, implying they represent the orientation of maximum binding energy and that the binding energy has a strong dependence on orientation.

Results for (100) faces of both HAP and CAP nanometer-scale platelets were similar to that observed on (100) faces of the much larger HAP hexagonal prisms. Most probable collagen alignment angles relative to the [001] vector on HAP (100) and CAP (100) faces were 70.0° and 72.5° (Fig. 1 D, E, and H), respectively. Thus, we conclude that collagen alignment on HAP and CAP is dependent only on the crystal face and not on crystal size, morphology, or degree of carbonate substitution.

We also investigated collagen adsorption onto the precursor OCP phase to study its potential role in determining collagen orientation on bone apatite (100). The alignment of collagen on the OCP (100) surface also fell along a specific orientation, with a most probable angle of 35.3° from OCP [001] (Fig. 1 F and H). This orientation matches OCP [012], which has a theoretical angle of 34.8°, as calculated from OCP structural models (36). The orientation of collagen on CDAP (100) was bimodal, with most probable angles of 0° and 90° from CDAP [001] (Fig. 1 G and H), as observed in bone (23).

Free Energies of Binding.

To quantify the strength of collagen–apatite binding, we used dynamic force spectroscopy (DFS) to measure the force required to rupture the collagen–HAP bond on (100) and (110) faces. We functionalized AFM tips with collagen using previously described methods (37). The collagen-decorated tip was put in contact with the crystal face in PBS for dwell times of 0 s and 5 s (Fig. 2A), and was retracted at pulling rates ranging from 399 nm/s to 4.34 µm/s. The force versus separation curves (Fig. 2B) exhibited a characteristic, complex profile with multiple rupture events, similar to that reported in previous studies of collagen stretching (38, 39). This pattern was reproducible both in terms of distance to rupture and the final rupture force.

Fig. 2.

Determination of binding free energy for collagen on HAP (100) and (110) faces. (A) Scheme shows collagen linked to gold-coated AFM cantilever by way of bifunctional linker LC-SPDP. Tip is placed directly on the face of individual HAP crystal. (B) Representative force–separation curves for collagen–HAP bond rupture at a loading rate of 1,900 pN/s. Curve shows multiple rupture events during retraction of AFM tip. Peak at largest tip–surface separation was used for free-energy analysis. (C and D) Dynamic force spectra for rupture of bonds between collagen and (100) (spring constant of 23.20 pN/nm) and (110) (spring constant of 30.03 pN/nm) faces of HAP, respectively, for dwell times of 0 s (blue) and 5 s (red). Solid curves are fits to harmonic potential model (SI Appendix, Eq. S7) with ν = 2. The number of bonds for the final rupture events was assumed to be 1. We took the instantaneous loading rate from the slope of the collagen extension curve close to the rupture event at the largest tip–surface separation.

We cannot differentiate unbinding of multiple collagen triple helices on the tip from sequential unbinding of a single collagen triple-helix molecule from different sites along its length. Consequently, quantitative rupture force analysis can only be applied to final rupture events, which give very consistent values of rupture force and for which correlated rupture of multiple collagen molecules is unlikely. Fig. 2C shows the collagen–HAP (100) rupture force vs. loading rate. The data exhibit the dependence expected from the theory of forced bond rupture (solid curve; see SI Appendix, SI Materials and Methods for details). The rupture force decreased as loading rate was reduced, approaching a plateau that marks the approach to equilibrium where the energy required to break the bond equals the binding free energy (37, 40). Depending on the specific model of collagen used for analysis of the data, for dwell times of 0 s and 5 s we obtained single-bond free energies in the ranges of −3.2 ± 0.3 to −4.4 ± 0.1 kcal/mol (−5.4 ± 0.5 to −7.5 ± 0.2 k_BT) and −3.3 ± 0.2 to −4.5 ± 1.2 kcal/mol (−5.6 ± 0.4 to −7.6 ± 2.4 k_BT) on HAP (100) and −3.8 ± 0.3 to −4.9 ± 0.2 kcal/mol (−6.3 ± 0.5 to −8.1 ± 0.3 k_BT) and −3.8 ± 0.4 to −4.8 ± 0.3 kcal/mol (−6.3 ± 0.7 to −8.0 ± 0.6 k_BT) on HAP (110) for dwell times of 0 s and 5 s, respectively (Fig. 2C and D; SI Appendix, Tables S1, S2, and S4). The results show the single-bond binding energy is independent of dwell time, implying that, even for the shortest dwell time possible with the instrument, the bond probed by the last rupture event has relaxed to the fully bound state. Moreover, the single-bond binding free energy for collagen on HAP (100) differs from that on HAP (110) by only about 1 k_BT.

We emphasize that the binding free energies determined here are single-bond energies for C-terminus binding only. They do not represent the total free energy of binding for an entire collagen triple helix, which makes multiple bonds to the surface as demonstrated by the multiple rupture events (Fig. 2B). This energy cannot be accurately extracted, because there is no way to deconvolve collagen–HAP unbinding events from internal energy dissipation due to collagen stretching, rupture of intracollagen bonds, or any bonds to the surface from other tip-bound collagen helices. However, we can estimate the total binding free energy from the area under the force–distance curves (area between blue curve and the horizontal axis in Fig. 2B) collected in the near-equilibrium regime of small loading rates. This is the work done during removal of a collagen triple helix from the surface and equals 208 ± 36 kcal/mol(350 ± 61k_BT) and 179 ± 29 kcal/mol(302 ± 49k_BT) for HAP (100) and (110) faces, respectively. Thus, whereas the single-bond binding free energy is slightly greater on the (110) face, the binding energy for the full collagen triple helix is ∼20% larger on the (100) face, suggesting that the stereochemical relationship of collagen to HAP favors better multisite binding on HAP (100) than on HAP (110).

Molecular Contacts That Control Binding.

To understand the atomic-level interactions that give rise to strong, orientation-dependent collagen–HAP binding energies, we performed MD simulations for binding to both the (100) and (110) faces by a type I collagen triple helix (∼80 Å) with the sequence (NH₃⁺-[proline(Pro)-hydroxyproline(Hyp)-glycine(Gly)]₁₀-COO⁻)₃ (see SI Appendix, SI Materials and Methods for details). The peptide was aligned horizontally on HAP (100) along the [0-11], [0-21], and [001] (c-axis) vectors, and on HAP (110), along the [001], [1-10], and [1-13] vectors. HAP is a dipolar crystal, constructed of layers of alternating net positive–negative charge that define apparent natural cleavage planes parallel to (100). Although there is no way of knowing a priori how the (100) surface is terminated, it is likely to be a modification of the positively charged calcium-rich layer in which there are surface-level calcium-ion vacancies (37, 41, 42). We prepared two such (100) surfaces for our models. The first, with 50% vacancies, shown in Fig. 3 A and C, is neutral on average across the solvent contact surface; the second, with all surface-level calcium ions removed, is negative. The only apparent choice for termination of the (110) surface has exposed hydroxide columns (Fig. 3D).

Fig. 3.

Molecular modeling representation of collagen adsorbed onto HAP (100) and (110). (A) Top view of (100) face. Repeating sections of collagen which make surface contact are indicated by boxes. (B) Top view of (110) surface. Repeating sections of collagen that make surface contact are indicated by boxes. (C) Side view of (100) surface, down the c axis. Periodicity at 20.06 Å along [0-21] of HAP is a close match to collagen's ∼19.9-Å periodicity. Carbonyls of the repeat Hyp-8B, Hyp-14C, and Hyp-20A residues are selected as representative of triple-helix periodicity. Surface grooves accommodate contact of prolines and hydroxyprolines; the triple-helix pitch is a near match for this alignment so that, for example, Hyp-14C (green) at center is stacked with Hyp-14B (green) behind it, in a common groove along [001] with Pro-13C (purple) in between. (D) Side view of (110) surface, 90° from c axis. Periodicity of HAP along c axis, of course, corresponds to unit cell parameter (c = 6.879 Å). Collagen's ∼19.9-Å periodicity roughly approximates a multiple of 3 unit cell lengths along the c axis.

Table 1 summarizes the computed binding energies for HAP (100) and (110). In exact agreement with the adsorption experiments, the collagen helix shows a clear preference for binding with an alignment along [0-21] on the (100) surface for both types of surface termination and along [001] (c axis) on the (110) surface. Moreover, in reasonable agreement with the DFS estimates for the complete collagen triple helix, the binding energy to HAP (100) is 1.5 times greater than to (110).

Table 1.

Collagen–HAP horizontal binding energies, kcal/mol

Surface helix alignment	(100)*			(110)*
	[001]	[0-11]	[0-21]	[001]	[1-10]	[1-13]
ΔΔEB†	+75.7 (+110.2)	+37.8 (+56.3)	0.0 (0.0)	0.0	+88.3	+94.5
ΔΔGB†	+59.5 (+48.1)	+46.2 (+85.2)	0.0 (0.0)	0.0	+30.1	+58.2

^*The first entries are for the HAP (100) surface termination shown in Fig. 4B. The second set of entries, given in parentheses, is for an alternative termination designated as (100)-2 in figure 2 of ref. 37.

^†Values are relative to the HAP (100) [0-21] binding energy and the HAP (110) [001] binding energy, respectively. Positive values indicate less favorable binding.

Fig. 3 A and C illustrates the structural reason for the preferred alignment on HAP (100): there is a close match of the collagen helix (∼19.9 Å) periodicity to that of HAP along [0-21] (20.06 Å). For the surface termination shown in Fig. 3C, the repeated binding motif along the helix–HAP (100) interface is particularly evident, anchored by repeating carbonyl–Ca²⁺ interactions ∼20 Å apart. The carbonyls belong to position-equivalent Hyp residues from alternate chains of the triple helix. Simulations of collagen binding to other (100) surface terminations also reflect the structural match along [0-21].

Fig. 3 B and D illustrates the preference for c-axis collagen alignment on HAP (110). Here, a poor match only allows for a short range of repeat interactions before falling out of synch. This may be why we observe collagen strands frequently crossing over to different (001) tracks on the (110) face, even though they generally follow (001) and may explain why the measured binding energy for the full collagen triple helix on (100) is greater than on (110), even though C-terminus binding alone is slightly larger on (110).

Collagen–Apatite Relationship in Bone and Dentine.

To relate these measurements and simulations to the organization of apatite in native bone, we performed high-resolution TEM imaging on ultrathin sections of rat calvarial bone and human dentine tubules to determine the major exposed face with or without collagen in natural mineralized tissues. TEM images show the circular structure of dentine tubules enclosed by plate-like apatite crystallites ∼5 nm in thickness (Fig. 4A). The hexagonally symmetric pattern indicates the electron beam goes along the [001] zone axis of apatite (Fig. 4B) and the 0.272-nm d-spacing corresponds to the HAP (300) plane. Hence, the platelet face parallel to the tubule direction is (100). For the bone samples, lower-magnification TEM images exhibit low-contrast, face-on views and high-contrast, edge-on views of platelets (Fig. 4C). High-resolution images show all apatite crystals are aligned with (300) adjacent to the fibrils (Fig. 4D), in agreement with a previous suggestion based on lower-resolution images (16). The minor face remains undetermined.

Fig. 4.

TEM images of thin slices of fully mineralized dentine and bone cut by ultramicrotome. (A) Lower-magnification image of dentine shows a tubule in the middle with apatite crystals aligned along circumferential direction of tubule. (B) Higher-magnification image of apatite crystal in white rectangle in A. (C) Overall image of bone shows flat-lying apatite crystals in lower contrast and upstanding crystals with cross-section in higher contrast. (D) Higher-magnification image of apatite crystals in white rectangle in C.

Discussion

Reconciling Collagen Alignment with Bone Apatite Composition.

Hydroxyapatite and carbonated apatite are often used as models of bone mineral. As shown by the collagen model of Orgel et al. (5) based on XRD (SI Appendix, Fig. S5), the largest angle between the collagen axis and apatite [001] is ∼15°, even when local collagen twist is considered. In addition, bone apatite exhibits a secondary orientation with the c axis perpendicular to the collagen fibril axis (23). However, the preferred collagen orientations on the (100) faces of HAP, CAP, and OCP are along [0-21], [0-21], and [012], respectively; these are either ∼70° (HAP and CAP) or ∼35° (OCP) away from the c axis. Moreover, although collagen aligns along [001] on HAP (110), no exposed (110) faces were found in bone and dentine samples, indicating this face plays little role in collagen–apatite interactions. Only in the case of CDAP are preferred angles of ∼0° and 90°observed on the (100) face. Thus, our findings show that the alignment of collagen observed in bone is successfully reproduced only when collagen is adsorbed onto CDAP (100). This conclusion fits well with Raman analyses showing bone mineral is indeed CDAP being calcium-deficient, containing hydrogen phosphate (HPO₄²⁻), carbonate (CO₃²⁻), and other ions, but relatively little hydroxide (43), and containing 4–7 wt % carbonate replacing phosphate (32). The distinction of bone apatite from HAP is highlighted by comparing spectra of native bone with the same collagen matrix (rat tail tendon) following remineralization with hydroxyapatite (SI Appendix, Fig. S6). Because the relative probability of collagen alignment along two different orientations at equilibrium is proportional to the exponential of the difference in binding free energies for those two orientations, the results imply that the energy of the collagen–mineral interface is minimized when collagen is aligned along 0° and 90° only for the case of CDAP.

The Strength of Collagen–Apatite Binding.

The force spectra give reasonable values for all of the single-bond parameters (SI Appendix, Table S1). Because the MD simulations predict dominant interactions between carbonyl groups of collagen and Ca²⁺ ions in the crystal lattice, and DFS measurements show the C-terminus binding energy is nearly equal for the different crystal faces, we expect the energy required to remove a collagen triple helix from an apatite surface to be similar for all of the apatite phases. This is supported by the similar values of binding energy determined by MD for the HAP (100) and (110) faces, despite their distinct structures. Thus, we expect the total binding energy to be hundreds of kcal/mol for the (100) faces of all of the apatite phases, although the extent to which this energy is enhanced or reduced due to the inherent disorder in the Ca-deficient carbonate-substituted lattice of bone mineral is unknown.

The Source of Apatite Alignment and Morphology in Bone.

The combination of these energetic analyses and the CDAP model for bone mineral suggests a structural cause for the plate-like morphology of apatite in bone and an energetic source for the alignment. With respect to the c-axis alignment of apatite parallel to the long axis of collagen, we cite the relationship between binding free energies and nucleation barriers. Recent investigations of nucleation on organic films in the CaCO₃ system demonstrated a direct relationship between the film–crystal binding free energy ΔG_b and the interfacial energy α between the forming nucleus and the film surface (44), with α decreasing linearly as ΔG_b increases. Because nucleation probability scales exponentially with α³, the collagen–apatite binding free energy should exert a tremendous control over the position, orientation, and rate of nucleation. Indeed, previous measurements of ACP and HAP nucleation rates demonstrated α is significantly reduced on collagen relative to its value in solution, leading to greatly enhanced nucleation rates (17). Both the DFS measurements and the MD simulations show that, for the collagen–apatite interface, binding energies are hundreds of k_BT. Thus, when CDAP nucleates, whether from ACP (45) or OCP, based on the results with collagen alignment on CDAP (100) faces we should expect preferential c-axis alignment both parallel to and orthogonal to the long axis of collagen. Moreover, the local variations in collagen orientation by up to 15° are then consistent with a similar spread in bone apatite c axis, as is observed (22).

The hypothesis that alignment stems from collagen–apatite binding energetics contrasts with the view that physical confinement alone leads to alignment. In the latter model, because HAP grows fastest along [001], nuclei that form with (001) along the fibril direction rapidly fill the interfibrillar channels whereas crystals aligned otherwise are blocked at small size (11, 21). Neither model provides an explanation for all relevant observations. For example, predictions of the free-energy model are at odds with in vitro mineralization experiments in which apatite crystals that nucleated on the outside of collagen fibrils exhibited no common alignment direction, whereas those on the interior exhibited a degree of alignment similar to that seen in native tissue (11, 13). On the other hand, in a well-ordered hexagonal bundle of fibers, there are three planar channels that span the entire fibril, permitting the fast-growth axis to attain any angle relative to the long axis of the fibril within those channels. Moreover, the real structure of collagen is far more complex and does not provide continuous channels along the length of the fibril (SI Appendix, Fig. S5). In addition, one is hard pressed to explain why the clear stereochemical matching of the matrix to the mineral plays no role in directing growth given the demonstration of this effect in even simple systems (44, 46). Thus, both mechanisms may work in concert to exert the observed control. The environment within a fibril is likely to amplify the energetic effects measured here, because it brings together numerous collagen strands at distances comparable to diameters of both the amorphous precursors (13) and critical nuclei (17), whereas any tendencies toward channel alignment along fibrils will exert a further pressure to select a single-crystal alignment.

With respect to morphology, because CDAP has been found to possess monoclinic symmetry (47) and forms through recrystallization of either ACP or OCP, there is no reason why the habit of bone apatite platelets should mirror the hexagonal symmetry of HAP. Moreover, a plate-like habit is consistent with monoclinic symmetry. In conclusion, the findings presented here provide insight into the structural and energetic characteristics of the collagen-bone apatite interface that play a central role in determining both the mineral–matrix spatial relationship and the mechanical properties of the composite.

Materials and Methods

Full details of crystal preparation, collagen adsorption, AFM tip decoration, DFS measurement and analysis, collagen orientation analysis, collagen mineralization, tissue sample preparation and TEM imaging, and MD simulations are provided in SI Appendix, SI Materials and Methods.

Crystal Preparation.

Micrometer-sized HAP hexagonal prisms were prepared by recrystallization of HAP nanocrystals in K₂SO₄ molten salt. HAP platelets with (100) and (110) faces, CAP plates, OCP, and CDAP crystals were synthesized using hydrothermal methods with controlled ammonia or CO₂ release.

Collagen Adsorption on Crystal Surfaces.

Crystals were transferred from water into 500 µL collagen (40 nM) in PBS solution (Sigma-Aldrich) and kept static for 30 min. The collagen-adsorbed crystals were then transferred onto freshly cleaved mica and set in PBS solution for another 10 min before imaging.

Tip Decoration and DFS Measurement.

Details of tip decoration were reported previously (37). Briefly, Au-coated Si₃N₄ AFM tips (Bruker, MSCT) were modified with a heterobifunctional cross-linker succinimidyl 6-(3-[2-pyridyldithio]-propionamido)hexanoate (LC-SPDP) (Thermo Scientific), which bears a pyridyl disulfide that binds to Au, leaving a low density of N-hydroxysuccinimide ester groups to form a stable amide bond with a primary lysine residue or terminal amine of collagen. For force measurements, a constant approach velocity of 1 µm/s and dwell times of 0 s and 5 s were used for six different pulling speeds ranging from 399 nm/s to 4.34 µm/s at equal intervals (natural log units).

MD Simulation Methods.

Charge-neutral HAP slabs were constructed for the (100) and (110) surfaces using Cerius² crystal builder software (Accelrys). The CHARMM22 force-field parameter set (48) was assigned to the collagen peptide, with nonstandard hydroxyproline parameters taken from Park et al. (49). Simulations of HAP–collagen systems were carried out using NAMD 2.8 (50) with a dielectric imposed representing water (ε = 80) under periodic boundary conditions.