Dependence of Protein Crystal Stability on Residue Charge States and Ion Content of Crystal Solvent

Abstract

Protein crystallization is frequently induced by the addition of various precipitants, which directly affect protein solubility. In addition to organic cosolvents and long-chain polymers, salts belong to the most widely used precipitants in protein crystallography. However, despite such widespread usage, their mode of action at the atomistic level is still largely unknown. Here, we perform extensive molecular dynamics simulations of the villin headpiece crystal unit cell to examine its stability at different concentrations of sodium sulfate. We show that the inclusion of ions in crystal solvent at high concentration can prevent large rearrangements of the asymmetric units and a loss of symmetry of the unit cell without significantly affecting protein dynamics. Of importance, a similar result can be achieved by neutralizing several specific charged residues suggesting that they may play an active role in crystal destabilization due to unfavorable electrostatic interactions. Our results provide a microscopic picture behind salt-induced stabilization of a protein crystal and further suggest that adequate modeling of realistic crystallization conditions may be necessary for successful molecular dynamics simulations of protein crystals.

Introduction

X-ray crystallography is the most dominant experimental method for determining high-resolution structures of biological macromolecules and is responsible for >85% of structures currently deposited in the Protein Data Bank (1). However, optimal crystallization conditions in a typical crystallographic study are still usually determined in a trial-and-error manner, whereby a large set of variables are scanned until suitable crystals are produced (2). Different precipitants, which fall into three broad categories of salts, polymers, and organic additives, are typically used to facilitate crystallization of macromolecules. Specifically for proteins, the presence of precipitants generally increases attractive interactions between them and changes the phase behavior of the crystallization solution, but the underlying microscopic mechanisms vary between different classes of precipitants (3). As the most commonly used precipitant, salts are usually excluded from the protein surface (4,5) and their influence on the local water structure, in terms of the water-structure-making or water-structure-breaking propensities, has long been assumed to be the reason for the ability of specific ions to precipitate proteins from solution. In fact, different ions have been ordered in the classical Hofmeister series according to this ability (6). However, it has been shown by thermodynamic studies of water molecules in salt solutions, as reviewed by Zhang and Cremer (7) that a direct influence on water structure is not the main mode of action of ions and, therefore, the focus has shifted toward direct interactions of ions with macromolecules and water molecules in their first hydration shell. Currently, most of the efficiency associated with salts in the process of protein crystallization is attributed to the interplay between attractive and repulsive intermolecular forces between proteins, which are experimentally assessed by the second virial coefficient, B₂ (8), although its determination still remains difficult (9). Of importance, most of these effects remain largely unexplored at the molecular level (10), with some exceptions including a study in which ions have been implicated in facilitating attractive interactions between proteins through participation in crystal contacts (11).

In parallel with technological advances (12,13), molecular dynamics (MD) simulations have over the years become the method of choice to study microscopic features of protein crystals, continuing an already rich tradition. Namely, MD simulations have historically been used to address various challenges in biomolecular crystallography including assessment of the precision of atomic positions determined by crystallographic refinement (14), analysis of crystallographic refinement parameters (15), comparison of the effects of different environmental conditions on protein conformation (16,17) and also the very process of refinement itself (18,19). Although the early studies involved relatively short simulations, each several nanoseconds long and containing a single unit cell, recently one could witness an increase in the number of simulated unit cells (16,20,21) and the total simulation time (20,22,23), allowing for a better sampling of microscopic heterogeneity and a more realistic comparison with the experiment. However, a question that arises is to what extent should MD simulations of protein crystals reproduce the exact experimental crystallization conditions? This problem becomes especially relevant if one considers that over 40% of the mass of a typical crystal consists of crystallization solution (24), which usually exhibits high ionic strength, especially if salts are used as precipitants, and requires a careful treatment of electrostatic interactions. The usage of different electrostatic schemes on protein stability has been tested previously, both in solution (25–28) and crystal simulations (29), and subtle, but potentially important differences between reaction field and particle mesh Ewald (PME) approaches have been demonstrated. Although PME has been known to introduce artificially periodic behavior in nonperiodic systems (25), maintaining periodicity may be a desired feature in crystal simulations. For these reasons, PME is the most commonly applied scheme in such simulations due to its accuracy and a generally stabilizing effect. Given the basic physical foundations of the PME method, one is required to apply it to a neutral system, which is achieved by adding neutralizing counterions to the solvent. The impact of counterions on most reported systems is not large (29,30), but when one studies highly charged proteins, their contribution may become significant (27,31). In particular, in the case of proteins with low stability, neutralizing counterions may not be sufficient to maintain a stable structure and full ionic strength has to be modeled explicitly (32). Moreover, explicit inclusion of all crystallization solvent components has been shown to result in better preservation of the experimental x-ray structure compared to the simulations that contain just pure water as solvent (22). However, inclusion of all the components present in the solvent is often a difficult task due to the frequent lack of quality force-field parameters for many relevant moieties. Usage of problematic parameters has in fact been associated with artifacts such as unphysical clustering or general inability to reproduce physical properties of such mixtures (22).

In this study, we have performed extensive MD simulations to examine the stability of a compact protein crystal with a highly charged asymmetric unit as a function of its crystal solvent composition and especially its ion content. For this purpose, we have chosen a crystal of the 35-residue villin headpiece domain, which contains 10 titratable groups including the termini. We show that in the absence of ions in the system, the unit cell exhibits large rearrangements of its asymmetric unit and a general loss of symmetry. However, by increasing salt concentration, these rearrangements become negligible without noticeably affecting protein dynamics. Furthermore, similar results are also achieved by neutralizing several charged residues, which further hints at the underlying causes of the observed large changes in the positions of proteins in the unit cell. Overall, our study provides a microscopic picture behind salt-induced stabilization of a protein crystal and furthermore simultaneously explores the necessary conditions required for successful MD simulations of such systems.

Methods

MD simulations

A double mutant of the villin headpiece domain (residues K24 and K29 changed to norleucines) has been used to create a single unit cell of a protein crystal by applying C222₁ symmetry operators to the model deposited in the PDB (code: 2F4K) (33). The model was stripped of water molecules and only the positions of A rotamers were used in the simulations. Two different sets of trajectories were generated: 1), a single unit cell containing eight copies of the protein with Lys, Arg, and N-terminus in the protonated state and Asp, Glu, His, and C-terminus in the deprotonated state with varying concentrations of sodium sulfate (Table 1), and 2), a single unit cell of the same protein with varying protonation states of the following amino acids: Leu-1 (N-terminus), Asp-3, Asp-5, and Arg-14 with no added ions, except the sodium and chloride counterions (Table 2). Three independent 100-ns-long trajectories of each subsystem were produced for a total of >8 μs over all setups using GROMOS 45A3 force field (34) and the GROMACS 4.0.7 biomolecular simulation package (35). Because this model contains mutations of two lysines to norleucines (K24 and K29), which are not a part of the GROMOS 45A3 force field, the parameters for this amino acid were obtained from the Vienna-PTM server (36,37).

Table 1.

Simulation details for the system with varying salt concentrations

Salt conc. (M)	N(Na+)	N(SO42−)	N(H2O)	N(atoms)	Rmin (Å)
0.00	0	0	494	4466	6
0.08	6	3	482	4451	6
0.16	12	6	466	4424	6
0.32	22	11	443	4390	6
0.48	34	17	414	4345	6
0.64	46	23	384	4297	6
0.80	56	28	362	4266	6
0.96	68	34	335	4227	6
1.12	80	40	307	4185	5
1.28	90	45	284	4151	5
1.44	102	51	254	4103	5
1.60	114	57	226	4061	4

The number of ions and water molecules present in each simulation setup and the minimum distance between sodium ions is shown. Three independent 100-ns-long trajectories at each salt concentration were generated.

Table 2.

Simulation details for the system with different protonation states of Leu-1, Asp-3, Asp-5, and Arg-14

Neutralized residues	N(Na+)	N(Cl−)	N(H2O)	N(atoms)
–	0	0	494	4466
Arg-14	8	0	488	4448
Asp-3, Arg-14	0	0	492	4460
Asp-3, Asp-5, Arg-14	0	8	486	4458
Leu-1, Asp-3, Asp-5, Arg-14	0	0	492	4460
Leu-1, Asp-3, Arg-14	8	0	486	4442
Asp-5, Arg-14	0	0	499	4481
Leu-1, Asp-5, Arg-14	8	0	491	4457
Leu-1, Arg-14	16	0	483	4433
Asp-3	0	8	484	4452
Asp-3, Asp-5	0	16	474	4438
Leu-1, Asp-3, Asp-5	0	8	486	4458
Leu-1, Asp-3	0	0	496	4472
Asp-5	0	8	485	4455
Leu-1, Asp-5	0	0	493	4463
Leu-1	8	0	488	4448

The number of ions and water molecules present in each simulation setup is shown. Three independent 100-ns-long trajectories of each simulation setup were generated.

Each simulation box had the following dimensions: 19.677 Å, 39.901 Å, and 75.089 Å, containing eight copies of the protein, and was prepared and simulated according to the following protocol. First, the system was energy minimized by steepest-descent algorithm in vacuum, which was followed by the addition of sulfate ions using the genbox routine for the systems with varying ionic concentration (this step was skipped for the systems with various protonation states). In both cases, the box was solvated with SPC (38) water molecules and neutralized by the addition of sodium or chloride ions (where applicable). Another cycle of energy minimization with the previously mentioned algorithm was performed on the solvated boxes, which were then equilibrated according to the following protocol: the initial velocities were taken from the Maxwell distribution at 100 K and the system was gradually heated to 300 K at constant volume during 100 ps with atom-position restraints decreasing uniformly from 25,000 kJ mol⁻¹ nm⁻² to 5000 kJ mol⁻¹ nm⁻². In the end, the system was equilibrated for an additional 20 ps under the same conditions. Production simulations were run for 100 ns with a 2-fs integration step without any position restraints and coordinates were output every picosecond in the NVT ensemble. During the simulations, the solute and solvent were coupled separately to a heat bath at 300 K using the Berendsen thermostat with a relaxation time τ_T of 0.05 ps (39). Bond lengths were constrained using LINCS (40), whereas van der Waals interactions were treated with a cutoff of 8 Å. Electrostatic interactions were computed using the PME method (41,42) with a direct sum cutoff of 8 Å and Fourier spacing of ∼1.2 Å using fifth-degree B-splines.

Analyses of trajectories

Radii of gyration, solvent accessible surface area (SASA), root mean-square deviations (RMSD), root mean-square fluctuations (RMSF), and displacements of the centers of mass from their initial positions were calculated for each monomer in the unit cell using g_gyrate, g_sas, g_rms, g_rmsf, and g_traj routines implemented in GROMACS (35), respectively. All atoms were used for rototranslational alignment in the context of all-atom RMSD and RMSF calculations. The displacements of the centers of mass were averaged over the last 10 ns of each simulation and compared to the initial positions. Diffusion coefficients of ionic species and water molecules were calculated from a linear fit of mean square displacements over time in three dimensions using Einstein’s diffusion equation:

$$D=\frac{\langle \sum {\left[r_i\left(t+\Delta t\right)\mathrm{-}{r}_i\left(t\right)\right]}^2\rangle }{6\Delta t},$$ (1)

where $r_i\left(t\right)$ is the position of the center of mass of particle i at time t.

The number of favorable interactions was calculated for residues Leu-1, Asp-3, Asp-5, and Arg-14 the following way: ions with charges of the opposite sign were counted if they were in close (<6 Å) and long-lasting (>3.5 ns) contact with the charge groups of these residues in the period between 0.5 and 5.5 ns, which is the time during which crystal rearrangements occur. Distances were calculated with g_dist, whereas their running averages were determined with a time step of 500 ps.

Local pK_a calculations

pK_a values for each titratable residue within the unit cell were calculated using the H++ algorithm (43) involving standard continuum solvent methodology (44) and the Poisson-Boltzmann model (45,46) at three different salt concentrations: 0, 0.8, and 1.6 M using default parameters. For pK_a calculations, norleucines in the unit cell were replaced with leucines due to the program’s lack of parameters for these residues. We do not expect this to have any major effect on the final results.

Results and Discussion

The x-ray model of villin headpiece used in our simulations was resolved at 1.05 Å with a rather low solvent content of 32.27% and a high Matthews coefficient of 1.82 Å³ Da⁻¹. Villin headpiece, a three-helix bundle domain, has frequently been used in MD studies of protein folding as it is one of the fastest-folding proteins known (47–49). However, the principal reason we have used villin headpiece for this study is its relatively high number of titratable groups (10 of 35 amino acids are titratable, including the termini). When this is combined with the molecule’s high compactness, it is reasonable to expect that the stability of the crystal will exhibit strong dependence on the presence and local concentration of salt in the crystal solution. Indeed, for three independent 100-ns simulations of a unit cell containing only water molecules, we observe large rearrangements of proteins in the unit cell already after ∼2.5 ns (Fig. 1). On average, protein centers of mass shift along the x axis by 6 Å, along the y axis by 5 Å, and only 0.3 Å along the z axis. To the best of our knowledge, such large translations of all molecules in the unit cell causing a complete loss of crystal symmetry have not been observed previously in MD simulations. This effect is observed even if crystallographic waters are kept as a part of the initial setup (Fig. S1 in the Supporting Material), although their presence seems to have a stabilizing effect on the x axis shifts if the waters are position-restrained in the same manner as the protein during the equilibration stage. Of importance, however, the major shifts along the y axis are not affected by the presence of position-restrained crystallographic water molecules. In addition, if one compares our results with the ones obtained by Cerutti et al. (20), where a loss of symmetry has also been reported with the average displacements between centers of mass of proteins of 1 Å, one can appreciate how drastic the changes in our system are, with the average center-of-mass displacements of 4.5 Å and a maximum of 8 Å.

Figure 1.

Snapshots taken from the simulation of the unit cell of villin headpiece domain in three different views: (A) yz-plane, (B) xy-plane, and (C) xz-plane. In each panel, the left side shows the starting frame, whereas the right side shows the frame after 100 ns. Select residues are shown in stick representation (Arg - red, Lys - orange, Asp - blue, and Glu - green). To see this figure in color, go online.

Considering the high number of charged residues in the protein, it is possible that the unfavorable interactions that are causing these large rearrangements are at least partly electrostatic in nature and can be screened with the addition of ions. The presence of ions could also affect the stability of individual monomers as suggested by MD simulations of villin headpiece in solution by van der Spoel and Lindahl (49). Furthermore, crystallization solution used in the experiment had a high concentration of ammonium sulfate (1.6 M) present in the reservoir solution, together with 7.5% of triflouroethanol and buffer Bicine (pH 9), all of which played a role in the crystallization process. In our simulations, we have paired sulfate ions with sodium, which was available as part of the GROMOS 45A3 force field, as sodium sulfate is also often used in the crystallization process and contains the same number of ions. Sulfate ions were added before the hydration of the system, whereas sodium ions were added by randomly replacing the equivalent number of water molecules in the system.

It is typically difficult to determine the exact composition of crystal solvent, regardless of its reported components in the crystallization process. With this in mind, we have simulated 12 systems with different salt concentrations to examine their effect on the overall stability of the crystal (Table 1). Analyzing the displacements of centers of mass along the axes for these systems (Fig. 2), one can see that they become smaller along the x and y axes with increasing salt concentration, although their changes along the z axis remain constant throughout at ∼0.8 Å. Plateau values for displacements are reached at 0.8 M salt concentration, corresponding to 50% of the concentration reported for the reservoir solution: at this concentration, the average displacements along the x and the y axis approach the values observed for the z axis. This observation confirms the necessity for a higher ionic content in maintaining a stable system when the proteins involved have a large number of charged residues and are arranged in a compact unit cell. Furthermore, to check whether the initial ion placement in the systems with low salt concentrations can stabilize the crystal, we have performed five additional independent runs of the system with 0.08 M salt concentration in which the ions were randomly placed at different positions (Fig. S2). It can be seen that in certain cases the shifts can be reduced along the x axis, but in none of the cases was this observed for the y-axis shifts, thereby confirming the necessity for higher salt concentrations.

Figure 2.

Dependence of shift per monomer along each of the axes on salt concentration: (A) x axis, (B) y axis, and (C) z axis. Values for each independent run and each monomer are shown in black, whereas the average value for each concentration is shown in gray.

We have also calculated the average force-field potential energies and their components for the first 5 ns (Table S1) and for the whole 100 ns (Table S2) of each simulation, as well as the potential energy profiles for the first 5 ns (Fig. S3). It can be seen that in all cases the total potential energy decreases rapidly in the first few ns and retains these values for the remainder of the simulations with an average decrease of 0.4%. Furthermore, the greatest contribution to the potential energy comes expectedly from electrostatic interactions and the addition of ions reduces the potential energy by 3.1 times when comparing simulations on the opposite ends of the concentration range. In addition, the stabilization of motion can be observed at the level of the diffusion coefficient calculated for water molecules and both ionic species (Fig. S4), which decrease rapidly with increasing salt concentration and reach values that are 200 and 1000 times lower, respectively, than the experimental water self-diffusion coefficient in pure solution (2.3 × 10⁻⁵ cm² s⁻¹) (50). In light of these results, we wanted to make sure that high salt concentration did not considerably constrain the internal dynamics and structural heterogeneity of the protein and have therefore evaluated several commonly used structural measures, such as all-atom RMSD from the starting structure (Fig. 3 A), radius of gyration (Fig. 3 B), and SASA (Fig. 3 C). Values for all of these measures are very similar across different salt concentrations and clearly show that the molecules, regardless of crystal compactness and ionic composition, manage to achieve a satisfactory level of structural heterogeneity (as quantified by the average all-atom RMSD of 2.47 ± 0.48 Å), but still retain their global structure (as captured by the radius of gyration and SASA with average values of 9.47 ± 0.25 Å and 3496 ± 106 Å², respectively). In a few exceptional cases, the last few residues of the α₃-helix unfold or α₁-helix changes its orientation and position with respect to the other two helices. This effect is also the cause for the large values seen in some cases for the distances between centers of mass of phenylalanine residues that form the hydrophobic core (Fig. S5) and their SASAs, as well as the SASA values for the α₁-helix (Fig. S6). On average, however, structural measures remain quite stable across different salt concentrations. On the other hand, there are noticeable differences at the level of RMSF, especially for Arg-14 and the residues in close proximity of the N-terminus (Fig. 4 A). In general, all of these residues show the same behavior—their mobility decreases with the addition of salt. Combined with the observed reduction in the displacements of proteins, this could indicate that the interactions between these residues play an important role in destabilizing the crystal.

Figure 3.

Structural features of villin headpiece as a function of time and salt concentration: (A) all-atom RMSD values from the starting structure, (B) radius of gyration, and (C) SASA. The data sets are represented with boxplots where median is shown as a thicker gray line within the box and the outliers that are outside of 1.5 interquartile range limits from 25% and 75% quartile are shown as black dots.

Figure 4.

(A) RMSF values (shown for 0, 0.8, and 1.6 M concentration and averaged over three independent runs), (B) a cluster of charges formed between two symmetry related villin headpiece domains with charged residues shown in stick representation (Arg - red, Lys - orange, Asp - blue, Glu - green, and Leu-1 - purple) with the minimal distances between the charged groups of the same sign explicitly shown, and (C) dependence of shift per monomer along the x axis and y axis on the number of favorable interactions defined as the number of ions with the charge of the opposite sign in close (<6 Å) and long-lasting (>3.5 ns) contact with residues Leu-1, Asp-3, Asp-5, and Arg-14. To see this figure in color, go online.

If one closely examines the location of the aforementioned residues in the simulated unit cell, it can be seen that a cluster of charges is formed consisting of N-terminal Leu, Asp-3, and Arg-14 (Fig. 4 B). More specifically, these residues are found in a conformation that was previously speculated to provide stabilizing interactions between α₁- and α₂-helices of villin headpiece through hydrogen bonding of the guanidinium group of Arg-14 with the backbone oxygen of Leu-1 and carboxyl oxygen of Asp-3 (51). Despite the assumed favorable interactions, these residues are positioned near their symmetry related equivalents in a distance range of 2.8–3.6 Å, most likely having a destabilizing effect due to the electrostatic repulsion between charges of the same sign. However, the presence of Asp-5 in close proximity to the N-terminus could have a stabilizing effect on it. To analyze this possibility, the number of ions with a charge of the opposite sign that are in close (<6 Å) and long-lasting (>3.5 ns) contact with the previously mentioned residues was counted for the period of 0.5–5.5 ns of each simulation, which is approximately the time during which crystal rearrangements and shifts occur. Subsequently, this number of oppositely charged ions was compared with the average shift per monomer along the x axis and y axis (Fig. 4 C). It can be seen that the shifts along both axes reduce rapidly with an increase in favorable ionic interactions, thereby showing how the presence of ions in the vicinity of these residues diminishes the overall translation of the monomers, and consequently the loss of symmetry.

To provide further proof for this suggestion, unit cells with all possible combinations of protonation states of the selected residues have been simulated without any ions except for those needed for the overall charge neutralization (Table 2). If one analyzes individual displacements of centers of mass along unit cell axes across different systems (Fig. 5), it becomes apparent that neutralization of certain charges can have a stabilizing effect, which is similar to the effect of using high salt concentrations. More specifically, the displacements along the x axis are highly reduced compared to the native structure in most cases if any of the principal three residues (Leu-1, Asp-3, and Arg-14) is neutralized (Fig. 5 A). This is also observed for any combination involving these three residues, whereas their complete neutralization results in the lowest displacements across all systems. On the other hand, neutralization of Asp-5 actually introduces instabilities into almost any combination and, consequently, increases the displacements. This effect can also be noticed in the case of displacements along the y axes (Fig. 5 B) where at least two principal residues or Leu-1/Arg-14 have to be neutralized to reach the low values with little variety across monomers. However, if Asp-5 is included in the neutralization, larger displacements are observed in almost all cases. Similar to the system with varying salt concentration, there is almost no effect on the displacements of molecules along the z axis with a change in protonation states of certain residues (Fig. 5 C). Furthermore, upon visual inspection of the trajectories, it can be observed that the drastic displacements of monomers on x and/or y axes, as depicted in Fig. 1, appear in only 5 out of 16 systems that were simulated: 1), the native one with all the selected residues charged, 2), the one with Asp-5 neutralized, 3), the one with Asp-3 and Asp-5 neutralized, 4), the one with Asp-5 and Arg-14 neutralized (mainly the x axis), and 5), the one with Asp-3 neutralized. Displacements on a smaller scale were observed for the following neutralizations: 1), Asp-3, Asp-5, and Arg-14, and 2), Leu-1 and Asp-5. These systems also display a higher degree of structural diversity in terms of RMSD, radius of gyration, and SASA values (Fig. 6, A–C), than the rest of the systems with neutralized residues, or the systems with varying concentrations of salt (Fig. 3). In addition, some obvious outliers can be observed for these values that stem mostly from the changes in the orientation and displacement of the α₁-helix compared to the other two helices. This can be seen from larger values observed in the same systems for the distances between centers of mass of phenylalanines that form the hydrophobic core (Fig. S7) and their SASAs, as well as the SASA values for the α₁-helix (Fig. S8). Moreover, the diffusion coefficients for water molecules calculated for this data set show little variation across different systems, but they tend to increase with lower structural variety and smaller displacements (Fig. 6 D). Furthermore, their values are comparable to the ones obtained for low salt concentrations, i.e., ∼200 times lower than the experimental water diffusion coefficient in pure solution (50). In addition, we have calculated the average force-field potential energies and their components for the first 5 ns (Table S3) and for the whole 100 ns (Table S4) of each simulation, as well as the energy profiles for the first 5 ns (Fig. S9). It can be seen that in all cases the total potential energy decreases in the first few ns and retains these values for the remainder of the simulations with an average change of 0.16% that in most cases falls within the range of energy fluctuations. Once again, the greatest contribution to the potential energy comes from electrostatic interactions, although it is difficult to discern whether the contribution comes from neutralization of particular residues, addition of counter ions, or their combined effect. By taking all the aforementioned results into account, it can be concluded that simultaneous neutralizations of Leu-1 and Arg-14 give on average the most stable systems. This is corroborated further by calculating the average RMSF values for systems that include these two neutralizations and comparing it to the average RMSF values of the remaining systems (Fig. S10). The obtained RMSF profiles indicate a reduction of mobility for the neutralized Leu-1 and Arg-14, as well as Phe-6 and Phe-10, which are implicated in the already described changes involving α₁-helix. Furthermore, they display very similar characteristics to the profiles obtained for high salt concentrations (Fig. 4 A). Therefore, it is clear how a similar degree of crystal stabilization can be obtained by neutralizing a few select charges or by increasing the ionic content of the crystal.

Figure 5.

Dependence of shift per monomer along each of the axes on the protonation state of the chosen residues: (A) x axis, (B) y axis, and (C) z axis. The names of residues that have been neutralized in each system are also shown. Values for each independent run and each monomer are shown in black, whereas the average value for each state is shown in gray.

Figure 6.

Structural features of villin headpiece as a function of time for the system with varying protonation states of residues Leu-1, Asp-3, Asp-5, and Arg-14: (A) all-atom RMSD from the starting structure, (B) radius of gyration, (C) SASA, and (D) diffusion coefficient of water. The data sets are represented with boxplots where median is shown as a thicker gray line within the box and the outliers that are outside of 1.5 times the interquartile range limits from 25% and 75% quartile are shown as black dots.

Is it possible that local neutralization of charges actually occurs in the real crystal of villin headpiece? Considering that the experimental structure was solved at pH 9, we can conclude from the experimental pK_a values of individual residues (52,53) that Glu (pK_a = 4.2), Asp (pK_a = 3.5), and His (pK_a = 6.6) are most likely deprotonated, whereas Arg (pK_a = 12.48) is protonated. However, the N-terminus and lysine have experimental pK_a values of 7.7 and 10.5, respectively, which does not allow one to immediately detect their protonation state at pH = 9, especially if one takes into the account how susceptible these values are to the local environment (54,55). Therefore, we have calculated the charges (Fig. 7 A) and local pK_a values for all titratable side chains in our unit cell for three different salt concentrations by using H++ algorithm (43). The obtained pK_a values and titration curves suggest, in addition to the aforementioned protonation states of Arg, Glu, Asp, and His, that all lysine molecules are protonated, whereas the N-termini are not (Fig. 7, B and C). These results vary with changing salt concentration, but the charge of the unit cell at pH 9 stays at −8 for 0.8 and 1.6 M salt concentrations, although it changes slightly to −7.88 for 0 M concentration due to two N-termini a small fraction of which is charged at pH 9 (0.05 and 0.07). Although deprotonation of N-termini alone was sufficient to generate a crystal with displacements comparable to the ones in simulations with higher salt concentration, it did not produce the system with the least displaced monomers among the systems with neutralized residues. Therefore, these findings indicate that the stability of the crystal used in the experiment was most likely maintained through the interplay between deprotonated N-termini and the screening of charges with high salt concentrations. Additionally, this study emphasizes the importance of charged groups in affecting the stability of protein crystals, especially in compact systems with a relatively high number of charged residues. Furthermore, it cautions one to take great care while setting up MD simulations by carefully considering protonation states of all titratable residues to obtain a stable system. It is our hope that with further improvements in force-field parameters of precipitants and the inclusion of polarizability, extensive MD studies of large protein crystals could allow one to study in detail intermolecular interactions that control protein crystallization and phase behavior, similarly to the field of small-molecule crystallography (56). This would then allow one to obtain valuable information about the crystallization process, which could be used to quickly determine optimal crystallization conditions and simplify crystallization protocols.

Figure 7.

(A) Charge of the unit cell calculated as a function of pH calculated for three different salt concentrations (0, 0.8, and 1.6 M), together with titration curves for the N-terminus (B) and for lysine side chains (C). Average values for eight monomers at the same salt concentrations together with standard deviations.