Nuclear Magnetic Resonance and Metadynamics Simulations Reveal the Atomistic Binding of l-Serine and O-Phospho-l-Serine at Disordered Calcium Phosphate Surfaces of Biocements

Interactions between biomolecules and structurally disordered calcium phosphate (CaP) surfaces are crucial for the regulation of bone mineralization by noncollagenous proteins, the organization of complexes of casein and amorphous calcium phosphate (ACP) in milk, as well as for structure–function relationships of hybrid organic/inorganic interfaces in biomaterials. By a combination of advanced solid-state NMR experiments and metadynamics simulations, we examine the detailed binding of O-phospho-l-serine (Pser) and l-serine (Ser) with ACP in bone-adhesive CaP cements, whose capacity of gluing fractured bone together stems from the close integration of the organic molecules with ACP over a subnanometer scale. The proximity of each carboxy, aliphatic, and amino group of Pser/Ser to the Ca2+ and phosphate species of ACP observed from the metadynamics-derived models agreed well with results from heteronuclear solid-state NMR experiments that are sensitive to the 13C–31P and 15N–31P distances. The inorganic/organic contacts in Pser-doped cements are also contrasted with experimental and modeled data on the Pser binding at nanocrystalline HA particles grown from a Pser-bearing aqueous solution. The molecular adsorption is driven mainly by electrostatic interactions between the negatively charged carboxy/phosphate groups and Ca2+ cations of ACP, along with H bonds to either protonated or nonprotonated inorganic phosphate groups. The Pser and Ser molecules anchor at their phosphate/amino and carboxy/amino moieties, respectively, leading to an extended molecular conformation across the surface, as opposed to an “upright standing” molecule that would result from the binding of one sole functional group.


INTRODUCTION
Bone mineral constitutes nanoparticles of a structurally disordered and carbonate-bearing form of Ca hydroxyapatite [HA; "apatite"; Ca 10 (PO 4 ) 6 (OH) 2 ]. 1−5 Vast research efforts have been spent to understand the mechanisms of bone mineralization, 5−10 which remain controversial but are believed to be governed by noncollagenous proteins (NCPs) that carry a high density of negatively charged carboxy-bearing (Asp/ Glu) and phosphorylated residues. 5,9−11 For decades, mainstream models for the NCP/mineral interactions involved "charge-matching" arguments assuming that the protein adopts a secondary structure with its negatively charged sidechains matching the Ca 2+ positions at the apatite mineral surface to provide epitaxial crystal growth. 6,7 However, doubts thereof arose from the subsequently accumulating evidence that (i) the crystal-binding domains of most NCPs lack a well-defined secondary structure 10,11 and (ii) both synthetic and biogenic nanocrystalline apatite particles formed from aqueous solutions�such as body fluids�consist of a "core" of an ordered HA lattice coated by a 1−2 nm thick surface layer ("shell") of amorphous calcium phosphate (ACP), 4,12−16 often termed the "hydrated surface layer". 2,3,17 These recent insights have led to a paradigm shift advocating simpler electrostatic models for which the net charge of the protein and its underlying distribution control the NCP binding at biogenic apatite. 18−21 An accurate atomistic probing of biomolecular adsorption at structurally disordered inorganic calcium phosphate (CaP) surfaces by experimental techniques is hampered by the particle fragility, coupled with their structural disorder. The most detailed current insight is provided by magic-anglespinning (MAS) nuclear magnetic resonance (NMR) experi-ments, often utilizing proteins with isotopic 13 C/ 15 N labeling at specific sites in its "crystal"-binding domain. Some MAS NMR reports targeted biomolecular binding at bone mineral, 22−26 but adsorption on model systems of HA nanoparticles is most commonly encountered, encompassing the surface binding of small biomolecules 27−32 and various mineralization-controlling NCPs such as statherin, 33,34 osteopontin, 35 osteonectin, 36,37 and osteocalcin. 38 Here, advanced NMR techniques relying on through-space dipolar interactions, such as 13 C{ 31 P} and 15 N-{ 31 P} rotational-echo double resonance (REDOR) 39 NMR experiments, have been exploited for obtaining (semi-)quantitative 13 C− 31 P and 15 N− 31 P interatomic distance-information along with 2D 13 C− 13 C correlation NMR experiments that offer constraints on the surface-bound molecular conformation.
Considering the difficulties in experimental probing of the surface binding at atomic resolution, computer modeling by atomistic molecular dynamics (MD) and/or metadynamics simulations offers a rich source of structural information on the organic/inorganic interface. 18−20,40−48 They may reveal the precise binding sites of the biomolecule along with its detailed surface-immobilized conformation�henceforth referred to as the binding mode of the molecule. Yet, outstanding problems in computational modeling of biomolecular adsorption at an in vitro-or in vivo-generated nanocrystalline apatite surface concern how its structural disorder and potentially pHdependent phosphate speciation are accounted for. As discussed further in the Supporting Information, these critical aspects remain essentially ignored in all but a few very recent modeling studies. 44−49 Interfaces between phosphorylated biomolecules and disordered CaP phases are not only of pivotal importance for understanding bone mineralization but also underpin casein− ACP complex-formation in milk 50−53 and structure−function relationships of hybrid organic/inorganic (bio)materials, such as the bone-tissue-adhesive properties of CaP cements incorporating O-phospho-L-serine (Pser), 54−59 which by their capacity to glue bone tissues together makes them promising for accelerating bone-fracture healing. As unveiled by an array of advanced MAS NMR techniques, we recently demonstrated that the "bone-gluing" strength of such a cement correlates well with its content of an amorphous "ACP/Pser" phase of Pser molecules intimately integrated with ACP across a subnm scale. 60 An analogous "ACP/Ser" component forms in Lserine (Ser) doped cements which, however, exhibit poor bone-adhesive properties, 60 as discussed and rationalized further herein.
Herein, we advance the atomic-scale insight into the organic/inorganic interface further by examining cements prepared from uniformly 13 C/ 15 N−enriched L-serine and Ophospho-L-serine (the latter synthesized herein for the first time), thereby enabling direct experimental probing of the proximity of each carboxy/aliphatic and amino group to the inorganic phosphate moieties of ACP by 13 C{ 31 P} and 15 N{ 31 P} REDOR NMR experimentation, respectively. These results are contrasted with information from heteronuclear 13 C{ 31 P} and 1 H{ 31 P} correlation 2D NMR experiments that reveal the contacts between the organic functional groups of Pser/Ser and the inorganic HPO 4 2 /PO 4 3 phosphate moieties of ACP. We also discuss the similarities and differences between the inorganic/organic contacts in the amorphous ACP/Pser and ACP/Ser biocement components with that of nanocrystalline HA particles grown from a Pser-bearing aqueous solution, henceforth referred to as "Pser@HA", and constituting a simplified model of a carboxy-bearing or/and phosphorylated protein residue interacting with bone mineral. Moreover, the NMR-derived 13 Figure S1) from the corresponding BocNH-Ser-CO 2 -tert-Bu analogues via phosphoramidation with tert-butyl N, N′-diisopropylcarbamimidate followed by peroxide oxidation to yield the protected phosphate ester, which was converted into the desired product by global deprotection under acidic conditions; see Section S3 for details. These isotopically labeled Ser and Pser powders are for simplicity abbreviated as Ser* and Pser*, respectively. They were used for producing a nanocrystalline HA powder with surface-immobilized Pser* molecules, as well as cements comprising N mol % of Ser* or Pser*, which are henceforth denoted by SerN and PserN, respectively.
2.1.1. Pser@HA Specimen. 5.0 mL of a 500 mM aqueous solution of CaCl 2 in deionized water was pipetted in a 20 mL flask placed in a water bath at 37 ± 2°C, whereupon Pser*·HCl was added to the solution to yield a concentration of 10 mM. 5 mL of 300 mM (NH 4 ) 3 PO 4 (aq) was added at 1 mL/min with continuous magnetic stirring. The pH of the solution was subsequently raised to 7.5 by dropwise addition of 1 M NaOH(aq), leading to precipitation of floccular ACP particles. Deionized water was added to a final volume of 20 mL, and the flask was sealed. The suspension was aged for one week at 37 ± 0.2°C, leading to a final pH value of 5.3. The as-formed Pser@HA particles were isolated by centrifugation, cleaned twice with deionized water, and then dried in a desiccator at room temperature for 4 days.
The Pser content was estimated as ≈ 5 wt % by contrasting the integrated 15 N NMR intensity from the Pser@HA specimen with that of the Pser16 cement with known Pser content. The transmission electron microscopy images of Figure S2 reveal agglomerates of crystalline domains with variable sizes (from a few nm to 10−20 nm) that are fused together by ACP. The surface area was estimated to be 159 m 2 /g by the Brunauer−Emmett−Teller model 63 (N 2 uptake at relative pressures (P/P 0 ) of 0.05−0.15, using a Micrometrics ASAP2020 volumetric adsorption analyzer).
The Pser@HA synthesis protocol was preceded by extensive testing of optimal preparation conditions by using Pser (Flamma SpA) with concentrations in the 5−200 mM range. As verified by Figure S3 Table S1), whereupon a powder of α-Ca 3 (PO 4 ) 2 (α-TCP) (see refs 54 and 60 for preparation details) was added at liquid-to-powder (L/P) ratio of 0.24 mL/g. The powder and liquid were mixed with a spatula for ≈30 s. The cement paste was cured at 21°C and 30% relative humidity for 15−30 min and then transferred to a sealed plastic bag that was stored at 37°C for 7 days at 100% humidity. All cement specimens were thereafter stored under dry conditions in a desiccator. For practical reasons, pH measurements of the cement pastes prior to their setting were performed on larger SerN/PserN batches of 3.0 g and a slightly higher L/P = 0.4 mL/g ratio.  Figure 1a): one Ser or Pser molecule in a water phase (2600 H 2 O molecules) that interfaced a "HA slab", whose interior consisted of an HA lattice of the biologically relevant P6 3 /m modification. 66 The "surface" segment was generated according to ref 45, which mimics a disordered surface at a nanocrystalline HA-particle by introducing acidic protons at randomly selected phosphate groups accompanied by Ca 2+ -cation removal until a charge-neutral surface is obtained, whose {H PO  68 for the Pser/Ser molecules, and TIP3P 69 (without Lennard-Jones terms for H 70 ) for water. Well-tempered metadynamics 61,62 with a bias factor of γ = 5 and 32 independent "walkers" 62,71 were employed to ensure an efficient sampling of the molecular conformations and accelerate the convergence, using the variational enhanced sampling (VES) protocol 72 implemented in the PLUMED2.4 software. 73 Two collective variables were exploited for locating the most stable surface-bound molecular conformation, involving the distance between the center of the HA slab and the COO − / P H O 4 atom of the respective Ser/Pser molecule along with an interaction-energy dependent function defined in Section S2. The reported modeled parameters and their uncertainties are averages over 4 independent simulations. Figure 2 displays 31 P MAS NMR spectra recorded from the nanocrystalline Pser@HA sample and the PserN/SerN cements with N = {8, 16, 30}. The peak intensities of the single-pulse-acquired NMR spectra of the left panel quantitatively reflect the relative phase constituents of each sample, whereas those of the right panel of Figure 2 were obtained by 1 H → 31 P CP, thereby only revealing 31 P NMR signals from phosphate groups nearby protons. The directly excited 31 P MAS NMR peak shapes from the cements are complex due to the contributing signals from unreacted α-TCP ( Figure S4). The absence of protons in the α-TCP structure, however, renders the 1 H → 31 P CPMAS spectra considerably simpler because they only comprise 31 P resonances from 1 H- bearing phases, which predominantly involve the amorphous ACP/Pser or ACP/Ser components. 60 We henceforth focus on the 1 H → 31 P CPMAS NMR spectra along with the deconvolutions into their underlying NMR-peak components and the associated best-fit parameters presented in Table S6. The NMR spectra from the cements in Figure 2 overall match those presented in ref 60 from near-identical preparations with 13 C/ 15 N isotopes at natural abundance. Both the directly excited and CP-derived 31 P MAS NMR spectra of the Pser@HA specimen (Figure 2a,b) are typical for nanocrystalline HA particles, which involve a crystalline HA "core" coated by a surface layer ("shell") of ACP. 2−4,12−17 The "core" and "shell" components produce a narrow and broad resonance, respectively, 4,12−14 centered at the corresponding 31 P chemical shifts δ P ≈ 3.0 ppm and δ P ≈ 2.2 ppm ( Figure  2a,b and Table S6). The lower shift of the ACP component reflects the acidic solution (pH = 5.3) surrounding the Pser@ HA particles before their isolation, which yields a surface layer of ACP enriched in protonated phosphate moieties 4, 13,14,16,74 resonating at lower 31 P shifts than nonprotonated PO 4 3 groups. 75−77 Moreover, the close 1 H− 31 P distances of HPO 4 2 /H 2 PO 4 − groups emphasize the "ACP" contribution in the 1 H → 31 P CPMAS NMR spectrum (Figure 2b) relative to the directly excited counterpart ( Figure 2a); also see Table S6.

Local 31 P Environments Probed by MAS NMR.
Cements prepared from α-TCP and water in the absence of Pser consist of disordered HA. 60,78−80 Although ACP and HA particles are unstable in acidic aqueous solutions, they become stabilized by negatively charged organic additives in weakly acidic solutions. 4 The pH value of the precursor paste before the cement setting is reduced for increasing Pser/Ser content, while at a fixed doping level N, Pser yields a markedly lower pH value than Ser (Table S1). Hence, the highly acidic PserN cement pastes preclude HA formation, whereas the Ser8 and Ser16 samples comprise significant HA contributions ( Figure  2d,f and Table S6), as proved unambiguously by the heteronuclear correlation NMR results of Section 3.2. The progressively reduced pH values for the Pser-bearing cements also manifest as 31  molecules that may either constitute an integral component of the inorganic ACP and HA structures ("structure-bound"), associated with the inorganic/organic ACP/Pser and ACP/Ser components or being mobile physisorbed species. The latter 1 H 2 O molecules typically resonate in the 4.5−5.5 ppm spectral region, 13,14,16,74,85,86 where Figure 3 suggests that they constitute a significant fraction of the entire proton reservoir in the Pser@HA and PserN/SerN samples. Moreover, the characteristic 1 H NMR peak at δ H ≈ 0 ppm [12][13][14]16,74,85,86 from OH groups in the HA lattice is observed from several specimens. We refer to Mathew et al. 60 for discussions on the various 1 H resonance assignments made from nominally identical PserN and SerN cement compositions.
The remainder of the article focuses on the probing of the organic/inorganic interface in the Pser@HA, Pser16, and Ser16 specimens, which were examined by dipolar-based MAS NMR experimentation, such as the dipolar-mediated heteronuclear multiple-quantum coherence (D-HMQC) 1 H{ 31 P} NMR spectra 60,82,87,88 shown in Figure 4. They were recorded from the Pser@HA, Pser16, and Ser16 specimens using a short HMQC excitation period (τ exc = 176 μs) to ensure detection predominantly of 1 H and 31 P sites separated by at most a few hundreds of pm. In each D-HMQC spectrum, a 2D NMR correlation peak centered at the chemical-shift pair {δ 1 , δ 2 } ≡ {δ P , δ H } evidences close spatial proximity between 1 H and 31 P sites resonating at the (average) chemical shifts δ H and δ P , respectively. PserN cements. Note that no NMR peak from remnants of the proton-free α-TCP precursor ( Figure S4) appear in the CPMASderived spectra; the latter are shown together with the best-fit spectra (orange traces) and the deconvolutions into the as-indicated peak components given in each legend. The narrow NMR peaks at 1.4 ppm and −1.0 ppm stem from minor impurities of brushite (CaHPO 4 · 2H 2 O) and CaPser (Ca[O-phospho-L-serine]·H 2 O), respectively, while that marked by an asterisk in (d) derives from an unknown impurity. Table S6 lists the best-fit NMR parameters. Hence, it depends strongly on the pH value before cement setting (i.e., on the Pser content; Table S1). Indeed, the higher pH = 5.3 of the solution that immersed the Pser@HA particles renders the 2D NMR spectrum in Figure 4c closer to that reported previously from a Pser4 specimen 60 than that from Pser16. As expected from the results of Figures 2 and 3, the D-HMQC NMR spectra recorded from the Pser@HA powder (see Figure 4c) and the Ser16 cement ( Figure 4a) manifest the HA-characteristic correlation at {δ P , δ H } = {2.9, 0} ppm. 13,14,16,74,86 Correlations between the organic protons of the {NH 3 , CH n } moieties and P H O 4 2 / P H O 2 4 groups of ACP dominate the 1 H NMR spectral range of δ H ≲ 10 ppm, as becomes evident by contrasting the projection of the 2D NMR spectra of Figure 4a,b along the 1 H dimension with the single-pulseacquired 1 H MAS NMR spectra from the crystalline Pser and Ser samples. The comparatively more intense 2D NMR-peak intensities of the H N 3 ··· + PO 4 contacts with 1 H shifts ≈9 ppm relative to those of CH n ···PO 4 (4−5 ppm) ppm of either cement suggest much shorter distances between the inorganic phosphate species and the positively charged NH 3 + moiety than the aliphatic groups that do not bond directly to the surface, as   3) and discussed further in Section 3.6. Moreover, the HMQC NMR spectrum of Pser@HA reveals two broad but resolved 2D NMR peaks (marked by blue/ yellow rectangles in Figure 4c) not observed from the cements. They are tentatively attributed to either aliphatic protons or water molecules nearby inorganic phosphate groups, where the 2D correlation centered at {δ P , δ H } ≈ {1.6, 5.8} ppm and extending toward lower 31  species in the HA lattice. 74 As discussed further in Section S4, the signal at δ H ≈ 7 ppm in the 1 H{ 31 P} D-HMQC NMR spectra from Pser and Pser@HA is characteristic of structure-bound H 2 O molecules of "ACP", encompassing the amorphous surface of nanocrystalline HA. 16 (100) and (001) faces interfacing a water phase comprising one Ser or Pser molecule with protonation states for each of pH = {4.5, 7.4}; see Figure 1 and Section S2.
Numerous experimental studies on HA nucleation/growth in the presence of both small and large biomolecules suggest a preference for molecular adsorption at the larger (100) or (101) HA surfaces relative to their smaller (001) counterpart, 28 48 along with those obtained herein from Ser. Hence, we focus on the results for (100) at each experimentally relevant pH = 7.4 for Ser16 and pH = 4.5 for Pser16/Pser@HA, whose most probable/representative stable binding modes are exemplified in Figure 5. No aliphatic CH/ CH 2 groups of either molecule are discussed because they do not bind directly at the HA surface.
There are two main groups of A···B contact modes (i.e., "bonding types") between an organic atom site A of Ser/Pser and an inorganic surface-atom B: (i) electrostatic ("ion−ion") interactions among negatively charged O sites of carboxy/ phosphate groups and positive Ca 2+ cations of the ACP layer at nanosized HA particles, and (ii) H bonds between an organic (inorganic) proton and an inorganic (organic) O site. Notably, although carboxy/phosphate groups of biomolecules adsorb via both interaction types, each electrostatic bond (e.g., CO··· Ca 2+ ) is around 2.5 times stronger than its H-bond counterpart (e.g., CO···HPO 4 2 ). 48 These relative interaction strengths underlie the current consensus that ion−ion interactions dominate the energy landscape of biomolecular adsorption, 18−21 notwithstanding that the H bonds (140−220 pm) are shorter than the O···Ca 2+ distances (240−330 pm); see Figure 5. (100) and (001) HA Faces. Our comments made in Section S2.5 about biomolecules interacting with inorganic species at an essentially amorphous HA surface might seem to preclude any preferential adsorption at a specific HA surface type. This apparent contradiction, however, may be reconciled by noting that the consistently stronger adsorption at the "(100)" surface does not stem primarily from crystallographic/structural features�where the (hkl) notation rather specifies the crystallographic origin of the disordered (100) and (001) surfaces�but merely from its higher molar ratio n Ca /n P ≈ 1.55 relative to that of n Ca /n P ≈ 1.15 for (001) across the pH-range of 3.8−7.4. Consequently, the comparatively higher Ca 2+ abundance (and larger n Ca /n P ratio) at the disordered (100) Figure 5. Representative examples of the most stable/probable metadynamics-derived molecular binding modes at a "disordered (100) HA surface" of (a) Ser at pH = 7.4 and (b) Pser at pH = 4.5. All red numbers mark selected distances (in pm) between directly bonded Ser/Pser···HA atoms, while those in black indicate C−P and N−P distances relating to the experimental constraints from NMR. The green numbers in (b) represent intramolecular C−P distances of Pser. For visualization purposes, only a few surface contacts are shown for each organic moiety. Notably, because none of the surface-binding modes of either Ser or Pser involve the sole anchoring of one functional group (Table 1), both molecules assume an extended conformation that "caps" the HA surface. We underscore that owing to the distributions of stable binding modes, no single graphical picture can capture all details of the molecular adsorption (Tables 1, S3, and S4). surface relative to its (001) counterpart emphasizes the electrostatic CO/PO···Ca 2+ interactions that predominantly govern the net biomolecular adsorption energy, [18][19][20][21]48 as confirmed by Table S3.

Distinct Biomolecular Binding at
The above-quoted n Ca /n P values were estimated from the chemical speciations of the two outermost layers at each (100) and (001) surface at the end of the metadynamics MD simulation (≈40 ns); see Table 1 of ref 48 for the corresponding precise speciations at the outermost surface layer relevant for the pH values of the present study. Notably, due to minor ion-dissolution processes, the exact Ca 2+ / phosphate surface speciations vary slightly throughout each metadynamics simulation, thereby not necessarily being identical to those plotted in Figure 1b they account for ≈60% of all stable Ser binding modes, with the remaining constituting a dual carboxy/amino binding ( Table 1). The absence of any significant binding mode by one functional group alone leads to a near-parallel "capping" of the Ser molecule along the ACP surface, as illustrated in Figure 5a. Although typically all three {COO − , NH 3 + , OH} moieties bind at the HA surface, Table 1 reveals strikingly different relative contributions of {64, 16, 10}% among the respective groups toward stabilizing/driving the Ser adsorption. The overwhelming carboxy-group contribution stems from its prevalent contact mode of strong electrostatic CO···Ca 2+ interactions (Table S3), whereas the modest net contribution of ≈26% to the total adsorption energy from the NH 3 + and OH groups together reflect their primary (for the amino group exclusive) contact mode of weaker H bonds.
In neutral and alkaline solutions, Pser preferentially anchors at the ACP surface by all three {PO 4 2 , COO − , NH 3 + } moieties, 48 leading to a significantly more negative adsorption energy than that for Ser ( Table 1). The stronger binding originates primarily from the organic phosphate group of Pser, which is the main adsorption promoter and involved in all stable binding modes regardless of the precise pH and (100)/ (001) surface type; 48 see Table S3. However, the Pser−ACP binding weakens significantly in the acidic solutions relevant for the Pser16 and Pser@HA sample preparation conditions (3.9 ≤ pH ≤ 5.3). This feature may be traced to a lower amount of Ca 2+ cations at the CaP surface and thereby fewer CO···Ca 2+ and PO···Ca 2+ electrostatic contacts, where the latter are diminished further because they are superseded by weaker POH···H n PO 4 bonds (Table S4) accompanying the onset of protonation of the organic phosphate group for pH < 6.8 ( Figure 1). These effects combine into a significantly weakened Pser adsorption at pH = 4.5 (Table 1), which incidentally nearly matches that of Ser at the comparatively Caricher HA surface at pH = 7.4 that promotes electrostatic interactions.
Relative to the Pser surface immobilization at pH = 7.4, the weaker Pser···ACP contacts in acidic solutions are reflected in a larger distribution of distinct binding modes at pH = 4.5 (Table 1), along with an overall more modest COO − participation: roughly half of all surface-bound Pser molecules anchor by a dual binding of their phosphate and amino groups, as depicted by Figure 5b, whereas all other binding constellations occur either by the phosphate/carboxy moieties (≈23%) or by all three groups together (≈15%); see Table 1.
(We remind that all binding modes not listed in Table 1 are insignificant, such as the anchoring of one functional group alone of either molecule). Yet, although the NH 3 + and COO − moieties participate in ≈90% and ≈40% of all binding modes, respectively, Table S3 reveals that their corresponding net energy contributions to stabilizing the adsorption only amount to ≈8% (NH 3 + ) and ≈20% (COO − ) due to the higher CO··· Ca 2+ interaction-energy per bond relative to that of NH···PO and the overall dominant PO···Ca 2+ interactions.
Out of all functional groups of Pser, the simulations predict the strongest binding at the ACP surface by the phosphate group. However, the broad 31 P NMR peak from the ACP/Pser phase (Figures 2 and 4) cannot discriminate between the organic and inorganic phosphate contributions, which underscores the very intimate Pser···ACP contacts in the Pser/ACP phase across a sub-nm scale. Indeed, NMR experiments sensitive to the 31 P− 31 P distance distributions revealed essentially equal average distances in synthetic/pristine ACP and the ACP/Pser components in PserN cements. 60 3.4. 13 C− 31 P Correlation NMR Reveals Ser/Pser−ACP Contacts. Figure 6 presents 1 H → 13 C CPMAS spectra observed from the polycrystalline Ser, Pser, and CaPser powders along with that of the nanocrystalline Pser@HA specimen and the PserN/SerN cements with N = {8, 16, 30} prepared from the Pser*/Ser* precursors. The strikingly different 13 C NMR peak widths observed from the precursors relative to Pser@HA or any cement reflect the distinctly  13 C− 31 P proximity is revealed by a 2D NMR cross peak centered at the shift-pair {δ P , δ C }. Owing to the phosphate group of Pser, however, the 13 C{ 31 P} D-HMQC spectrum observed from Pser16 primarily reflects the intramolecular 13 C− 31 P distances, which also account for the observed NMRintensity increase along 13 CO < 13 CH < 13 CH 2 in Figure 7a; this is particularly evident when contrasting the various peak intensities of the HMQC projection with their counterparts of the corresponding 1 H → 13 C CPMAS NMR spectrum ( Figure   S5). The 2D NMR-peak intensities reflect semiquantitatively the relative through-space 13 C− 31 P distances. The significantly emphasized intensity and the higher 13 C chemical-shift

Chemistry of Materials pubs.acs.org/cm
Article dispersion of the 13 COO − ··· 31 P correlations from the Ser16 cement relative to the Pser16 counterpart (as is also evident from the 13 C CPMAS NMR spectra of Figure 6) corroborates the metadynamics predictions (Section 3.3): the carboxy group of Ser anchors directly at the ACP surface, in contrast with (a majority of) the Pser molecules. However, owing to the HMQC-signal buildup across longer distances, cross-peaks associated with all 13 C sites are detected for the present τ exc values (Figure 7), despite that none of the CH/CH 2 groups of either Pser/Ser molecule bind directly to any species of ACP. The close COO − ···ACP contacts of the Ser molecules are reflected in emphasized 2D NMR-signal intensities in the zoom around the 13 COO − region of the 2D NMR spectrum of the Ser16 cement (Figure 7c): four 2D NMR ridges are resolved at the 13 C chemical shifts {184.2, 176.8, 174.0, 170.0} ppm. Notably, none of them coincides with that of δ C = 175.2 ppm from polycrystalline Ser (Figure 6f). As is most transparent from Figure S5, the NMR peaks around δ C = {184, 170} ppm are markedly emphasized (the latter peak is barely discernible in the CPMAS NMR spectrum), whereas the comparatively reduced intensities between 181 ppm and 172 ppm stem from Ser molecules further away from the inorganic phosphate groups. Its significant 13  contacts, whose 13 C chemical shift incidentally matches that of the 13 COOH group of polycrystalline Pser that manifests analogous inter molecular COOH··· HPO 4 motifs. 65,99,100 Notably, Figure 6 reveals a lower NMRsignal intensity at 184 ppm from the Ser16 cement relative to its Ser8 counterpart, suggesting a concurrently reduced number of CO···Ca 2+ contacts for increasing batched Ser content, along with earlier and more qualitative findings by Mathew et al. 60 Figure S3).

Quantitative Probing of Ser/Pser−ACP Contacts by 13 C{ 31 P} REDOR NMR. 3.5.1. NMR-Derived Dipolar
Second Moments. For a quantitative probing of the relative proximities among the { 13 CO, 13 CH, 13 CH 2 } sites of Ser/Pser and the inorganic phosphate groups at the HA/ACP surface, we collected the 13 C{ 31 P} REDOR NMR dephasing curves presented in Figure 8. Here, a rapid (slow) dephasing reflects short (long) distances of a given 13 C j site to the inorganic phosphate groups of ACP (with the caveat of intramolecular 13 C j − 31 P interactions in Pser). Table 2 collects the set of REDOR-derived dipolar second moments 101−106 {M 2 (CO− P), M 2 (CH−P), M 2 (CH 2 −P)}, extracted by fitting the respective dephasing curves of each sample (Section S1.3). The precise M 2 (C j −P) value depends on the underlying set of interatomic distances {r(C j −P k )} between a given 13 C site and its nearby P atoms via a sum over [r(C j −P k )] −6 terms. This renders the shortest distance contributions most influential for the net M 2 (C j −P) value.
The NMR-derived {M 2 (C j −P)} data from the polycrystalline Pser/CaPser powders were validated against those calculated from their crystal structures. 64,65,99 As expected 103−106 and discussed further in Section S1.3, the NMR-derived dipolar second moments are consistently lower than their theoretical counterparts (M 2 calc ). Yet, the  Table 2 reflect distinctly different molecular conformations in the CaPser and Pser crystal structures, whose corresponding θ(P−O−C β −C α ) dihedral angles of 280°a nd 153°translate into intramolecular 13 CH···P distances of 341 pm and 384 pm, respectively. Notably, such widely differing Pser conformations are readily discriminated by the 13 C{ 31 P} REDOR NMR experiments. Hence, notwithstanding that each M 2 (C j −P) value is dominated by the intramolecular 13 C j − 31 P distance for all scenarios where intermolecular Pser··· Pser contacts are negligible (thereby obscuring the herein targeted C j ···ACP contacts), the M 2 (CH−P) parameter offers a valuable constraint on the conformation of the surface-bound Pser molecules, such as in the Pser@HA and Pser16 systems.

Validation of the Metadynamics-Derived Dipolar Second
Moments. The dipolar second moment M 2 (C j −P) reflects all { 13 C j − 31 P k } distances of the adsorbed molecule to its adjacent inorganic phosphate groups (Section S1.3), but cannot unveil the precise underlying distance distribution. However, because the metadynamics simulations do offer such atomistic details (Figure 5), we first validated the modeled M 2 (C j −P) data against the experimental counterparts.

Chemistry of Materials pubs.acs.org/cm Article
Considering that all REDOR-derived M 2 (C j −P) values are underestimated by 24% (Table S5 and Section S1.3), a "perfect match" between the metadynamics-generated models and the experiments should result in M M / 0.76 2 NMR 2 model for each 13 C j − 31 P contact. Notwithstanding a somewhat larger scatter in the ratios of Table S5 (which stems from higher data uncertainties of the simulated systems than the very accurate C/P atom coordinates of the Pser/CaPser crystal structures 64,99 ), it is gratifying that the data in Tables 2 and S5 confirmed our expectations for all 13  . The somewhat stronger COO − ···ACP contacts in both Pser@HA and Pser16 specimens than those predicted by the metadynamics simulations imply that the carboxy group contributes more to the Pser binding than that suggested by the binding mode statistics of Table 1. However, besides noting that the phosphate/amino binding-mode population is presumably slightly overestimated at the expense of (primarily) the phosphate/carboxy/amino counterpart, more quantitative corrections cannot be made. We remind that the 13 C{ 31 P} D-HMQC NMR spectra also suggested weaker COO − ···ACP interactions of the Pser molecules than those of Ser (Section 3.4).
3.5.3. Discussion. The NMR-derived dipolar second moments of the aliphatic groups of Ser (Table 2) suggest M 2 (C j −P) 9 < kHz 2 as the marker of an absence of direct surface binding of any atom of a given 13 C j functional group at the ACP surface. We remind that regardless of the (non)adsorption of Pser at ACP, the intramolecular 13 C j − 31 P dipolar interactions render all M 2 (C j −P) values of the Pser@HA and Pser16 specimens markedly higher than those from Ser16, as is evident from the dephasing curves of Figure 8. However, the simulation-derived model enables a separation of the intra/ intermolecular contributions to the net M 2 (C j −P) value: indeed, Table 2 confirms the expectation that both CH/CH 2 groups of Pser exhibit very low dipolar second moments once their intramolecular contributions are excluded (particularly that of M 2 (CH 2 −P), for which the organic phosphate group accounts for ≈95% of the net value).
It is gratifying that each of the three {M 2 (CO−P), M 2 (CH− P), M 2 (CH 2 −P)} NMR-derived data agrees mutually very well among the Pser@HA and Pser16 samples, which suggests overall (very) similar Pser contacts/distances to the inorganic phosphate moieties. Hence, despite the formally distinct nature of the ACP/Pser phase of the biomedical PserN cements and the Pser adsorption at a nanocrystalline "HA" surface (Pser@ HA), the local structure of their organic/inorganic interfaces must be similar in both specimens, thereby consolidating the current consensus that nanocrystalline HA is coated by a layer of "ACP" 4,12−16 (although its precise chemical/structural nature remains unknown). This aspect also justifies that the single metadynamics simulation at pH = 4.5 mimics well the Pser···ACP interactions in both Pser@HA and Pser16 specimens, as well as supporting the physical relevance of the herein employed HA-surface preparation procedure. 45 These important issues are discussed further in Section S2.5.
We now return to the partially overlapping 13 C NMR peaks in the carboxy domain of the NMR spectrum from the Ser16 cement (Figure 6h), which, according to their distinct 13 COO − ···ACP contacts, were grouped into three regions in the 13 C{ 31 P} D-HMQC spectrum of Figure 7c. As expected from the δ C = 184 ppm resonance attributed to CO···Ca 2+ Figure 8. 13 C{ 31 P} REDOR NMR dephasing curves (ΔS/S 0 ) recorded at B 0 = 14.1 T and ν r = 10 kHz and plotted for increasing dipolar recoupling/dephasing periods (τ rec ) for the 13 CO, 13 CH, and 13 CH 2 functional groups of the (a,b) polycrystalline Pser and CaPser powders ( 13 C at natural abundance) along with the 13 C-enriched (c) Pser@HA, (d) Pser16, and (e) Ser16 specimens. Each curve in (a−e) corresponds to the best fit of the {τ rec , ΔS/S 0 } data to eq S2, which yielded the dipolar second moments {M 2 (C j −P)} listed in Table 2. The 13 COO − NMR spectral region of the Ser16 sample comprises three distinct resonances at δ C = {184, 177, 174.5} ppm, whose associated dephasing curves are labeled by their chemical shifts in the legend in (e). Note the different horizontal scale in (e) relative to (a− d).
Chemistry of Materials pubs.acs.org/cm Article motifs (Section 3.4), its very rapid dipolar dephasing is consistent with a sizable dipolar second moment of 23.6 kHz 2 ( Table 2). In contrast, the spectral region marked by a yellow rectangle in Figure 7c and deconvoluted into two peak components around 177/174.5 ppm reflects more weakly surface-bound COO − groups with lower dipolar second moments of 9.3/13.3 kHz 2 ( Figure 8 and Table 2). Although a large M 2 (CO−P) value is also anticipated from COO − moieties surface bound via H bonds and giving an NMR peak at 170 ppm, its minor NMR intensity (and thereby very small population) did not permit reliable analyses of the REDOR NMR data (e.g., see Figure S6). Altogether, the varying dipolar second moments of these COO − ···ACP contact modes/distances underlie the average value of M 2 (CO−P) ≈ 11.1 kHz 2 (Table 2), which qualitatively corroborates the metadynamics predictions of direct COO − ··· ACP bonds. We contrasted the D-HMQC NMR-derived and modeled relative populations of the three types of surface-bound COO − sites that produce the three spectral regions marked in Figure  7c and attributed to COO − sites bound solely by Ca 2+ cations (≈184 ppm), sites weakly bound by both electrostatic and Hbond interactions (181−172 ppm), and solely by H bonds (≈170 ppm). Quantitative agreements are not expected because the 2D NMR intensities depend strongly on the precise HMQC excitation/reconversion periods. Deconvolution of the 13 Table S4) compared to the much lower estimate by NMR (27%). The differences presumably stem from the difficulties by NMR to accurately quantify the contributions from the 181−172 ppm resonance-region stemming from "weakly bound" carboxy groups, which may involve nonnegligible 13 COO − NMR signals from more distant nonbonded molecules that are not accounted for in the simulation analysis.

15 N{ 31 P} REDOR NMR Reveals the Amino-Group
Binding. Figure 9a,b displays the 1 H → 15 N CPMAS NMR spectra of Pser, the 15 N-enriched Ser* and Pser* precursor powders, together with those of Pser@HA, Pser16, and Ser16. As for the 13 C NMR spectra (Figure 6), the Ser/Pser adsorption is mirrored by a significant 15 N resonance broadening along with a minor increase in the average chemical shift of ≈2 ppm and ≈5 ppm for the Ser and Pser bearing specimens, respectively. The amino-group binding at ACP was probed by 15 N{ 31 P} REDOR NMR experiments on the Pser@HA, Pser16, and Ser16 cements, whose dipolar N− 31 P and 13 C− 31 P dipolar second moments obtained for the as-indicated functional groups from 15 N{ 31 P} and 13 C{ 31 P} REDOR NMR experiments, respectively, and compared with data calculated either from metadynamics-derived structural models (for Ser16, Pser16, and Pser@ HA) or from the crystal structures of Pser and CaPser. 65 The M 2 (C j −P) data uncertainties are ±1.7 kHz 2 (NMR) and ±2.2 kHz 2 (metadynamics model), with kHz 2 ≡ 1000 s −2 . b Net experimental/calculated values; the NMR analysis afforded the extraction of three M 2 (CO−P) values of {23. 6, 9.3, 13.3} kHz 2 for the 13 CO shifts at {184, 177, 174.5} ppm, respectively. c Values within parentheses represent the contribution to the net M 2 (N− P) and {M 2 (C j −P)} values from the Pser···HA contacts alone; the contribution from the intramolecular 15 N− 31 P and 13 C j − 31 P dipolar interactions account for the difference. d The {M 2 (C j −P)} and M 2 (N−P) values were obtained from the Pser (Flamma) and isotopically enriched Pser* samples, respectively. dephasing curves are displayed in Figure 9c along with that from the Pser* powder. For the latter, Table S5 reveals a ratio of 0.71 between the NMR-derived M 2 (N−P) value and that calculated from the Pser crystal structure, 99 which is close to the expected ratio of 0.76 (Section 3.5.2). Moreover, the ratio of 0.77 between the experimental and modeled M 2 (P−N) data for the Pser@HA sample suggests a very faithful metadynamics modeling of its NH 3 ··· + ACP/HA contacts (Figure 5b).
Particularly, when recalling the very good mutual match between the {M 2 (C j −P)} sets among the Pser@HA and Pser16 specimens (Section 3.5), the significantly lower M 2 (N− P) value of the Pser16 cement (as well as for Ser16) relative to Pser@HA is surprising ( Ser16 cements, the binding-energy contribution from the amino group is higher for Ser than Pser (Table S3), which also accords with the dipolar second moments of Table 2: although both the experimental and modeled M 2 (N−P) values for Pser16 are slightly higher than their Ser counterparts, once excluding the intramolecular 15 N− 31 P Pser contribution, the expectation of a stronger surface binding of the NH 3 + group of Ser is confirmed by its 20% higher modeled M 2 (N−P) value than that of Pser. 3.7. Implications for Bone-Adhesive Properties. We recently reported a strong correlation between the amount of the amorphous ACP/Pser component and the measured shear strength of PserN cements used for gluing two cubes of either cortical bone 54 or steel 60 together across a wide composition range up to N = 87 mol %. 60 The shear strength reflects the bone-adhesive properties. 54 Notably, both parameters exhibit a nonmonotonic trend against the batched Pser content, with an initial increase up to a plateau of near-constant shear-strengths and ACP/Pser contents in cements incorporating 40−60 mol % Pser, followed by their concurrent decrease for increasing N because the bone-adhesive-promoting ACP/Pser component becomes gradually replaced by crystalline CaPser and unreacted Pser. 60 In contrast, SerN cements form an amorphous ACP/Ser phase that only develops with the batched Ser content up to N ≲ 16 mol % (which is insufficient for giving a high shear strength), whereas all remaining Ser remains unreacted. 60 Consequently, the formation of an amorphous component featuring both significant organic−organic and organic− inorganic interactions appears to be a prerequisite for favorable bone-adhesive properties of an α-TCP-derived cement. Hence, the results herein combined with those of ref 60 suggest that a significant bone-adhesion cannot stem from the adsorption strength of a given biomolecule at ACP alone, because the Pser···ACP binding energy at pH = 4.5 essentially matches with that of Ser···ACP at pH = 7.4 (Table 1), implying that both Pser16/Ser16 cements feature similar Pser···ACP and Ser···ACP net interaction strengths. Nonetheless, while both Pser and Ser molecules may enter ACP/Pser and ACP/Ser phases in the respective PserN and SerN specimens with N ≲ 16 mol %, their amounts develop very differently upon increasing organic content (vide supra). Consequently, the main distinction between the PserN and SerN cements concerns their respective degrees of Pser···Pser and Ser···Ser contacts.
Due to its low Pser content ( 5 wt %), the Pser@HA sample is expected to involve essentially "isolated" surfacebound Pser molecules with long Pser···Pser distances. Likewise, the metadynamics modeling involved one sole Pser (or Ser) molecule. Hence, the good agreement between the M 2 (C j −P) NMR results of the Pser@HA and Pser16 samples, as well as with the modeled data, suggest that 16 mol % of either Pser or Ser may be sufficiently low to be dispersed within the ACP matrix without any significant Pser···Pser or Ser···Ser aggregation (i.e., analogously with a "monolayer" adsorption scenario). However, the substantial Pser contribution to the ACP/Pser cement component in all Pser-rich PserN cements�for which the shear strength is maximal� cannot be reconciled with a monolayer Pser adsorption at ACP, but must involve a significant Pser···Pser aggregation, yet with the molecules remaining intimately integrated also with the inorganic species of ACP (see comments in Section 3.3.3 and ref 60). Although further work is required for a definite proof, we propose that the high bone-adhesion/shear-strength of the PserN cements with 40 ≲ N ≲ 60 mol % stems from a "stickiness" accompanying the high organic content of their ACP/Pser component, in conjunction with its dominance of the entire cement constitution. Naturally, the "stickiness" is low in cements with batched Pser contents ≲ 20 mol %, as well as for all SerN specimens 60 due to their insignificant tendency of Ser···Ser aggregation.

CONCLUSIONS
We have presented the first atomistic probing of the Pser and Ser binding at structurally disordered CaP surfaces by a synergistic combination of advanced solid-state NMR experimentation and metadynamics MD simulations, revealing the relative proximities of each molecular functional group and their respective underlying types of bonds, as well as the conformation of the adsorbed molecules. Our study encompassed the organic/inorganic interactions in a sample of surface-bound Pser at nanocrystalline HA particles (Pser@ HA) along with two biocements prepared from α-Ca 3 (PO 4 ) 2 doped with 16 mol % of either Pser or Ser. Notably, the very close sets of 13 C− 31 P dipolar second moments observed from the cement and the Pser@HA sample highlight the similarities of the Pser binding at ACP and the structurally disordered surface layer of nanocrystalline HA, thereby corroborating the current consensus that it is faithfully described as "ACP". 4, 13−16 The Pser and Ser adsorption is primarily mediated by electrostatic interactions between Ca 2+ cations and the negatively charged organic COO − /HPO 4 groups and, to a lesser extent, by H bonds to the inorganic phosphate groups, which involves NH···PO 4 and CO/PO···HPO 4 contacts for the amino and carboxy/phosphate groups, respectively. The dominance of electrostatic interactions for driving the adsorption implies that the phosphate group of Pser and the Chemistry of Materials pubs.acs.org/cm Article carboxy group of Ser are mainly responsible for stabilizing their surface binding, fully consistent with earlier inferences that biomolecules bind at bone minerals mainly via ion−ion interactions. 18−21 All detailed information about the number of electrostatic/ H-bond interactions and the accompanying interatomic distances were extracted from the metadynamics models. They were validated against the NMR-derived interatomicdistance constraints encoded by the dipolar second moments {M 2 (CO−P), M 2 (CH−P), M 2 (CH 2 −P)} that convey the relative proximities between the 13 C atoms of the respective {COO − , CH, CH 2 } group and the inorganic phosphate moieties of ACP, as well as the M 2 (N−P) counterpart informing about the NH 3 ··· + ACP contacts. The overall good agreement confirmed the accuracy of our metadynamics simulations, notably the validity of the herein employed HAsurface preparation protocol of ref 45, which produces a disordered apatite surface with pH-dependent phosphate speciation. For our experimental conditions of 3.8 ≤ pH ≤ 5.3 (Pser@HA and Pser16) and pH = 7.4 (Ser16), both Pser and Ser molecules anchor at their amino groups, together with the HPO 4 − group of Pser and the COO − group of Ser, which leads to an extended conformation of both surface-immobilized molecules. The OH group of Ser also participates in the binding at ACP via both electrostatic OH···Ca 2+ interactions and H bonds to the inorganic phosphate groups, but they contribute overall little to the net adsorption energy (≈10%). The only discrepancy between the experiments and models concerned an underestimation of the metadynamics-derived COO − ···ACP proximities relative to those deduced by NMR on the Pser@HA and Pser16 specimens.
Besides rationalizing the distinction in bone-adhesive properties of Pser and Ser doped α-Ca 3 (PO 4 ) 2 -based cements (Section 3.7), our findings settle some earlier suggestions/ speculations about which functional groups are involved in the molecular binding of Ser and Pser at nanocrystalline HA. 90,107−109 We stress that the binding modes discussed herein (Table 1 and Figure 5) are the most probable ones from an energetic viewpoint over a distribution of several distinct but stable modes. The nature of the comparatively weak adsorption of small biomolecules (such as amino acids and oligopeptides) at structurally disordered CaP surfaces must be analyzed/discussed in terms of "distributions" and/or "effective contacts", as those encoded by dipolar second moments. The existence of a distribution of very similar binding modes is indeed mirrored in the broad and typically asymmetric 13 C/ 15 N MAS NMR peak shapes observed from each functional group which, except for the COO − moiety of Ser16, remained unresolved. The 13 C− 31 P correlation NMR spectrum of the latter revealed four 13 COO − resonances from groups with different proximities to ACP: the two COO − environments closest to the inorganic phosphates were tentatively attributed to those solely involved in electrostatic COO − ···Ca 2+ interactions (≈184 ppm) and H-bonded COO − ···HPO 4 2 moieties (≈170 ppm). However, most of the COO − groups bind by both interaction types, as mirrored in a resonance-continuum across the 181−172 ppm spectral region.
We conclude by highlighting the power of the hereinimplemented combination of advanced solid-state NMR experiments with metadynamics simulations for an enhanced probing of the detailed biomolecular binding at structurally disordered CaP surfaces, which remains essentially untapped but is potentially very rewarding. Another ubiquitous tool exploited herein concerns the recently introduced Debye− Huckel-based analysis 48 reviewed in the Supporting Information, which offers a straightforward decomposition of the net modeled biomolecular binding energy into its contributions from the various functional groups of the surface-immobilized molecule, as well as for quantifying each individual electrostatic/H-bond interaction energy. ■ ASSOCIATED CONTENT
Experimental solid-state NMR conditions; metadynamics simulation parameters, data analysis, and further discussion; synthesis and characterization of Pser*; discussion on the 1 H NMR shift of water in ACP; cement batch compositions; further data on the modeled surface binding and relative dipolar second moments; best-fit 31 P NMR parameters; additional solid-state NMR spectra; and TEM images (PDF) ■ AUTHOR INFORMATION