Energetic basis for the molecular-scale organizationof boneJinhui Taoa,b, Keith C. Battlec, Haihua Pand, E. Alan Salterc, Yung-Ching Chiena,e, Andrzej Wierzbickic,1,and James J. De Yoreoa,b,1

aMolecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA 94720; bPhysical Sciences Division, Pacific Northwest National Laboratory, Richland,WA 99352; cDepartment of Chemistry, University of South Alabama, Mobile, AL 36688; dQiushi Academy for Advanced Studies, Zhejiang University,Hangzhou, 310027 China; and eDepartment of Preventive and Restorative Dental Sciences, University of California, San Francisco, CA 94143

Edited by Markus J. Buehler, Massachusetts Institute of Technology, Cambridge, MA, and accepted by the Editorial Board November 24, 2014 (received forreview March 12, 2014)

The remarkable properties of bone derive from a highly orga-nized arrangement of coaligned nanometer-scale apatite plateletswithin a fibrillar collagen matrix. The origin of this arrangement ispoorly understood and the crystal structures of hydroxyapatite(HAP) and the nonmineralized collagen fibrils alone do not providean explanation. Moreover, little is known about collagen–apatiteinteraction energies, which should strongly influence both themolecular-scale organization and the resulting mechanical proper-ties of the composite. We investigated collagen–mineral interactionsby combining dynamic force spectroscopy (DFS) measurements ofbinding energies with molecular dynamics (MD) simulations of bind-ing and atomic force microscopy (AFM) observations of collagenadsorption on single crystals of calcium phosphate for four mineralphases of potential importance in bone formation. In all cases, weobserve a strong preferential orientation of collagen binding, butcomparison between the observed orientations and transmissionelectron microscopy (TEM) analyses of native tissues shows thatonly calcium-deficient apatite (CDAP) provides an interface withcollagen that is consistent with both. MD simulations predict pre-ferred collagen orientations that agree with observations, andresults from both MD and DFS reveal large values for the bindingenergy due to multiple binding sites. These findings reconcile ap-parent contradictions inherent in a hydroxyapatite or carbonatedapatite (CAP) model of bone mineral and provide an energetic ra-tionale for the molecular-scale organization of bone.

biomineralization | bone | protein–mineral interface |dynamic force spectroscopy

Bone is a natural protein–mineral composite consisting ofnonstoichiometric nanometer-scale carbonated apatite crys-

tallites inside a fibrillar protein matrix. The matrix is mainlycomposed of type I collagen and is organized on multiple lengthscales (1, 2). At the shortest scale, three polypeptide chains forma triple helix referred to as a tropocollagen molecule that is ∼300nm in length and 1.5 nm in diameter. These helices are arrangedin a quasi-hexagonal bundle in which they overlap and intertwineto form microfibrils containing “hole zones,” where there is a gapbetween the N termini of one helix and the C termini of another(3–5). These microfibrils are further bundled both laterally andlongitudinally to form native collagen (3, 4).Within this highly organized scaffold, apatite crystallites form

nanometer-scale platelets (6–9) with their [001] axes preferen-tially aligned parallel to the fibril axis (10–15) and the plateletfaces defined by {100} crystal planes (16). Recent in vitroinvestigations of hydroxyapatite (HAP) formation within colla-gen fibrils revealed a multistage process in which amorphouscalcium phosphate (ACP) first infiltrated through the hole zonesand then converted into HAP platelets with initial mineraldeposition occurring near the hole zones (11, 13). In vitro trans-mission electron microscopy (TEM) and atomic force microscopy(AFM) studies found that conversion of ACP to HAP involved anintermediate octacalcium phosphate (OCP) phase (17). In accordwith these results, ACP was observed in vivo in developing

zebrafish fin bone (18). Micro-Raman spectra of forming murinecalvarial sutures also revealed an OCP-like phase depositedbefore the formation of apatite (19).From these studies and others, the basic steps in apatite for-

mation within collagen are becoming relatively clear, even ifimportant questions remain (11, 13). In contrast, reasons for thetopological organization of apatite within collagen that is key tothe remarkable mechanical properties of bone remain unclear.Why, for example, does apatite, which has a nominal hexagonalsymmetry, form platelets with the c axis in the plane of theplatelets in violation of the underlying HAP crystallographicsymmetry, and why do the platelets grow with their c axes par-allel to the fibril axis?The details of collagen fibril structure add to the mystery.

Until recently, collagen was viewed as a pack of parallel rodsbetween which laterally confined nuclei of apatite naturally growwith the fast-growth direction along the fibrils, giving the ob-served elongated plate-like morphology (20). This led to a modelin which c-axis alignment is due to confined growth, which nat-urally selects for the fast-growth axis along the channels betweenthe collagen helices (11, 21). However, structural studies haveshown collagen helices are actually twisted and interwoven (5).Moreover, electron diffraction shows that apatite platelets ex-hibit significant rotational and tilting disorder (11), with a c-axisspread of ∼15–20° (22). X-ray diffraction studies have evendocumented a secondary orientation with the c axis perpendic-ular to the collagen axis (23). Thus, collagen alignment alongthe apatite [001] vector represents a statistical average of the

Significance

The remarkable mechanical properties of bone are determined bythe organization and strength of binding at the mineral–collageninterface. Although the process through which collagen becomesmineralized has been extensively studied, little is known aboutthe mechanisms or energetics that underlie the organization ofthis mineral–matrix composite. Combining molecular-scale imag-ing and analyses of collagen adsorption on four bone-relatedcalcium phosphate phases, single-molecule force measurementsand molecular simulations of collagen binding to hydroxyapatite,and electron microscopy analyses of bone and dentine, we de-termine the magnitude and chemistry of collagen–hydroxyapa-tite binding and show that calcium-deficient apatite is the onlyphase consistent with observed structural relationships.

Author contributions: J.T., A.W., and J.J.D.Y. designed research; J.T., K.C.B., H.P., E.A.S.,and Y.-C.C. performed research; H.P. and Y.-C.C. contributed new reagents/analytic tools;J.T., K.C.B., E.A.S., A.W., and J.J.D.Y. analyzed data; and J.T., A.W., and J.J.D.Y. wrotethe paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission. M.J.B. is a guest editor invited by the EditorialBoard.1To whom correspondence may be addressed. Email: awierzbicki@southalabama.edu orjames.deyoreo@pnnl.gov.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1404481112/-/DCSupplemental.

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molecular-scale organization and the local relationship betweencollagen and apatite is far more diverse, implying a complexcollagen–apatite interaction.Insights regarding this interaction have come from simulations

in which HAP served as the mineral prototype (24, 25). The resultssuggest collagen peptides can induce solvated ions to form anapatite-like structure aligned along the collagen axis and thatterminal carboxyl groups and amine groups exhibit stronger af-finity to HAP (100) than to HAP (001). Subsequent 2D and 3Dmodels of the supramolecular structure of collagen fibrils havebeen developed in an attempt to reproduce the relationship be-tween collagen and HAP and understand the mechanical behavior(25–27). However, until now, experimental data that shed light onthe face- and orientation-dependent collagen–mineral interactionenergies that ultimately must underlie bone architecture have beennonexistent. Filling this gap has important implications beyondproviding an accurate description of bone formation. The inter-actions at the collagen–bone apatite interface are a determiningfactor in the properties of bone (28), such as its fracture modesand toughness, compressive strength, and shear strength (1). Theseinteractions must be approximated to engineer mineralized tissuesor 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 equi-librium collagen binding orientations and binding free energieson various calcium phosphate mineral surfaces thought to play arole in bone formation, including OCP, HAP, carbonated apatite(CAP), and calcium-deficient apatite (CDAP). We compare theresults to TEM analyses of collagen–apatite relationships in boneand dentine and then use molecular dynamics (MD) to explorethe nature of the interactions, as well as the structural factorscontrolling collagen orientation on apatite. In doing so, we de-velop an energetic and structural rationale for the molecular-scale organization of this unique mineral–matrix composite.

Preparation and Characterization of Mineral SurfacesSingle-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 CDAPexpressing (100) faces were prepared as described in SI Materialsand Methods. HAP, OCP, and CAP were crystallized directly ei-ther from molten salts or hydrothermal solutions, and CDAP wasprepared 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).The Raman spectra of all of the HAP crystals (Fig. 1A) exhibited

the expected peaks (29), and XRD patterns of both hexagonalprisms (SI Appendix, Fig. S1A, red curve) and platelets (SI Appendix,Fig. S1A, blue curve) corresponded to phase-pure HAP. TheRaman spectrum of CAP (Fig. 1A) matched that previously pub-lished; two distinct frequencies for the symmetric carbonatestretching mode (ν1) have been suggested depending on whethersubstitution is of hydroxyl (type A substitution) or phosphate (typeB substitution) at 1,107 and 1,070 cm−1, respectively (30). Thepresence of only the characteristic peak at 1,070 cm−1 indicates onlycarbonate replaced the phosphate of HAP. Based on the car-bonate dependence of the Raman intensity (SI Appendix, Fig.S2) (31), we obtained a carbonate content of 5%, which iswithin the range of carbonate concentration in bone (4–7%)(32). The Raman spectrum of OCP (Fig. 1A) matched the ac-cepted spectrum, with differences from that of HAP reflectingalternating apatitic and hydrated layers (SI Appendix, Fig. S3)(33).The hydrolysis of OCP to CDAP is evident by the de-creased 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 atomi-cally flat terraces separated by steps (SI Appendix, Fig. S1C) withheight of 0.815 ± 0.021 nm. This matches the 0.817-nm d-spacingof (100) (34) and indicates only one kind of surface terminationwas present (35). The HAP platelets expressed (110) faces, asshown by the step height of 0.475 nm, in good agreement withthe 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 exposedsurfaces for CAP and OCP are assigned to CAP (100) and OCP(100), due to the match of these step heights with the d-spacing of0.817 and 1.899 nm of these faces (34, 36). The surface step heightof CDAP matched half the thickness of the apatitic layer in theOCP precursor (1.35 nm) (36). We determined the face to be(100) by TEM selected area electron diffraction, and measuredangles between adjacent facets (Fig. 1G and SI Appendix, Fig. S4).

Results and AnalysisCollagen Alignment on Crystal Faces. The dominant alignment direc-tions for collagen on the various mineral faces were investigated in

Fig. 1. Collagen orientation on HAP (100), HAP (110), CAP (100), OCP (100), andCDAP (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, andCDAP. (B–G) AFM images of collagen adsorption on faces of (B) HAP hexagonalprism (100) where Inset shows optical micrograph of whole crystal with AFMimaged region highlighted by white square, (C) HAP (110) where Inset showsmagnified 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 indicatesteps 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 thatseen in TEM (SI Appendix, Fig. S4). (H) Histograms of collagen alignment angleswith respect to [001] on HAP hexagonal prism (100) face, HAP (110) face, HAPplatelet (100) face, CAP (100), OCP (100), and CDAP (100) showingmost probableangles of 72.5°, −0.01°, 70°, 72.5°, 35.3°, and 0° and 90°, respectively.

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PBS solution. Typical fibrils heights were 1.5 nm, which agrees withthe diameter of the collagen triple helix (3). In situ AFM images ofthe HAP hexagonal prism (100) face showed the most probableangle between collagen and the HAP [001] vector (c axis) was 72.5°(Fig. 1 B and H). Based on the HAP crystal structure (34), thiscorresponds to HAP [0-21], which has a theoretical angle of 69.9°from HAP [001]. On the (110) face of the HAP platelets, collagenadsorbed with a most probable alignment nearly along HAP [001](Fig. 1 C and H). However, individual collagen triple helices oftenexhibited “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 en-ergy and that the binding energy has a strong dependence onorientation.Results for (100) faces of both HAP and CAP nanometer-

scale platelets were similar to that observed on (100) faces of themuch larger HAP hexagonal prisms. Most probable collagenalignment angles relative to the [001] vector on HAP (100) andCAP (100) faces were 70.0° and 72.5° (Fig. 1 D, E, and H), re-spectively. Thus, we conclude that collagen alignment on HAPand CAP is dependent only on the crystal face and not on crystalsize, morphology, or degree of carbonate substitution.We also investigated collagen adsorption onto the precursor

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

Free Energies of Binding. To quantify the strength of collagen–apatite binding, we used dynamic force spectroscopy (DFS) tomeasure the force required to rupture the collagen–HAP bondon (100) and (110) faces. We functionalized AFM tips with col-lagen using previously described methods (37). The collagen-decorated tip was put in contact with the crystal face in PBS fordwell times of 0 s and 5 s (Fig. 2A), and was retracted at pullingrates ranging from 399 nm/s to 4.34 μm/s. The force versus sepa-ration curves (Fig. 2B) exhibited a characteristic, complex profilewith multiple rupture events, similar to that reported in previousstudies of collagen stretching (38, 39). This pattern was reproducibleboth in terms of distance to rupture and the final rupture force.We cannot differentiate unbinding of multiple collagen triple

helices on the tip from sequential unbinding of a single collagentriple-helix molecule from different sites along its length. Conse-quently, quantitative rupture force analysis can only be applied tofinal rupture events, which give very consistent values of ruptureforce and for which correlated rupture of multiple collagen mole-cules is unlikely. Fig. 2C shows the collagen–HAP (100) ruptureforce vs. loading rate. The data exhibit the dependence expectedfrom the theory of forced bond rupture (solid curve; see SI Ap-pendix, SI Materials and Methods for details). The rupture forcedecreased as loading rate was reduced, approaching a plateau thatmarks the approach to equilibrium where the energy required tobreak the bond equals the binding free energy (37, 40). Dependingon the specific model of collagen used for analysis of the data, fordwell times of 0 s and 5 s we obtained single-bond free energies inthe ranges of −3.2 ± 0.3 to −4.4 ± 0.1 kcal/mol (−5.4 ± 0.5 to−7.5 ± 0.2 kBT) and −3.3 ± 0.2 to −4.5 ± 1.2 kcal/mol (−5.6 ± 0.4to −7.6 ± 2.4 kBT) on HAP (100) and −3.8 ± 0.3 to −4.9 ±0.2 kcal/mol (−6.3 ± 0.5 to −8.1 ± 0.3 kBT) and −3.8 ± 0.4 to−4.8 ± 0.3 kcal/mol (−6.3 ± 0.7 to −8.0 ± 0.6 kBT) on HAP (110)for dwell times of 0 s and 5 s, respectively (Fig. 2C and D; SIAppendix, Tables S1, S2, and S4). The results show the single-bondbinding energy is independent of dwell time, implying that, even forthe shortest dwell time possible with the instrument, the bondprobed by the last rupture event has relaxed to the fully boundstate. Moreover, the single-bond binding free energy for collagenon HAP (100) differs from that on HAP (110) by only about 1 kBT.

We emphasize that the binding free energies determined hereare single-bond energies for C-terminus binding only. They donot represent the total free energy of binding for an entire col-lagen triple helix, which makes multiple bonds to the surface asdemonstrated by the multiple rupture events (Fig. 2B). Thisenergy cannot be accurately extracted, because there is no way todeconvolve collagen–HAP unbinding events from internal en-ergy dissipation due to collagen stretching, rupture of intra-collagen bonds, or any bonds to the surface from other tip-boundcollagen helices. However, we can estimate the total binding freeenergy from the area under the force–distance curves (area be-tween blue curve and the horizontal axis in Fig. 2B) collected inthe near-equilibrium regime of small loading rates. This is thework done during removal of a collagen triple helix from thesurface and equals 208 ± 36 kcal/mol(350 ± 61kBT) and 179 ±29 kcal/mol(302 ± 49kBT) for HAP (100) and (110) faces, re-spectively. Thus, whereas the single-bond binding free energy isslightly greater on the (110) face, the binding energy for the fullcollagen triple helix is ∼20% larger on the (100) face, suggestingthat the stereochemical relationship of collagen to HAP favorsbetter 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-dependentcollagen–HAP binding energies, we performed MD simulationsfor binding to both the (100) and (110) faces by a type I collagentriple helix (∼80 Å) with the sequence (NH3

+-[proline(Pro)-hydroxyproline(Hyp)-glycine(Gly)]10-COO−)3 (see SI Appen-dix, SI Materials and Methods for details). The peptide wasaligned 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 layersof alternating net positive–negative charge that define apparentnatural cleavage planes parallel to (100). Although there is no way

Fig. 2. Determination of binding free energy for collagen on HAP (100) and(110) faces. (A) Scheme shows collagen linked to gold-coated AFM cantileverby way of bifunctional linker LC-SPDP. Tip is placed directly on the face ofindividual HAP crystal. (B) Representative force–separation curves for colla-gen–HAP bond rupture at a loading rate of 1,900 pN/s. Curve shows multiplerupture events during retraction of AFM tip. Peak at largest tip–surfaceseparation was used for free-energy analysis. (C and D) Dynamic forcespectra for rupture of bonds between collagen and (100) (spring constant of23.20 pN/nm) and (110) (spring constant of 30.03 pN/nm) faces of HAP, re-spectively, for dwell times of 0 s (blue) and 5 s (red). Solid curves are fits toharmonic potential model (SI Appendix, Eq. S7) with ν = 2. The number ofbonds for the final rupture events was assumed to be 1. We took the in-stantaneous loading rate from the slope of the collagen extension curve closeto the rupture event at the largest tip–surface separation.

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of knowing a priori how the (100) surface is terminated, it islikely to be a modification of the positively charged calcium-richlayer 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, isneutral on average across the solvent contact surface; thesecond, with all surface-level calcium ions removed, is negative.The only apparent choice for termination of the (110) surfacehas exposed hydroxide columns (Fig. 3D).Table 1 summarizes the computed binding energies for

HAP (100) and (110). In exact agreement with the adsorptionexperiments, the collagen helix shows a clear preference forbinding with an alignment along [0-21] on the (100) surface forboth types of surface termination and along [001] (c axis) on the(110) surface. Moreover, in reasonable agreement with the DFSestimates for the complete collagen triple helix, the bindingenergy to HAP (100) is 1.5 times greater than to (110).Fig. 3 A and C illustrates the structural reason for the pre-

ferred alignment on HAP (100): there is a close match of thecollagen helix (∼19.9 Å) periodicity to that of HAP along [0-21](20.06 Å). For the surface termination shown in Fig. 3C, therepeated binding motif along the helix–HAP (100) interface is par-

ticularly evident, anchored by repeating carbonyl–Ca2+ interactions∼20 Å apart. The carbonyls belong to position-equivalent Hypresidues from alternate chains of the triple helix. Simulations ofcollagen binding to other (100) surface terminations also reflectthe 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 fora short range of repeat interactions before falling out of synch. Thismay be why we observe collagen strands frequently crossing over todifferent (001) tracks on the (110) face, even though they generallyfollow (001) and may explain why the measured binding energy forthe full collagen triple helix on (100) is greater than on (110), eventhough C-terminus binding alone is slightly larger on (110).

Collagen–Apatite Relationship in Bone and Dentine. To relate thesemeasurements and simulations to the organization of apatite innative bone, we performed high-resolution TEM imaging on ul-trathin sections of rat calvarial bone and human dentine tubules todetermine the major exposed face with or without collagen innatural mineralized tissues. TEM images show the circular struc-ture of dentine tubules enclosed by plate-like apatite crystallites∼5 nm in thickness (Fig. 4A). The hexagonally symmetric patternindicates the electron beam goes along the [001] zone axis ofapatite (Fig. 4B) and the 0.272-nm d-spacing corresponds to theHAP (300) plane. Hence, the platelet face parallel to the tubuledirection is (100). For the bone samples, lower-magnificationTEM images exhibit low-contrast, face-on views and high-contrast,edge-on views of platelets (Fig. 4C). High-resolution images showall 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.

DiscussionReconciling Collagen Alignment with Bone Apatite Composition.Hydroxyapatite and carbonated apatite are often used as mod-els of bone mineral. As shown by the collagen model of Orgelet al. (5) based on XRD (SI Appendix, Fig. S5), the largest anglebetween the collagen axis and apatite [001] is ∼15°, even whenlocal collagen twist is considered. In addition, bone apatiteexhibits a secondary orientation with the c axis perpendicular tothe collagen fibril axis (23). However, the preferred collagenorientations on the (100) faces of HAP, CAP, and OCP arealong [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, indicatingthis face plays little role in collagen–apatite interactions. Only inthe case of CDAP are preferred angles of ∼0° and 90°observedon the (100) face. Thus, our findings show that the alignment ofcollagen observed in bone is successfully reproduced only whencollagen is adsorbed onto CDAP (100). This conclusion fits wellwith Raman analyses showing bone mineral is indeed CDAP be-ing calcium-deficient, containing hydrogen phosphate (HPO4

2−),carbonate (CO3

2−), 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 bycomparing 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 collagenalignment along two different orientations at equilibrium is pro-portional to the exponential of the difference in binding free en-ergies for those two orientations, the results imply that the energyof the collagen–mineral interface is minimized when collagen isaligned along 0° and 90° only for the case of CDAP.

The Strength of Collagen–Apatite Binding. The force spectra givereasonable values for all of the single-bond parameters (SI Ap-pendix, Table S1). Because the MD simulations predict dominantinteractions between carbonyl groups of collagen and Ca2+ ionsin the crystal lattice, and DFS measurements show the C-ter-minus binding energy is nearly equal for the different crystalfaces, we expect the energy required to remove a collagen triple

Fig. 3. Molecular modeling representation of collagen adsorbed onto HAP(100) and (110). (A) Top view of (100) face. Repeating sections of collagenwhich make surface contact are indicated by boxes. (B) Top view of (110)surface. Repeating sections of collagen that make surface contact are in-dicated by boxes. (C) Side view of (100) surface, down the c axis. Periodicityat 20.06 Å along [0-21] of HAP is a close match to collagen’s ∼19.9-Å peri-odicity. Carbonyls of the repeat Hyp-8B, Hyp-14C, and Hyp-20A residues areselected as representative of triple-helix periodicity. Surface grooves ac-commodate contact of prolines and hydroxyprolines; the triple-helix pitch isa near match for this alignment so that, for example, Hyp-14C (green) atcenter 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 cellparameter (c = 6.879 Å). Collagen’s ∼19.9-Å periodicity roughly approx-imates a multiple of 3 unit cell lengths along the c axis.

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helix from an apatite surface to be similar for all of the apatitephases. This is supported by the similar values of binding energydetermined by MD for the HAP (100) and (110) faces, despitetheir distinct structures. Thus, we expect the total binding energyto be hundreds of kcal/mol for the (100) faces of all of the apatitephases, although the extent to which this energy is enhanced orreduced due to the inherent disorder in the Ca-deficient car-bonate-substituted lattice of bone mineral is unknown.

The Source of Apatite Alignment and Morphology in Bone. Thecombination of these energetic analyses and the CDAP modelfor bone mineral suggests a structural cause for the plate-likemorphology of apatite in bone and an energetic source for thealignment. With respect to the c-axis alignment of apatite par-allel to the long axis of collagen, we cite the relationship betweenbinding free energies and nucleation barriers. Recent inves-tigations of nucleation on organic films in the CaCO3 systemdemonstrated a direct relationship between the film–crystalbinding free energy ΔGb and the interfacial energy α between theforming nucleus and the film surface (44), with α decreasinglinearly as ΔGb increases. Because nucleation probability scalesexponentially with α3, the collagen–apatite binding free energyshould exert a tremendous control over the position, orientation,and rate of nucleation. Indeed, previous measurements of ACPand HAP nucleation rates demonstrated α is significantly re-duced on collagen relative to its value in solution, leading togreatly enhanced nucleation rates (17). Both the DFS mea-surements and the MD simulations show that, for the collagen–apatite interface, binding energies are hundreds of kBT. Thus,when CDAP nucleates, whether from ACP (45) or OCP, basedon the results with collagen alignment on CDAP (100) faces weshould expect preferential c-axis alignment both parallel to andorthogonal to the long axis of collagen. Moreover, the localvariations in collagen orientation by up to 15° are then consistentwith 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 con-finement alone leads to alignment. In the latter model, becauseHAP grows fastest along [001], nuclei that form with (001) alongthe fibril direction rapidly fill the interfibrillar channels whereascrystals aligned otherwise are blocked at small size (11, 21).Neither model provides an explanation for all relevant obser-vations. For example, predictions of the free-energy model are atodds with in vitro mineralization experiments in which apatitecrystals that nucleated on the outside of collagen fibrils exhibitedno common alignment direction, whereas those on the interiorexhibited a degree of alignment similar to that seen in nativetissue (11, 13). On the other hand, in a well-ordered hexagonalbundle of fibers, there are three planar channels that span theentire fibril, permitting the fast-growth axis to attain any anglerelative to the long axis of the fibril within those channels.Moreover, the real structure of collagen is far more complex anddoes not provide continuous channels along the length of thefibril (SI Appendix, Fig. S5). In addition, one is hard pressed toexplain why the clear stereochemical matching of the matrix tothe mineral plays no role in directing growth given the demon-stration of this effect in even simple systems (44, 46). Thus, bothmechanisms may work in concert to exert the observed control.

The environment within a fibril is likely to amplify the energeticeffects measured here, because it brings together numerouscollagen strands at distances comparable to diameters of boththe amorphous precursors (13) and critical nuclei (17), whereasany tendencies toward channel alignment along fibrils will exerta 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 re-crystallization of either ACP or OCP, there is no reason why thehabit of bone apatite platelets should mirror the hexagonalsymmetry of HAP. Moreover, a plate-like habit is consistent withmonoclinic symmetry. In conclusion, the findings presented hereprovide insight into the structural and energetic characteristics ofthe collagen-bone apatite interface that play a central role indetermining both the mineral–matrix spatial relationship and themechanical properties of the composite.

Materials and MethodsFull details of crystal preparation, collagen adsorption, AFM tip decoration,DFS measurement and analysis, collagen orientation analysis, collagenmineralization, tissue sample preparation and TEM imaging, and MD simu-lations are provided in SI Appendix, SI Materials and Methods.

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 +94.5ΔΔGB

† +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 inparentheses, 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. 4. TEM images of thin slices of fully mineralized dentine and bone cutby ultramicrotome. (A) Lower-magnification image of dentine shows a tu-bule in the middle with apatite crystals aligned along circumferential di-rection of tubule. (B) Higher-magnification image of apatite crystal in whiterectangle in A. (C) Overall image of bone shows flat-lying apatite crystals inlower contrast and upstanding crystals with cross-section in higher contrast.(D) Higher-magnification image of apatite crystals in white rectangle in C.

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

Collagen Adsorption on Crystal Surfaces. Crystals were transferred from waterinto 500 μL collagen (40 nM) in PBS solution (Sigma-Aldrich) and kept staticfor 30 min. The collagen-adsorbed crystals were then transferred onto freshlycleaved mica and set in PBS solution for another 10 min before imaging.

Tip Decoration and DFS Measurement. Details of tip decoration were reportedpreviously (37). Briefly, Au-coated Si3N4 AFM tips (Bruker, MSCT) were modi-fied with a heterobifunctional cross-linker succinimidyl 6-(3-[2-pyridyldithio]-propionamido)hexanoate (LC-SPDP) (Thermo Scientific), which bears a pyridyldisulfide that binds to Au, leaving a low density of N-hydroxysuccinimide estergroups to form a stable amide bond with a primary lysine residue or terminalamine of collagen. For force measurements, a constant approach velocity of1 μm/s and dwell times of 0 s and 5 s were used for six different pulling speedsranging 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). TheCHARMM22 force-field parameter set (48) was assigned to the collagen peptide,with nonstandard hydroxyproline parameters taken from Park et al. (49). Simu-lations of HAP–collagen systems were carried out using NAMD 2.8 (50) with a di-electric imposed representing water (e = 80) under periodic boundary conditions.

ACKNOWLEDGMENTS. The authors thank Mr. Michael Nielsen for assistancewith high-resolution TEM imaging and Dr. Pamela K. Den Besten and Dr. GraysonW. Marshall for their generosity in providing rat bone and human dentine,respectively. The authors gratefully acknowledge funding from the NationalInstitutes of Health–National Institute of Dental and Craniofacial Research(DE003223 and DK61673). This research was performed at Pacific Northwest Na-tional Laboratory and the Molecular Foundry, Lawrence Berkeley National Labo-ratory, which is supported by the Office of Science, Office of Basic Energy Sciences,US Department of Energy under Contract DE-AC02-05CH11231. Pacific NorthwestNational Laboratory is operated by Battelle for the US Department of Energyunder Contract DE-AC05-76RL01830. The simulations were partially supportedby a grant of high-performance computing resources and technical support fromthe Alabama Supercomputing Authority. NAMD was developed by the Theoret-ical and Computational Biophysics Group in the Beckman Institute for AdvancedScience and Technology at the University of Illinois at Urbana–Champaign.

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