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Difference in the Conformation and Dynamics of Aspartic Acid on the Flat Regions, Step Edges, and Kinks of a Calcite Surface: A Molecular Dynamics Study Hiroki Nada* National Institute of Advanced Industrial Science and Technology (AIST), 16-1 Onogawa, Tsukuba 305-8569, Japan S Supporting Information *

ABSTRACT: Molecular dynamics simulations were conducted to investigate the conformation and dynamics of an aspartic acid molecule near the {104} and {110} planes of a CaCO3 calcite crystal, near the acute and obtuse [114]̅ step edges on the {104} plane, and near kinks formed at the step edges. The simulations indicate that the amino acid binds indirectly to the {104} plane, whereas it binds directly to the {110} plane. The simulations also indicate that the acid binds directly to the acute step edge but does not bind to the obtuse step edge. These differences in the binding of the acid to the planes and the step edges were attributed to a difference in the structure of the surrounding water. The simulations also indicate that the acid binds to the kink formed at both the acute and the obtuse step edges, if a Ca2+ ion is placed at the corner of the kink. The binding was much stronger at the kink than at the planes and the step edges.

1. INTRODUCTION The control of CaCO3 calcite crystal growth by organic molecules is important in biomineralization processes,1−3 inhibition of scale formation in water,4 and the development of new functional hybrid materials.5,6 Therefore, the growth rate,7−9 morphology,10−13 and size of calcite crystals grown in the presence of organic molecules have been investigated experimentally.14,15 In addition, several experimental studies of calcite or other polymorphs of CaCO3 crystals grown in the presence of impurities have been conducted.16−20 The molecular-scale structures of calcite surfaces with organic molecules bound to them have also been investigated by atomic force microscopy.21−24 However, the mechanism by which organic molecules control calcite growth is still not well understood. In particular, various dynamic processes at the atomic and molecular scales need to be elucidated, including the diffusion of organic molecules near the calcite surface; the binding of organic molecules to the calcite surface; and the inhibition of Ca2+ and CO32− incorporation into crystal lattice sites at the surface by organic molecules.25 However, investigating these processes experimentally is difficult because it requires detailed molecularscale analysis of the conformation and dynamics of the organic molecules. Molecular dynamics (MD)26,27 simulations have been used for molecular-scale analysis of the conformation and dynamics of diphosphonates,28 phosphonate,29 ethanol,30 methanonic acid,31,32 mannose,32 methylamine acid,31 polysaccharides,33 polyaspartic acid,34 poly(acrylic acid) ,34−36 stearic acid,35 polypeptides,37 proteins,38,39 and polystyrenesulfonate40 near a calcite surface. Recently, several simulation studies have © 2014 American Chemical Society

suggested the importance of water for the conformation and dynamics of organic molecules near calcite surfaces.32,34,36,38−41 However, the effects of water on the conformation and dynamics have been investigated for only a few species of organic molecules and studies on various molecular species are required. These earlier simulation studies focused mainly on an organic molecule on a flat calcite surface, with or without a smooth step edge on the surface. However, a calcite crystal grows by capturing ions in kinks at the step edge of the surface. Therefore, it is particularly important to investigate the conformation and dynamics of an organic molecule near kinks in order to understand the mechanism of calcite growth control by organic molecules. Nevertheless, to the best of our knowledge, this has not yet been investigated. Organic molecules with carboxyl groups tend to bind to calcite surfaces.42,43 Aspartic acid (ASP), which bears two carboxyl groups, is convenient for MD simulations, because it is a small organic molecule with a simple structure. Investigating the conformation and dynamics of ASP on calcite surfaces contributes to understanding the mechanism of calcite growth control by organic molecules, because ASP induces a change in the morphology of [114̅] steps formed on calcite {104} planes.22 Moreover, proteins that control the growth of calcite crystals during biomineralization contain an abundance of ASP residues.22,44 Therefore, investigating the behavior of a single ASP molecule will help to elucidate the mechanism of calcite Received: March 11, 2014 Revised: June 16, 2014 Published: June 16, 2014 14335

dx.doi.org/10.1021/jp502332c | J. Phys. Chem. C 2014, 118, 14335−14345

The Journal of Physical Chemistry C

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growth control during biomineralization. So far, the binding energy of ASP at the acute and obtuse step edges has been calculated by a quantum chemical method.22 However, an MD simulation of the conformation and dynamics of ASP near a hydrated calcite surface has not yet been reported. In this study, MD simulations were conducted to investigate the conformation and dynamics of an ASP molecule near hydrated {104} and {110} calcite planes, near the acute and obtuse [114]̅ step edges on the {104} plane, and near kinks formed at those step edges. Differences in the conformation and dynamics of ASP between the planes and between the step edges were elucidated. We show that water is crucial for the differences in the conformation and dynamics of ASP, and the differences explain a change in the morphology of [114̅] steps formed on calcite {104} planes in the presence of ASP.22 We also show that ASP binds much more strongly at the kinks than at the planes and step edges if a Ca2+ ion is placed at the corner of the kinks.

2. SIMULATION METHODS 2.1. Potential Models. The interactions within calcite were estimated by means of the CaCO3 potential model proposed by Raiteri et al.45 In this model, the interaction between a pair of ions is represented as the sum of the Coulomb potentials plus the sum of the Buckingham potentials. The CO32− ion is treated as a rigid body; in the simulation, the C−O distance is fixed at the experimental value of 0.1284 nm, and ∠OCO is fixed at 120°. All four atoms of the CO32− ion (Cc and Oc atoms) are on a single plane. Although the CO32− ion in this model is a simplification of the actual CO32− ion, the model adequately reproduces the structure and thermodynamic stability of real calcite crystals,45 and the structure of amorphous CaCO3.46 The potential parameters for ASP were determined with the CHARMM22 force field.47 ASP was dissolved in liquid water and was therefore assumed to be fully ionized with a charge of −e (Figure 1a). Because the CHARMM potential parameters were optimized with the TIP3P model for H2O molecules,48 the TIP3P model was used here to estimate the interaction between a pair of H2O molecules. The potential parameters of the Raiteri CaCO3 model were optimized with the TIP4P-Ew model for the H2O molecules.49 However, use of the TIP4P-Ew model with the CHARMM force field underestimated the ASP−H2O potential energy by 22% relative to the energy obtained with the TIP3P model.50 The combination of the TIP3P model and the Raiteri CaCO3 model was confirmed to provide the same water structure on the calcite surface as the combination of the TIP4P-Ew model and the Raiteri CaCO3 model; that is, the former combination satisfactorily reproduced the interactions between the CaCO3 and H2O molecules (Figure S1a). Therefore, it was used for the present simulation. We checked that the H2O−H2O and H2O− CaCO3 potential energy near the calcite surface were almost the same for both the combination of the TIP3P model and the Raiteri CaCO3 model and the combination of the TIP4P-Ew model and the Raiteri CaCO3 model (Figure S1b). Therefore, we believe that the TIP3P model was sufficient for this study aimed at qualitative elucidation of difference in the conformation and dynamics of ASP at different parts of the calcite surface. However, if the purpose of a simulation was precise reproduction of water structure on the calcite surface in real systems, it might be better to use the TIP4P-Ew model or a polarizable model of H2O molecule.51

Figure 1. (a) Structure of ASP, (b) schematic of the simulation systems, and (c) structures of the calcite crystals in the {104}, {110}, step and kink systems. The arrangement of Ca2+ ions (green spheres) and CO32− ions (Cc atoms, gray spheres; Oc atoms, red spheres) in a layer of the calcite crystal is also shown for each system. The dashed lines show the contour of the calcite crystal in each system.

The H2O−CaCO3 interaction was estimated by the method used by Raiteri et al.45 The Coulomb potential between charged points, the Buckingham potential between an Oc atom and each of the O (Ow) and H atoms (Hw) in H2O, and the Lennard−Jones (LJ) potential between a Ca2+ ion and an Ow atom were used for the estimation of the interaction. The parameter values for the Buckingham and LJ potentials were the same as those determined by Raiteri et al.45 The ASP−CaCO3 interaction was estimated with the Coulomb potential between charged points and the LJ potential between each ASP atom and each Ca2+ ion and each Oc atom. The LJ parameters ε and σ were determined according to the Lorentz−Berthelot rules. The Ca2+−Ca2+ LJ parameters were determined by fitting the Ca 2+ −Ca 2+ Buckingham potential curve of the Raiteri CaCO3 model to an LJ potential function. The Oc−Oc LJ parameters were determined in the same manner. The Buckingham and LJ potential parameter values for the Ca2+ ion, CO32− ion, and H2O molecule in this simulation are listed in Table 1. The ASP−CaCO3 LJ potential estimated by means of the Lorentz−Berthelot rules may be an overestimate of the actual Table 1. Values of the Buckingham and Lennard−Jones Potential Parameters for CaCO3 and H2O Used in the Simulation Buckingham Ca Ca Oc Oc Oc

Oc 3.051 Cc 1.158 Oc 6.160 Ow 1.209 Hw 3.824 Lennard-Jones

Ca Ow Ca Oc 14336

A [kJ/mol]

Ow Ow Ca Oc

× × × × ×

5

10 1010 106 106 104

ρ [nm] 2.715 × 1.200 × 1.989 × 2.152 × 2.300 × ε [kJ/mol] 9.649 × 10−2 6.363 × 10−1 1.367 × 10−2 2.000

C [kJ/mol nm6] −2

10 10−2 10−2 10−2 10−2

0 0 2.692 × 10−2 1.167 × 10−2 0 σ [nm] 3.250 3.151 3.357 2.730

× × × ×

10−1 10−1 10−1 10−1



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CaCO3 calcite crystal at 298 K and 1 atm. The width of the calcite crystal in the z direction was approximately 2.5 nm for the {104} system, 2.7 nm for the {110} system and 2.5 nm for the step and kink systems. The width of each water phase in the z direction was approximately 2.5 nm for the {104} system, 3.0 nm for the {110} system and 2.0 nm for the step and kink systems. 2.3. Molecular Dynamics Simulation. The computation was carried out using a leapfrog algorithm with a time step of 1 fs.52 The temperature was maintained at 298 K by means of a Berendsen thermostat with a coupling parameter of 0.1 ps.26 Although ASP was treated as a flexible molecule, the O−H and N−H distances in the molecule were kept constant at their equilibrium values by means of the SHAKE algorithm.53 The MD simulation was performed with the DL_POLY_2.2 MD simulation package.54 The analysis of the MD simulation data was done using our own program. The Ewald summation method was used to estimate the long-range Coulomb potentials. The short-range Buckingham and LJ potentials were truncated at a site−site distance of 1 nm; in contrast, Raiteri et al. smoothly truncated the short-range potentials at a site−site distance of 0.6−0.9 nm by using a switching function.45 However, the difference between the short-range potential energy values calculated by these two different truncation methods was verified to be negligible. To identify the stable conformation adopted by ASP near the surface via a dynamic process, irrespective of its initial position, rather than the energetic stability of a selected binding conformation at the surface, many trajectories were created for the molecule, and each of the trajectories started with different initial positions and orientations. For the {104} system, the distance in the z direction between the initial center-of-mass (COM) position of ASP and the outermost Ca2+ ion layer of the calcite surface (dz) was varied from 0.57 to 0.92 nm in 0.05 nm intervals for each water phase. For the {110} system, dz was varied from 0.53 to 0.68 nm in 0.05 nm intervals for each phase. For each value of dz, the orientations of the ASP molecules in the two water phases were different. Thus, 16 different initial ASP configurations were examined for the {104} systems, and 8 configurations were examined for the {110} system. For all these initial configurations, the x and y coordinates of ASP were set as the center of the system. For the step system, three different initial COM positions for ASP near each of the acute and obtuse step edges were examined. For each of the step edges, the distance in the y direction between the initial COM position and the Ca2+ ions at the edge (dy) was either 0 or ±0.5 nm. For each value of dy, the orientations of the ASP molecules in the two water phases were different. Thus, for each of the acute and obtuse step edges, six different initial ASP configurations were examined. For all these initial configurations, the x coordinate of the COM was set as the center of the system, and dz was set to 0.57 nm. The same initial ASP configurations were also used for the kink system.

potential because the rules underestimate the equilibrium distance between ASP and CaCO3.35 However, we confirmed that the ASP−Ca and ASP−CO3 equilibrium distances did not significantly differ between the present potential models and the first principle calculation (Figure S2). In the present simulation, most of the ASP atoms did not approach the calcite surface, because of the water. Thus, the overestimation of the ASP−CaCO3 LJ potential was not significant, and the Lorentz−Berthelot rules were sufficient for this qualitative study of the differences in the conformation and dynamics of ASP near the {104} plane, the {110} plane, the acute step edge, the obtuse step edge, and the kinks. 2.2. Simulation System. Four simulation systems were prepared (Figure 1b,c): a system including two {104} planes (the {104} system); a system including two {110} planes (the {110} system); a system including two {104} planes with [114̅] acute and obtuse steps, each of which had a molecularly smooth edge (the step system); and a system including two {104} planes with [114̅] acute and obtuse steps, each of which had two kinks at the edge (the kink system). The kink system contained two different types of kinks: one with a Ca2+ ion at the corner (Ca2+-kink), and one with a CO32− ion at the corner (CO32−-kink). Each system was a rectangular parallelepiped consisting of a CaCO3 calcite crystal, two water phases, and two vapor phases. The crystal was placed at the center of the system so that its surfaces were perpendicular to the z-axis of the system. The crystal consisted of 512 Ca2+ and 512 CO32− ions for the {104} system, 432 Ca2+ and 432 CO32− ions for the {110} system, 828 Ca2+ and 828 CO32− ions for the step system, and 816 Ca2+ and 816 CO32− ions for the kink system. Each water phase consisted of 1000 H2O molecules for the {104} and {110} systems, and of 1500 H2O molecules for the step and kink systems. Each water phase contained an L-ASP monomer. Thus, the system contained two ASP molecules. The vapor phase corresponded to a vacuum phase at the beginning of the simulation and was 3 nm thick in the z direction. Periodic boundary conditions were imposed in the x, y, and z directions. The vapor phase was put in the system in order to avoid the migration of ASP between two calcite surfaces, which might cause clustering of two ASP molecules, via the periodic boundary condition by elongating the system in the z direction. We checked that the conformation of ASP on the calcite surface did not significantly depend on the size of the water phase in the system (Figure S3). Because the ASP molecule in each water phase had a negative charge of −e, a Ca2+ ion was added to each simulation system to maintain an electrically neutral state. This Ca2+ ion was fixed at the center of the x−y plane boundary of the system in the z direction. This Ca2+ ion had to be placed far from the calcite crystal and water phases to minimize its effect on the conformation and dynamics of the ASP molecules. This was the reason why a vapor phase was added to each water phase in the system. Note that adding a cation with charge of +e to each water phase is an alternative method for maintaining an electrically neutral state in the system.34 However, because the cation might influence the conformation and dynamics of ASP by interacting with it, that method was not used. During the simulation, the dimensions of the systems were fixed at 3.99 × 3.26 × 13.15 nm for the {104} system, 2.99 × 3.41 × 14.49 nm for the {110} system, and 3.83 × 6.25 × 12.81 nm for the step and kink systems. The dimensions in the x and y directions were determined from an MD simulation of a bulk

3. RESULTS 3.1. Water Structure on the Calcite Surface. Because this study focused on the effect of water on the conformation and dynamics of ASP, it was necessary to clarify the structure of water on each of the calcite planes. The structure of water on flat {100} and {110} planes was investigated in earlier studies.30,36,45,55 However, this study focused not only on flat {100} and {110} planes but also on the steps and kinks on the 14337



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As a result, Uww was positive for z ≤ 0.4 nm in the {110} system. Each H2O molecule in the {110} system was oriented so that it bound to the surface more tightly than for the {104} plane; Uw‑cal was much lower at z ≤ 0.5 nm for the {110} system than for the {104} system. A much smaller number of hydrogen bonds between H2O molecules on the {110} plane than on the {104} plane was also reported by Zhu et al. from a different CaCO3 potential model.36 Figure 3 shows the existence probability of H2O molecules in three thin layers (α, β, and γ) on the {104} plane for the step

{100} plane. Moreover, this study used different potential models from those earlier studies. Thus, in this study, the structure of water on each of the calcite planes was investigated by means of an MD simulation for each of the systems without ASP. Figure 2a shows the number density profiles, ρ, of Ow and Hw (ρO and ρH) along the z direction for the {104} and {110}

Figure 2. (a) Number density profiles of the Ow and Hw atoms (ρO and ρH) along the z direction for the {104} and {110} systems without ASP. The origin of the z component was the outermost layer of Ca2+ ions in the calcite crystal. The lower panel shows the structure of a {110} plane, which was obtained by an MD simulation of the {110} system without ASP. (b) Potential energy between a pair of H2O molecules (Uww) and between a H2O molecule and the calcite crystal (Uw‑cal) along the z direction for the {104} and {110} systems. The dashed line shows the experimental Uww value of bulk water at 298 K and 1 atm (−41.5 kJ/mol).48 The Uww value of bulk water at 298 K and 1 atm for the TIP3P model is −41.3 kJ/mol.48

Figure 3. Existence probabilities of H2O molecules in three thin layers (α, β, and γ) on the {104} plane for the step system. The thickness of each layer in the z direction was approximately 0.13 nm. The existence probabilities were estimated from a separate MD simulation of the step system in which ASP was not present in the liquid water phase.

systems without including ASP molecules. A layered water structure consisting of approximately three H2O molecular layers formed on the {104} plane, which is consistent with results reported in previous studies for different potential models of H2O30,45,55 and for a different potential model of CaCO3.36 In the {110} system, layers of water did not form. This was because the ideal crystal arrangement of Ca2+ and CO32− ions was disrupted at the outermost layer of the {110} plane (see lower panel of Figure 2a), reflecting the energetic instability of the ideal structure of the {110} plane. In connection with the energetic instability of the ideal {110} plane structure, the occurrence of a large relaxation of the {110} plane structure has been reported by de Leeuw and Parker.56 Figure 2b shows profiles of the H2O−H2O potential energy (Uww) and the H2O−CaCO3 potential energy (Uw‑cal) along the z direction for the {104} and {110} systems, along with the experimental value of Uww for bulk water (−41.5 kJ/mol).57 For the {104} system, the extremely low Uw‑cal values at z ≤ 0.3 nm indicate that the H2O molecules near the {104} plane interacted strongly with the plane. Remarkably, Uww was negative at even z = 0.2 nm, which means that hydrogen bonds formed between the H2O molecules, although the average number of hydrogen bonds per H2O molecule (0.54 at z = 0.2 nm) was much smaller than that in bulk water (3.5). However, for the {110} system, the strong interaction of H2O molecules with the Ca2+ and CO32− ions of the disrupted plane hindered the formation of layers of H2O molecules and the formation of hydrogen bonds between the H2O molecules.

system. The difference between the water structures for the acute and obtuse steps was clear in layer β. The H2O molecules in layer β were broadly distributed near the acute step edge, whereas they were ordered near the obtuse step edge (region enclosed by the dashed oval). Thus, our simulation suggested that the structures of the water near the edge were different for the acute and obtuse steps. In connection with the present result, a difference in the density of water near the step edge between the acute and obtuse step edges has been reported in published studies.39,58 The same difference in the structures of water near the edge was also detected in the kink system. 3.2. ASP on the Hydrated Calcite Surface. 3.2.1. {104} System. Figure 4 shows the number density profiles for the ASP carboxyl O atoms (ρOc) and for the ASP amine N atom (ρN) along the z direction of the {104} system. The large peaks in ρOc around z = 0.4 nm for both the main- and side-chain carboxyl groups, as well as the peak in ρN around z = 0.48 nm, indicate that ASP preferred an indirect binding state, in which the molecule occupied positions separated from the {104} plane by a layer of H2O molecules. An indirect binding state was also reported for polystyrenesulfonate near the calcite surface by Shen et al.,40 and for an acrylic acid dimer near the calcite surface by Zhu et al.36 The appearance of small peaks in ρOc around z = 0.22 nm for both the main-chain and the sidechain carboxyl O atoms indicates that ASP frequently adopted a direct binding state in which its carboxyl O atoms were bound 14338



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conformations (conformations A and B) and in the indirect binding conformation. Snapshots of ASP at 1, 4, and 6 ns for each of the three conformations are shown in Figure 5b. For all three conformations, UASP‑w was much lower than UASP‑cal, which strongly suggests that near the {104} plane, ASP interacted much more strongly with the surrounding water than with the plane. Table 2 shows the time-averaged value of UASP‑cal for each of the conformations that ASP adopted. For comparison, the value Figure 4. Number density profiles of the carboxyl O atoms (ρOc) and the amine N atom (ρN) of ASP along the z direction for the {104} system. The ρ values were calculated with the simulation data for a period of 5 ns beginning 1 ns after the start of the simulation for all 16 trajectories.

Table 2. UASP‑cal Averaged over a Period of 5−6 ns for Each Conformation in the Hydrated System, and UASP‑cal for the Anhydrous System, Which Was Estimated from a 0.2 ns MD Simulation Started with the Final Configuration for Each Conformation in the Hydrated System from Which H2O Molecules Were Removed

directly to the surface. Two direct binding conformations were observed: one in which the main-chain carboxyl O atom was bound to the surface (conformation A), and one in which the side-chain carboxyl O atom was bound to the surface (conformation B). Figure 5a shows the ASP−CaCO3 potential energy (UASP‑cal) and the ASP−H2O potential energy (UASP‑w) as a function of time for three ASP trajectories that ended in the direct binding

system

conformation

hydrated system

{104} {104} {104} {110} {110} step step kink kink

A B indirect C D E F G H

−6.9 × 103 9.6 × 101 1.3 × 104 −4.8 × 104 −3.2 × 103 5.3 × 103 −6.3 × 103 −7.8 × 104 −8.4 × 104

anhydrous system −9.5 −7.7 −1.0 −1.2 −8.0 −1.3 −3.2 −1.3 −1.3

× × × × × × × × ×

104 102 105 105 104 105 104 105 105

of UASP‑cal for the “anhydrous” system is also shown. The value of UASP‑cal for the anhydrous system was estimated from a 0.2 ns MD simulation, which started with the final configuration of the simulation for the hydrated system from which H2O molecules were removed. If water strongly affected the conformation of ASP, the conformation would significantly change between the hydrated and anhydrous systems, and UASP‑cal would also change significantly. Thus, a change in UASP‑cal between the hydrated and anhydrous systems serves as a measure of how much water affected the conformation of ASP. A large change in UASP‑cal between the hydrated and anhydrous systems for conformations A, B, and C, which are seen in Table 2, support that water strongly affected those conformations. Figure 5a shows that there were large fluctuations in UASP‑w for conformation A, particularly from 2.7 to 4.8 ns. There were also dramatic instantaneous decreases in UASP‑cal for conformation A at 3.5 and 3.7 ns. These fluctuations and decreases arose from transient changes in the conformation (Figure 5b). The transient changes in the conformation imply that there were several metastable conformations. For conformation B, UASP‑w and UASP‑cal shifted sharply at 2.1 ns, which indicates that the conformation changed from the indirect binding conformation to conformation B. The change in conformation is shown in Figure 5b from 1 to 4 ns. Similarly, a transition in the opposite direction, from conformation A to the indirect binding conformation, was observed in one of the other trajectories with a different initial configuration. No transition between the direct and indirect binding conformations occurred in the other 14 trajectories. This suggests that the transition between the direct and indirect binding conformations had a large activation energy, originating from the layers of water on the {104} plane. Because transitions between the indirect and direct binding conformations occurred, the thermodynamic stability of the indirect binding

Figure 5. (a) Potential energy between ASP and calcite (UASP‑cal) and between ASP and liquid water (UASP‑w) as a function of time for three ASP trajectories that ended in conformation A, conformation B, or the indirect binding conformation, respectively. UASP‑cal was calculated as the sum of the ASP-CaCO3 interactions for all CaCO3 ions, and UASP‑w was calculated as the sum of the ASP-H2O interactions for all H2O molecules. (b) Snapshots of ASP conformation A, conformation B, and the indirect binding conformation at 1, 4, and 6 ns. The gray cylinders represent hydrogen bonds between H2O molecules. The carboxyl O atom and Ca2+ ion that are bound directly to each other are indicated by the orange circles. 14339



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conformation is expected to be similar to that of the direct binding conformations. 3.2.2. {110} System. Figure 6 shows the ρOc and ρN profiles for the {110} system, which differed from the profiles for the

Figure 6. Number density profiles of the carboxyl O atoms (ρOc) and the amine N atom (ρN) for ASP along the z direction for the {110} system. The profiles were created using all eight trajectories, which had different initial configurations. The origin of the z component was the outermost Ca2+ ion layer of the {110} plane.

{104} system. A large peak in the ρOc profile was observed for the ASP side-chain carboxyl group around z = 0.2 nm, indicating that its O atoms were stable at positions close to the plane. Moreover, a large peak in the ρN profile around z = 0.33 nm suggests that the amine N atom was also stable close to the plane; in contrast, in the {104} system, the large peak appeared around z = 0.47 nm (Figure 4). This difference suggests that ASP preferentially adopted the direct binding conformation at the hydrated {110} plane. The direct binding conformation was stable in seven of the eight trajectories. In one of the trajectories, ASP did not adopt the direct binding conformation, because the molecule migrated toward the vapor phase, and the simulation run was not long enough for the ASP to approach the plane. ASP bound directly to the calcite surface far more readily for the {110} system than for the {104} system, because layers of water were not formed on the {110} plane. Here, once the ASP molecules adopted the direct binding conformation, they did not subsequently adopt the indirect binding conformation. Therefore, the direct binding conformation was thermodynamically more stable than the indirect binding conformation for the {110} system. Figure 7a shows UASP‑cal and UASP‑w as a function of time for two of the direct binding conformations (C and D) in the {110} system. For both conformation C and conformation D, UASP‑w was much lower than UASP‑cal, as was the case for the {104} system. A large change in UASP‑cal between the hydrated and anhydrous systems occurred for conformations C and D (Table 2). These results indicate that those conformations were influenced more strongly by the interactions with the surrounding water than by the interactions with the calcite surface. In addition, transient changes in the binding conformation, which correspond to transitions among several metastable conformations, were also observed for the {110} system (Figure 7b). The values of UASP‑cal and UASP‑w for conformation C were different from those for conformation D. The difference in the U values reflects the difference in binding conformations C and D (Figure 7b); in conformation C, two bonds were formed between the side-chain carboxyl O atom and the surface Ca2+ ion, whereas in conformation D, only one bond was formed. 3.2.3. Step System. Figure 8 shows the existence probabilities of the carboxyl O atoms in the y−z plane for

Figure 7. (a) Potential energies UASP‑cal and UASP‑w as a function of time for two ASP trajectories that ended in direct binding conformations at the {110} plane (conformations C and D). (b) Snapshots of ASP in conformations C and D at 1, 4, and 6 ns.

Figure 8. Existence probabilities of ASP carboxyl O atoms near the acute and obtuse steps in the step system. The blue regions indicate a high existence probability for the O atoms, and the green regions are the positions of the calcite Ca2+ ions.

the step system; a notable difference between the existence probabilities was observed around the step edge for the acute and obtuse steps. The carboxyl O atoms were near the acute step edge (indicated by dashed circles) and not the obtuse step edge. This strongly suggests that ASP bound to the acute step edge but not to the obtuse step edge. Of the six trajectories with different initial configurations that ended near the acute step edge, four adopted the direct binding conformation at the acute step edge. The conformation and dynamics of ASP in the step system were influenced strongly by the surrounding water, as was the case for the {104} and {110} systems. Figure 9a shows the time dependence of UASP‑cal and UASP‑w for two of the four ASP trajectories that adopted the direct binding conformation at the acute step edge (conformations E and F). For conformations E and F, UASP‑w was much lower than UASP‑cal. Moreover, one of 14340



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Figure 10. (a) Existence probabilities of ASP carboxyl O atoms near the acute and obtuse steps in the kink system. The black regions represent a high existence probability for the O atoms. The green, gray and red regions indicate the positions of the calcite Ca2+ ions, Cc atoms, and Oc atoms, respectively. (b) Potential energies UASP‑w and UASP‑cal as a function of time for two ASP trajectories that ended in direct binding conformations at the Ca2+-kink (conformations G and H). (c) Snapshots of ASP in conformations G and H at 2.5 and 6 ns.

Figure 9. (a) Potential energies UASP‑cal and UASP‑w as a function of time for two ASP trajectories that ended in direct binding conformations at the acute step edge (conformations E and F). (b) Snapshots of ASP in conformations E and F at 1, 4, and 6 ns.

(conformation G) and the obtuse step edge (conformation H). Snapshots of ASP conformations G and H are shown in Figure 10c. These figures show that the conformation and dynamics of ASP near the Ca2+-kink were influenced strongly by the surrounding water, as they were in the {104}, {110}, and step systems. However, a change in UASP‑cal between the hydrated and anhydrous systems for conformations G and H was not large as compared with the cases for conformations A− F (Table 2). This result implies that the influence of water on conformations G and H was not as great as in the cases for conformations A−F. Notably, U ASP‑cal at the end of the simulation for conformations G and H were much lower than those for conformations A−F (Figures 5b, 7b, and 9b), indicating that the binding of ASP to the Ca2+-kink was much stronger than the binding to the {104} plane, {110} plane, and the acute step edge. This difference in UASP‑cal originated from a difference in the strength of the Coulomb interaction that ASP experiences from the calcite surface. When the carboxyl O atom of ASP approaches a Ca2+ ion at the calcite surface, ASP experiences an attractive Coulomb interaction from the surface Ca2+ ion. ASP also experiences a repulsive Coulomb interaction from CO32− ions at the calcite surface. However, the absence of a CO32− ion adjacent to the corner Ca2+ ion at the Ca2+-kink means that the repulsive Coulomb interaction is weaker for the Ca2+-kink than for the {104} plane, {110} plane, and acute step edge. This explains why binding of ASP is stronger at the Ca2+-kink than at the {104} plane, {110} plane, and acute step edge. For both the Ca2+- and the CO32−-kinks, the ideal kink structure was slightly modified during the simulation; the position of the corner ion in the kink was shifted from its ideal position (Figure 10c). However, we used an MD simulation of a system for dehydrated Ca2+- and CO32−-kinks with ideal structures to check that ASP bound preferentially to the Ca2+kink even if it had an ideal structure. Therefore, we believe that

the ASP carboxyl O atoms was bound to the edge, and the other ASP atoms were exposed to water (Figure 9b). A large change in UASP‑cal between the hydrated and anhydrous systems occurred for conformations E and F (Table 2). Transient changes in the conformation were also observed for the step system. Figure 3 shows that the structure of water near the obtuse step edge was ordered, whereas that near the acute step edge was not. Thus, as in the {104} system, ordered water near the obtuse step edge created a large activation energy for direct binding of ASP to the edge. The difference in the structure of water between the acute and obtuse step edges caused a significant difference in ASP dynamics near the edge, and can explain why ASP bound to only the acute step edge. Analogous to this study, the effect of water structure on the binding of ovocleidin-17 protein to the acute step edge was investigated by Freeman et al.39 3.2.4. Kink System. Figure 10a shows the existence probabilities of the carboxyl O atoms in the x−y and y−z planes on one of the two {104} planes in the kink system. The carboxyl O atoms were near the Ca2+-kink at both the acute and obtuse step edges, but not near the CO32−-kink at the step edges. This suggests that ASP bound preferentially to the Ca2+kink. Similarly, the carboxyl O atoms were near only the Ca2+kink at both the acute step edge and the obtuse step edge on the other {104} plane in the kink system. The preferential binding of ASP to the Ca2+-kink occurred because ASP was negatively charged. Of the 12 trajectories with different initial configurations, 3 adopted the direct binding conformation at the Ca2+-kink: 2 for the obtuse step edge and 1 for the acute step edge. The structure of water near the Ca2+-kink did not create an energy barrier that inhibited the direct binding. Figure 10b shows the time dependence of UASP‑cal and UASP‑w for ASP trajectories that adopted the direct binding conformation at the Ca2+-kink of the acute step edge 14341



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conformation for the {104} system. Further studies are required to determine which binding conformation is more stable. Compared with the profile for the {104} system, the ΔA profile for the {110} system was relatively flat for the entire z range, indicating that dehydration due to the direct binding of ASP to the {110} plane did not cause an increase in free energy. Moreover, in the direct binding conformations on the {110} plane, the carboxyl O atoms and the amine N atom appear mainly in the z range from 0.25 to 0.7 nm (Figure 7), where the free energy of the H2O molecules was generally higher than that of the bulk water. Thus, the direct binding conformation of ASP on the {110} plane decreased the free energy of the system, explaining why this binding conformation was thermodynamically stable. Figure 11b shows ΔA of H2O molecules near the step edge as a function of z for the step system. ΔA for the acute step was on the whole higher than that of the bulk water and that for the obtuse step. Especially, in the z range of 0.4−0.45 nm, where one of the carboxyl O atoms of ASP that adopted the direct binding conformation at the acute step edge appeared, ΔA for the acute step was higher by approximately 4.5 kJ/mol than that for the obtuse step. Thus, the direct binding conformation at the acute step edge decreased the free energy of the system, explaining why the direct binding conformation was stable only at the acute step edge. Although ΔA was not estimated for the kink system, as in the {104}, {110}, and step systems, it is expected that ΔA near the kink affected the binding conformation. Thus, we confirmed that water is crucial for the binding conformation of ASP on the calcite surface, as it was for the binding conformation of ovocleidin-17 protein on the calcite surface.39 Extensive free energy calculation for many conformations of ASP is needed to evaluate precisely the effect of water on the conformation and dynamics of ASP near each part of the calcite surface. Strictly speaking, details on the conformation and dynamics of ASP on the calcite surface would slightly change if a different potential model of H2O was used. However, we checked that the TIP4P model,48 which is one of popular potential models for the simulation of water, also provided indirect binding conformations stably on the {104} plane (Figure S4). Thus, we expect that the present results do not significantly depend on the potential model of H2O. More detailed studies are needed to confirm this expectation. Preferably, the present results should also be compared with the results obtained by ab initio MD simulation, which we intend to perform in the future. 4.2. Comparison with Experimental Results. Elhadj et al. experimentally observed the formation of hillock structures consisting of obtuse and acute steps on a calcite {104} plane in the presence of ASP.22 They observed surface roughening at only the acute step edge; therefore, they proposed that ASP preferentially binds to the acute step edge. Our simulation, which clearly showed that ASP bound to only the acute step edge, directly supports this proposal. Elhadj et al. attributed the preferential binding of ASP to the acute step edge to a difference between the binding energies of ASP on the acute and obtuse step edges.22 They estimated the binding energy by a quantum chemical method, which indicated that the value is lower for the acute step edge than for the obtuse step edge. In this study, the UASP‑cal values of energetically stable binding conformations at a dry step edge were calculated for both the acute and the obtuse steps, using a separate MD simulation for the step system in which the water

the modification of the kink structure did not significantly alter the conformation and dynamics of ASP near the kink.

4. DISCUSSION 4.1. Effect of Water on ASP Binding Conformation. Here, we discuss the effect of water on the binding conformation of ASP on the calcite surface in detail. Figure 11a shows the excess Helmholtz free energy (ΔA) of H2O

Figure 11. (a) Excess Helmholtz free energy of H2O molecules (ΔA) as a function of z for the {104} and {110} systems. (b) ΔA of H2O molecules near the step edge as a function of z for the step system. Here, an H2O molecule was defined to be placed near the step edge if the distance in the y direction from the H2O molecule to the Ca2+ ion at the step edge was less than 0.3 nm (see an illustration in the figure).

molecules as a function of the z component for the {104} and {110} systems. ΔA at a particular z component value (za) was estimated by integrating the average force in the z direction ( fz) acting on each H2O molecule from z = ∞ to za.59 The minimum of ΔA, which occurred at z = 0.2 nm in the {104} system, corresponds to the first layer of water on the {104} plane. The free energy of H2O molecules in the first layer was much lower than that of the molecules in the bulk water. Therefore, although the direct binding of ASP to the {104} plane decrease the free energy of the system from the decrease in UASP‑cal, the resulting dehydration simultaneously increases the free energy of the system. Thus, only one of the carboxyl O atoms bound to the plane, to minimize the increase in the free energy of the system caused by the dehydration. The other carboxyl O atoms and the amine N atom of ASP appeared mainly in the z range from 0.3 to 0.55 nm (Figure 4), where the free energy of the H2O molecules was generally higher than that of the bulk water (Figure 11). Therefore, the direct binding conformation of ASP on the {104} plane decreases the free energy of the system. In the indirect binding conformation on the {104} plane, UASP‑cal was positive (Figure 5), causing an increase in the free energy of the system. However, the carboxyl O atoms and the amine N atom also appeared mainly in the z range from 0.3 to 0.55 nm (Figure 4). Thus, the indirect binding conformation also decreases the free energy of the system. This result supports the hypothesis that the indirect binding conformation was as thermodynamically stable as the direct binding 14342



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kink. This binding to the Ca2+-kink was much stronger than the binding to the acute step edge. Normally, the density of the kinks formed at the step edges depends on supersaturation. Therefore, our simulation implied that the extent of the change in step morphology in the presence of ASP depends on supersaturation. Our study is the first to show the conformation and dynamics of an organic molecule near kinks formed on the calcite surface using an MD simulation. In conclusion, our simulation qualitatively elucidates significant differences in the conformation and dynamics of ASP at different parts of the hydrated calcite surface, which may be related to the control of calcite growth by ASP in real systems. The degree to which water affects the binding conformation and dynamics of an organic molecule and calcite growth control by organic molecules may depend on the type of organic molecule. Further studies of various other organic molecules should be conducted in the future.

phases were excluded. UASP‑cal was slightly lower for the acute step edge than for the obtuse step edge, which qualitatively agreed with Elhadj et al.22 However, the difference in UASP‑cal between the step edges was only 102 kJ/mol. This difference was small compared with the absolute UASP‑cal values, which were larger than 103 kJ/mol. Therefore, it seems that this energy difference alone is insufficient to explain why ASP bound to only the acute step edge. Our simulation suggests an alternative explanation for the preferential binding of ASP to the acute step edge; the difference in water structure near the smooth step edges cause a significant difference in ASP dynamics near the edge, and can explain the preferential binding. Thus, our simulation suggests that the step morphology changes in the presence of ASP because of the surrounding water. Similarly, water may significantly influence the control of calcite growth by organic molecules in nature. Notably, in our simulation, ASP bound to the Ca2+-kink at both the acute and the obtuse step edges, and the binding was much stronger at the Ca2+-kink than at the acute step edge. Thus, if the density of the kink at the step edge is equally high for both the acute and the obtuse steps, the difference in the number of ASP molecules that are bound to the step edge between the acute and the obtuse steps becomes small. Normally, the density of kinks formed at the step edges depends on the growth rate of the step, and the growth rate of the step depends on supersaturation. Thus, our simulation implies that the extent of the changes in step morphology in the presence of ASP depends on supersaturation. This can be confirmed by experimental studies.

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ASSOCIATED CONTENT

S Supporting Information *

Number density profiles of the Ow and Hw atoms for both the TIP3P and TIP4P-Ew models along the z direction of the {104} system, and potential energy between a pair of H2O molecules and between an H2O molecule and the calcite along the z direction for the {104} system. The potential energy U between an ASP molecule and a Ca2+ ion as a function of the distance between the Ca2+ ion and a carboxyl C atom of the ASP molecule, and U between an ASP molecule and a CO32− ion as a function of r between the C atom of the CO32− ion and the N atom of the ASP molecule, calculated using a first principle method and our potential models. Comparison of ASP conformation between in the {104} system and a larger {104} system in which the water phase consisted of 2000 H2O molecules. Indirect binding conformations that appeared in the simulation of the {104} system with the TIP4P model. This material is available free of charge via the Internet at http:// pubs.acs.org.

5. CONCLUSIONS The conformations and dynamics of ASP near a calcite surface were analyzed by MD simulations for {104}, {110}, step, and kink systems. The ASP conformations and dynamics for the {104} and {110} planes differed significantly. In the {104} system, ASP adopted an indirect binding conformation, because a layered water structure formed on the {104} plane and hindered the direct binding. Our simulation implied that the thermodynamic stability of the indirect binding conformation is similar to that of direct binding conformations on the {104} plane. In the {110} system, the ASP preferentially adopted a direct binding conformation, because no layers of water were formed on the {110} plane where the ideal ion arrangement was disrupted. Similar binding conformations of an acrylic acid dimer on these planes have been reported.36 In this study, we also investigated the dynamics of ASP near each of the planes, where transitions between stable and metastable conformations frequently occurred. In the step system, ASP bound to the acute step edge but not to the obtuse step edge. This is consistent with the experimental observations of Elhadj et al., who reported that surface roughening occurred at only the acute step edge.22 They proposed that ASP preferentially binds to the acute step edge, because the binding energy is lower for the acute step edge than for the obtuse step edge. In our simulation, water near the obtuse step edge had a highly ordered structure, whereas water near the acute step edge had a disordered structure. This difference in water structure near the steps can also explain the preferential binding of ASP to the acute step edge. In the kink system, ASP bound to the Ca2+-kink formed at both the acute and the obtuse step edges but not to the CO32−-

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +81-29-861-8231. Fax: +81-29-861-8722. E-mail: hiroki. [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The author thanks Prof. Helmut Cölfen (University of Konstanz, Germany) for helpful comments about this study and Dr. Seiji Tsuzuki (AIST, Japan) for helpful suggestions about the first principle calculations. This work was supported by a Grant-in-Aid for Scientific Research (No. 22107004) on Innovation Areas of “Fusion Materials” (Area No. 2206) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT). Some of the computations in this work were done using the facilities of the Supercomputer Center, Institute of Solid State Physics, University of Tokyo.

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REFERENCES

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