Subnanometer atomic force microscopy of peptide–mineral interactions links clustering and competition to acceleration and catastrophe

Abstract

In vitro observations have revealed major effects on the structure, growth, and composition of biomineral phases, including stabilization of amorphous precursors, acceleration and inhibition of kinetics, and alteration of impurity signatures. However, deciphering the mechanistic sources of these effects has been problematic due to a lack of tools to resolve molecular structures on mineral surfaces during growth. Here we report atomic force microscopy investigations using a system designed to maximize resolution while minimizing contact force. By imaging the growth of calcium-oxalate monohydrate under the influence of aspartic-rich peptides at single-molecule resolution, we reveal how the unique interactions of polypeptides with mineral surfaces lead to acceleration, inhibition, and switching of growth between two distinct states. Interaction with the positively charged face of calcium-oxalate monohydrate leads to formation of a peptide film, but the slow adsorption kinetics and gradual relaxation to a well-bound state result in time-dependent effects. These include a positive feedback between peptide adsorption and step inhibition described by a mathematical catastrophe that results in growth hysteresis, characterized by rapid switching from fast to near-zero growth rates for very small reductions in supersaturation. Interactions with the negatively charged face result in formation of peptide clusters that impede step advancement. The result is a competition between accelerated solute attachment and inhibition due to blocking of the steps by the clusters. The findings have implications for control of pathological mineralization and suggest artificial strategies for directing crystallization.

The interaction of proteins with inorganic constituents is a defining feature of biomineral systems. They direct crystallization of precursors (1), inhibit pathological mineralization (2, 3), and initiate mineral resorption (4). In vitro observations reveal major effects on structure, growth, and composition including stabilization of amorphous phases (5), acceleration (6) and inhibition of kinetics (2), and alteration of impurity signatures (7). Defining the microscopic mechanism behind these effects has been difficult due to a lack of tools to resolve either proteins or the molecular structure of mineral surfaces during growth. In principle, atomic force microscopy (AFM) has the resolving power to investigate interactions between proteins and crystal surfaces at the molecular scale. However, in practice this scenario presents the difficult challenge of imaging soft biomolecules on a hard, dynamic surface and requires a delicate balance between lateral resolution, temporal resolution, and sample disruption. To capture the morphological evolution of atomic steps and their interaction with macromolecules, one must scan rapidly. Thus cantilever stiffness must be low to minimize the force applied as it passes over topographic features such as steps and weakly adsorbed macromolecules. At the same time, high-resolution imaging requires sharp probes. Silicon probes, which offer excellent sharpness, are too stiff to scan at high rates in contact mode without displacing adhered molecules or fracturing the brittle tip. The common solution is to use cantilever probes fabricated from silicon nitride, which are much softer; but the malleability of silicon nitride renders these probes dull and limits their resolving power. To overcome these limitations, we employed probes comprised of sharpened Si tips on flexible, low-stress Si₃N₄ cantilevers (Applied Nanostructures). To augment the relatively weak laser signal reflected from the thin Si₃N₄ cantilever beam (600 nm thick, uncoated), we utilized a 3-mW diode laser instead of the ∼1-mW lasers usually employed.

We used this system to investigate peptide interactions with calcium-oxalate monohydrate (COM, CaC₂O₄·H₂O), the dominant mineral phase in human kidney stones (8) (see Methods for a description of materials and imaging conditions). Aside from clinical relevance, COM is an excellent system for investigating peptide interactions, because it presents two strongly contrasting faces. One—(-101)—is calcium-rich and electrostatically positive, whereas another—(010)—is oxalate-rich and strongly negative (9).

The importance of both specific and nonspecific interactions between COM surfaces and polypeptides or polyionic molecules has been demonstrated previously. Polypeptides altered step kinetics in a face- and step-specific manner, and their presence in solution reduced adhesion forces between carboxylate-functionalized AFM tips and COM surfaces (10, 11). In vitro studies of clinical relevance found that COM growth was strongly inhibited by acidic urinary molecules, particularly citrate and osteopontin (OPN) (12, 13). [In this regard, COM is reminiscent of calcium carbonate in that proteins commonly found in association with carbonate biominerals are highly acidic and rich in carboxylic side chains (14).] However, the consequences of introducing polyanions to COM differ significantly between small molecules and polypeptides. For example, the effects of citrate on COM growth were well explained by classical growth models of step pinning (15), and electrostatic models of citrate binding provided a clear rationale for the face- and step-specific effects (12): Due to repulsive and attractive interactions of the carboxylic groups with oxalate and calcium ions, respectively, citrate had little effect on the negative face while binding strongly to the positive face. In contrast, OPN, which contains peptide segments consisting of more than 50% aspartic acid (Asp) residues, exhibited face-specific effects that appear to contradict this simple picture. On the positive face, they formed surface-aggregates having little effect on growth but strongly inhibited growth of the negative face (12). Clearly, the simple binding rationale applicable to small molecules such as citrate is not conserved in their larger, polypeptide counterparts bearing similar chemical functionality.

The underlying source of these differences is undoubtedly the unique adsorption behavior of polypeptides at surfaces (16). Polypeptide binding to an oppositely charged surface requires crossing a series of kinetic barriers, such as displacement of shielding counterions, configurational relaxation of the polymer, and coordination with oppositely charged sites on the crystal to reach the final collapsed state in which the polypeptide residues form specific bonds to lattice sites (16). In contrast, at like-charged surfaces, polypeptide solutions containing di- and trivalent counterions exhibit fluctuating polarizations that can diminish the double-layer repulsion between like-charged objects, allowing the van der Waals attraction to dominate (16, 17). This effect can lead to polypeptide clustering (dictated by the balance of enthalpic gain and entropic cost of aggregation) as well as nonspecific binding to the surface.

Results

Atomic Resolution of COM Crystal Surfaces During Growth.

To attain high-resolution control images of the surface, we performed in situ AFM on the (-101) and (010) faces of COM at supersaturation ∼0.8, in the absence of peptide. (Supersaturation is defined by , where Δμ represents the difference in chemical potential per COM molecule between solution and crystal, k_B is Boltzmann’s constant, T is the absolute temperature, the a_i’s are the activities of the respective components, and K_sp is the solubility constant. See Methods for details.) As Fig. 1 shows, even at room temperature, we obtained true single-molecule resolution of faces, atomic steps, kinks, and even what appear to be single attachment events during growth. In Figs. 1A and B, the AFM images of the steps on the (010) face are compared to the interpretations on the basis of the crystal structure. Image enhancement by Fourier filtering revealed submolecular details such as protruding ends of vertically aligned oxalate groups (high “peaks”) and recessed, flat-lying oxalate groups (low “holes”) (Fig. 1C). (See also Fig. S1.) Comparison of Fig. 1C with Fig. 1D shows the greater vertical relief of the (010) face as compared to the (-101) face. The overlying molecular models are based on classical molecular dynamics (MD) simulations as described below.

Fig. 1.

(A–B) AFM height images of steps on the (010) face showing individual kinks and single molecules at the step edge. Also given are schematics showing the relationship between AFM images and underlying COM structure. Color scheme: Red—O, green—Ca, and gray—C. (C) AFM deflection image of the (010) face showing step, kinks, and electrostatic map of (DDDS)₆DDD for configuration of highest binding energy. (D) AFM deflection image of the (-101) face and electrostatic map for configuration of highest binding energy for (DDDS)₆DDD as predicted by the in vacuo MD simulations. Red is most negative; blue is most positive. In an intuitive and simple electrostatic picture of binding, the negative (yellow) oxygen atoms of the oxalate ions that protrude from the (010) terrace are expected to repel the negative (yellow-to-red) carboxyl side groups along the peptide. In contrast, on the (-101) face, the MD simulations predict that the positive (blue) calcium-rich terrace should provide a favorable binding environment for the carboxyl-rich peptide. Unit cell parameters (9) are a = 9.976 Å, b = 14.588 Å, c = 6.291 Å, and β = 107.05°. Electrostatic potentials in C and D were rendered by using MOE 2005.06 (Chemical Computing Group). Molecular structures in Figs. 1 and 3 were rendered by using WebLab ViewerPro 3.7 (Molecular Simulations).

Peptide Adsorption and Step Interactions on COM Surfaces.

To investigate the consequences of polypeptide adsorption dynamics in a well-controlled system, we synthesized two 27-residue peptides consisting of (DDDX)₆DDD (X = S or G) designed to act as surrogates for the Asp-rich region of OPN, which contains 19 Asp residues occurring primarily in groups of two to three. Not surprisingly, in vacuo simulations of binding supported the simple electrostatic picture: The negative oxygen atoms of the oxalate ions that protrude from the (010) terrace were predicted to repel the negative carboxyl side groups along the peptide (Fig. 1C), whereas the positive calcium-rich (-101) terrace provided a favorable binding environment (Fig. 1D). Peptide binding to the positive face was predicted to be nearly three times greater than to the negative face (see Methods). Thus, one might naively expect the impact of these peptides to mimic that of citrate. However, our in situ observations presented a strikingly different picture.

As Figs. 2B and 3B show, at low resolution, the morphologies of the two faces were similar. But high-resolution imaging revealed starkly contrasting peptide adsorption behavior. As expected, peptides bound to the (-101) face so that, even at peptide concentrations < 10 nM, the face was covered by peptides (Fig. 3C). In contrast, the (010) atomic structure was still well resolved in the presence of peptide, showing that individual peptides did not bind to that face (Fig. 2C). Instead, despite the like charge of the peptides and the face, the peptides formed surface-adsorbed clusters about 10 nm in size (Figs. 2B and C). Cluster number density increased with peptide concentration (Fig. S2), but cluster size remained nearly constant.

Fig. 2.

The (010) face. (A) A typical dislocation hillock under pure growth conditions. (B) Morphology during growth in 5 nM (DDDS)₆DDD, at low ionic strength (I = 7 × 10^-4 M), showing peptide clusters and pinned steps. (C) High-resolution image of peptide clusters on the terraces, one in front of the approaching steps and one within with the upper step. The crystal lattice is well resolved, and the adsorbed peptides are confined to the clusters (I = 0.15 M). (D) Step speed versus supersaturation σ at various concentrations of (DDDS)₆DDD showing dual functionality—inhibition at low supersaturation (or high peptide level) and acceleration at high supersaturation (or low peptide level). Standard errors in step speed measurements range from 10% at the lowest values of supersaturation to < 0.5% at the highest values. In all cases, the standard errors are smaller than the symbols. Solid curves are fits to the model combining step pinning by peptide clusters with reduction in the activation barrier by an amount proportional to the peptide concentration (see Supplementary Information for details.) (Figs. S1 and S2 show dependencies of cluster density and degree of inhibition/acceleration on peptide concentration.)

Fig. 3.

The (-101) face. (A) Steps originating at a dislocation hillock under pure growth conditions. (B) Morphology during growth in 10 nM (DDDS)₆DDD solution, at low ionic strength (7 × 10^-4 M), showing extensive step pinning. (C) High-resolution image collected in pure solution showing lattice structure overlaid with a ball-and-stick model. The color scheme is the same as in Fig. 1A and B. (D) High-resolution image showing that, unlike the (010) face, the (-101) face becomes covered by a uniform film of peptide preventing visualization of the underlying lattice [(DDDS)₆DDD, I = 0.15 M]. (E) Step speed versus supersaturation for various concentrations of (DDDS)₆DDD. Symbols are experimental values taken after introducing the indicated peptide concentration into otherwise pure solution. Red squares and blue circles were collected while reducing and increasing supersaturation, respectively. Standard errors are as described in Fig. 2. Solid curves give the theoretical dependence that takes into account the slow adsorption kinetics of the peptides for decreasing (downward arrow) and increasing (upward arrow) supersaturation. (See Supplementary Information for details.) The model is in excellent agreement with the data and predicts two distinct states of growth with a discontinuous drop in step speed to zero as supersaturation is reduced and a slow steady rise as supersaturation is increased.

By following the step dynamics at molecular resolution, we found that these contrasting adsorption behaviors led to distinct, face-specific controls on growth (Fig. 4). On the (-101) face, as steps moved through the adsorbed peptides, they became severely roughened due to a high density of pinning sites. But on the (010) face, the steps still consisted of straight segments with visible kinks. When a step encountered a peptide cluster, it formed a hinge point where it was temporarily stopped. Eventually, the steps overcame these obstacles and recovered to their straight morphology, leaving the peptide clusters unperturbed by the passing step. This process occurred repeatedly without any significant change to cluster location or shape (movies of these growth processes are provided in SI Text).

Fig. 4.

(A–F) Series of sequential images showing interaction of step on (010) face with peptide clusters in a solution containing 10 nM DDDS (I = 0.15 M). An individual step approaches two adjacent clusters (A and B), is transiently pinned (C and D), and then recovers (E and F). Frame interval, 4.2 seconds. (G–L) Time sequence showing inhibited growth of step on the (-101) face under I = 0.15 M. A single large peptide aggregate near the center of the image provides a point of reference. The continuous film of peptides on this face transiently pins subsegments of the oncoming step at many sites along the step front. Frame interval, 8.4 seconds. Note the sudden extension of the step towards the reference cluster in H, followed by inhibition of the same step region in I. This behavior of slight acceleration as steps approach clusters was often observed on both faces.

Crystal Growth Kinetics in the Presence of Peptide.

Quantification of the atomic step speed v revealed unreported consequences of these distinct adsorption behaviors on growth kinetics as well as insights into previously unexplained effects. On the (-101) face, the steps exhibited two distinct states: Upon decreasing supersaturation σ from high values, v suddenly jumped from that of the pure system into a “dead zone”—i.e., a region of finite supersaturation in which no growth occurs (Fig. 3E, red, yellow, and green curves). But upon increasing σ from near-equilibrium values, v followed a smooth trajectory with no abrupt changes (Fig. 3E, blue curve). In contrast, on the (010) face, dual functionality was exhibited: At low supersaturation or high peptide concentration, v was reduced, whereas at high σ or low peptide concentration, steps accelerated (Figs. 2D and Fig. S3). This dual effect is similar to what was observed for calcite, both with these same peptides as well as other Asp-rich peptides (6). Hence this behavior is apparently not an anomalous phenomenon.

Discussion

Asymmetric Growth Kinetics from Slow Peptide Adsorption Kinetics.

We propose that the phenomenon of bistable growth observed on the (-101) face is a natural consequence of polypeptide adsorption kinetics at faces to which they strongly bind through specific interactions. The series of barriers that slow the adsorption of polypeptides (16) results in their passage through multiple configurations before reaching a lowest-energy collapsed state (18). Under supersaturated conditions, step growth competes with this slow peptide binding: When an approaching step arrives at a peptide binding site, if the peptide is well-bound, it can block solute access to kinks; but if it is weakly adhered, as the peptide bonds to the crystal fluctuate, step propagation can proceed past the site. Thus, whether a peptide impedes step motion depends on the characteristic time scale τ available to relax into the well-bound state.

The time window for peptide binding is the terrace exposure time T, which is given by L/v, where L is the distance between steps. Analysis of the step speed data on the (-101) face shows that the characteristic time τ for (DDDS)₆DDD adsorption is ∼40 s and, at the higher values of σ used in these experiments, T ≪ τ (19). However, because L and v decrease and increase with supersaturation, respectively, upon reduction of σ, T rapidly increases. When sufficiently low σ is reached, the coverage of well-bound peptides is then large enough to appreciably slow the steps. As they slow, T increases further, resulting in yet higher peptide coverage, which again reduces v, raising the peptide coverage yet again, and so on. Because of this positive feedback, step speed exhibits the characteristic feature of a mathematical “catastrophe” (20); i.e., there is a point at which v spontaneously jumps from a finite value to zero and does not exhibit intermediate values. In contrast, when the crystal is first exposed to peptides at a value of σ below the jump, step speed is near zero (T≫τ) and peptide adsorption proceeds unperturbed until equilibrium coverage of well-bound peptides is reached. Even as σ increases, these peptides present a large barrier to desorption that steps cannot overcome. As a consequence, the dynamic relation between time scales is lost and v follows a trajectory well-predicted by the classic pinning model (13, 15) in the absence of time dependence (Fig. 3E).

Thus the slow, multistate binding of peptides to the (-101) face breaks the symmetry in the step kinetics: Upon decrease of σ from high levels, weakly bound peptides are displaced by rapidly advancing steps, but upon increase from equilibrium, the peptides present nearly permanent adsorbates, the symmetry is broken, and the step exhibits two distinct states—uninhibited growth or arrested growth. Because the surface peptide coverage will increase with solution peptide concentration, the supersaturation at which the jump between states occurs should also increase, as is observed experimentally. The red and blue curves in Fig. 3E give the predictions of this model for a two-state adsorption mechanism. (See SI Text for details of the model.)

Antagonistic Effects of Enhanced Desolvation and Step Blocking.

We propose that the dual modulation of growth on the (010) face derives from the unique behavior of polyelectrolytes adhering to like-charged surfaces as discussed above (16, 17). The clusters, which result from nonspecific adhesion mediated by van der Waals attraction, are weakly bound and present only a transient barrier to solute addition to steps. Their effects should become significant only at high coverage where they impede step motion. On the other hand, simulations predict that Asp residues on peptides in solution can assist cation desolvation at mineral surfaces (21), which is generally recognized to be the rate-limiting step in mineral growth (22, 23). This phenomenon should lead to step acceleration. Thus we suggest that Asp-rich peptides near the (010) face impose two opposing controls on step advancement: Peptides in solution near the step lower the barrier to solute incorporation into the step, whereas adsorbed clusters cause transient blocking of step advancement. At low peptide concentrations, when cluster density is low, enhancement by peptides in solution near the step dominates, whereas at high peptide concentration, when the cluster density is high, step blocking by the clusters overcomes the enhancement. The curves in Fig. 2D were calculated by including a decrease in the desolvation barrier of a magnitude proportional to the concentration of peptides in solution along with pinning by peptide clusters according to the classic step-pinning model (13, 15). (See SI Text for details.)

Conclusion

The results from this simple system demonstrate that the high-resolution in situ imaging obtainable with hybrid AFM probes can provide unique insights into the consequences of interactions characteristic of macromolecules at inorganic surfaces. Moreover, those consequences create a versatile palette of controls over mineral growth: Depending on the strength of the interaction with the faces and steps, the adsorption dynamics and the tendency towards cluster formation, macromolecules act as "switches, throttles, or brakes" on crystal formation.

Methods

Molecular Modeling.

Energy minimizations were performed on the peptide/COM system by using the Compass force field as implemented in MS Modeling version 4.0 software (Accelrys) with the dielectric constant equal to 20 to attenuate the Coulomb force acting on the peptide at the COM surface. During minimizations, the COM lattice was held fixed. Binding energies were obtained by subtracting the optimized energy of the adsorbate–surface system from the energies of the surface and adsorbate when separated beyond the interaction distance. Flat and stepped surfaces of COM were built by using CERIUS version 4.2 surface builder (Accelrys) from the unit cell derived from the crystallography data published by Deganello and Piro (9). Because the reported unit cell by Deganello and Piro did not include hydrogen atoms, hydrogen atom positions were determined computationally by using a commercial density functional theory software package (CASTEP; Accelrys) with optimization at the Perdew-Burke-Ernzerhof exchange-correlation functional of the generalized gradient approximation level of theory with 3D periodic boundary conditions applied to the COM unit cell; the geometric dimensions of the unit cell were fixed at its crystallographically determined values, and all atoms were frozen except the hydrogens, which were free to move.

AFM Imaging.

All in situ images were collected at 25 °C in contact mode (Digital Instruments E scanner; Nanoscope IIIA) on surfaces of COM crystals anchored inside the enclosed fluid cell. The AFM head was equipped with a 3-mW laser diode, and the probes consisted of hybrid silicon tips on silicon nitride cantilevers (HYDRA rectangular lever, k = 35 pN/nm, and tip radius < 8 nm; Applied Nanostructures, Inc, www.appnano.com). Solution flow was temporarily interrupted during high-resolution image collection. Details of the temperature control and flow systems, image collection, and data analysis are provided elsewhere (24, 25).

Peptide Synthesis.

Peptides were synthesized according to standard procedures (26) by sequential addition of Fmoc amino acids. After synthesis, the peptides were purified and molecular weights verified by mass spectrometry as described previously (27).

Materials

The COM crystals used for these experiments were grown in vitro with a gel method (28). Aqueous solutions of calcium oxalate with calcium-to-oxalate ratio = 1 were prepared by using reagent-grade K₂C₂O₄ and CaCl₂·2H₂O dissolved in distilled deionized (18 MΩ) water. The ionic strength was fixed by using reagent-grade KCl.

Inductively coupled plasma–atomic emission spectroscopy was used to confirm the purity of all reactants. Solution pH was adjusted to 7.0 ± 0.05 before each experiment by using a calibrated glass electrode and potassium hydroxide. The calcium and oxalate concentrations were varied from 0.1 to 0.35 mM, respectively, leading to a range of supersaturation between 0 and 1.2. Here we ignore the activity of water, which is assumed to be close to unity and unchanged during the experiments. Similarly, the activity of the pure calcium-oxalate monohydrate solid is unity and is independent of peptide level. The relationship between the calcium and oxalate activities and the respective solution concentrations can be found in ref. 13.

Ionic activities were estimated through speciation calculations in which the Davies equation was used to approximate activity coefficient corrections. Equilibrium activities were taken to be those at which the speed of atomic steps on the COM crystal surface was measured to be zero. In a previous study, for calcium-oxalate solutions at ionic strength 0.05 M, we determined the value of K_sp to be 1.56 × 10^-9 M², which was close to the reported value of 1.66 × 10^-9 M² (29).