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Protein Eng Des Sel. 2010 January; 23(1): 27–33.
Published online 2009 November 16. doi:  10.1093/protein/gzp069
PMCID: PMC2791050

The relationship between water bridges and the polyproline II conformation: a large-scale analysis of molecular dynamics simulations and crystal structures

Abstract

It has been suggested that denatured proteins are predisposed toward the left-handed polyproline II (PII) conformation. One possible source of PII stability in the denatured state is water bridges. Water bridges are networks of water molecules that link nearby hydrogen bond acceptors and/or donors on proteins. On the basis of the proposed behavior of PII and water bridges, the propensity of a residue to participate in water bridges should be correlated with its PII propensity. To test this hypothesis, we analyzed the following data sets: 2351 high-resolution crystal structures, and the native and denatured states of 188 different proteins from all-atom, explicit-solvent molecular dynamics (MD) simulations, which are part of our Dynameomics effort. We found that water bridges do not explain the high frequency of PII in denatured states; such bridges are less frequent around PII than around other conformations. Thus, this analysis casts doubt on water bridges as a dominant factor determining the residue-based PII propensities.

Keywords: coil library, denatured state, molecular dynamics, polyproline II, water bridges

Introduction

The denatured state is an ensemble of interconverting conformations that retain some residual structure (Bond et al., 1997; Kazmirski and Daggett, 1998; Wong et al., 2000; Kazmirski et al., 2001). This collection of structures is important because it guides the early stages of protein folding. Another motivation for studying these structures is that many regions resembling the denatured state are found in folded proteins. For example, one-third of eukaryotic proteins contain a stretch of at least 30 disordered residues (Mittag and Forman-Kay, 2007).

Ever since the presence of the PII conformation was discovered in disordered peptides (Tiffany and Krimm, 1968; Krimm and Tiffany, 1974), there has been a lively debate regarding its prevalence and role in denatured proteins (Shi et al., 2002a, b, 2006; Rath et al., 2005). Specifically, it has been asserted that left-handed polyproline II (PII) is an important contributor to denatured state structure (Shi et al., 2006). The ideal dihedral angles for this PII conformation are ([var phi], ψ) = (−79°, 149°). If consecutive residues are in PII, a left-handed PII helix is formed (Fig. 1). This helix has three residues per turn, and backbone amide hydrogen atoms and carbonyl oxygen atoms are partially exposed to solvent.

Fig. 1
A six-residue left-handed PII helix. (A) Side view of a PII helix. This picture illustrates that this structure is extended. (B) Top view of a PII helix. This depiction emphasizes that this helix completes one turn every three residues. Both illustrations ...

Kallenbach and co-workers have proposed that the frequency of residues having PII [var phi]/ψ angles is 50% in acid- and cold-denatured proteins (Shi et al., 2002b), the majority of the time in the XAO peptide (Shi et al., 2002a), and 50–80% in GGXGG peptides (Shi et al., 2005). Circular dichroism, nuclear magnetic resonance (NMR) and 2D infrared spectroscopy experiments have been cited as evidence for this proposal (Shi et al., 2002a; Schweitzer-Stenner et al., 2004; Schweitzer-Stenner and Measey, 2007). However, many groups, while stating that denatured states contain some PII, argue that these frequencies are too high (Zagrovic et al., 2005; Makowska et al., 2006, 2007). For example, in exhaustive molecular dynamics (MD) simulations of GGXGG peptides, the PII population over all 20 naturally occurring amino acids ranges from 10% to 25% (Beck et al., 2008a).

Many groups have proposed possible reasons for why PII would be so stable (Sreerama and Woody, 1999; Pappu and Rose, 2002; Drozdov et al., 2004; Garcia, 2004; Mezei et al., 2004; Fleming et al., 2005). One proposal was that water bridges promote PII (Sreerama and Woody, 1999). Many studies have been performed on water bridges, some of which have probed the relationship between this interaction and PII. These water bridge studies have explored native states (Bella et al., 1994, 1995; Robert and Ho, 1995; Beck et al., 2003), denatured states (Petukhov et al., 1999; Kazmirski et al., 2001; Beck et al., 2003) and states along the unfolding pathway of proteins and peptides (Sundaralingam and Sekharudu, 1989; Daggett and Levitt, 1992; Dougan et al., 2008; Ravikumar and Hwang, 2008). Though water bridges are important in some contexts, it is unclear whether they promote PII. In MD simulations of octa-Ala, Woody's group found that water bridges stabilize PII more than β (Sreerama and Woody, 1999). Other groups disagree (Drozdov et al., 2004; Mezei et al., 2004). In Monte Carlo simulations of di-Ala peptides, one- and two-molecule water bridges surround β residues more often than residues in PII (see Fig. 4 in Drozdov et al., 2004).

To test the water bridge hypothesis, we analyzed water bridge frequencies of loop regions in three data sets. The first two data sets are based on the Dynameomics project (Beck et al., 2008b; Kehl et al., 2008; Simms et al., 2008), an attempt to simulate a member of every globular protein fold family (Day et al., 2003). In this project, our lab has performed native state (298 K) and unfolding (498 K) MD simulations of targets from 188-fold families (Beck et al., 2008b). These targets account for 67% of all known protein structures. In addition, we have developed tools for mining these trajectories (Kehl et al., 2008; Simms et al., 2008). The two data sets from this effort include the native state simulations and portions of the unfolding simulations that represent the denatured state. The third is a collection of 2351 high-resolution crystal structures. We explored loops in crystal structures and native MD simulations because these regions are often considered to be a model for the denatured state (Serrano, 1995; Swindells et al., 1995; Smith et al., 1996; Fitzkee et al., 2005; Jha et al., 2005). We were able to benchmark the native state simulations against X-ray crystallography structures by comparing the properties of their respective loops. The denatured structures from unfolding simulations were investigated to better model the denatured state and to ascertain how well water bridge properties of loop regions in the native state match the conformational properties of denatured proteins.

Materials and methods

A water bridge is a type of water network. This network must form hydrogen bonds to two different atoms on the protein, and the water molecules must be connected by a series of hydrogen bonds. For this study, water bridges needed to contain one or two water molecules. In addition, if two different water bridges connected the same pair of backbone atoms, then only the shortest of these bridges was counted. Also, only backbone atoms could anchor the water bridge, and these atoms needed to be ≤2 residues apart. Furthermore, the secondary structure of protein atoms in the bridge was required to be neither α-helix (H) nor β-sheet (E), as assessed by the Define Secondary Structure of Proteins (DSSP) program (Kabsch and Sander, 1983) (i.e. this is our definition of a loop). Individual residues in the αR, αL or β conformations could be involved in bridges as long they were not part of an α-helix or β-sheet. The criteria for hydrogen bonds were the following. The distance between the donor hydrogen and the acceptor heavy atom was ≤2.6 Å, and the angle defined by the donor heavy atom, the donor hydrogen (vertex) and the acceptor heavy atom was ≥145°.

Water bridges were labeled as s_ab, where s is the residue separation between the two protein atoms in the bridge; a the N-terminal protein atom and b the C-terminal protein atom. Eight types of water bridges satisfied s ≤ 2: 0_HO, 1_HH, 1_OH, 1_OO, 2_HH, 2_HO, 2_OH and 2_OO. For example, in a 2_OH water bridge, the backbone carbonyl oxygen of the ith residue and the backbone amide hydrogen of the i + 2th residue were involved in the bridge.

Water bridges were calculated for crystal structures, native state MD simulations and thermal unfolding MD simulations. First, a library of 298 K MD simulations of 188 structurally diverse proteins was used (Beck et al., 2008b). In cases where experimental data were available, these simulations have been validated against NMR order parameters, Nuclear Overhauser Effect cross-peaks and chemical shifts (Beck et al., 2008b). The simulations were run for at least 21 ns, and structures from 1 to 21 ns were analyzed at 100 ps granularity. The calculations in Table I and Fig. 3 were repeated at 1 ps granularity, which confirmed that the values calculated at 100 ps granularity were not systematically different from the 1 ps granularity values (data not shown). Next, a library of 498 K simulations was used. These simulations were run for at least 31 ns, and structures from the last 10 ns were analyzed at 100 ps granularity. All of these trajectories were generated by the molecular mechanics package in lucem molecular mechanics (ilmm) (Beck et al., 2000–2009), and the force field has been described previously (Levitt et al., 1995, 1997; Beck and Daggett, 2004). More specifically, a flexible three-center (F3C) water model was used (Levitt et al., 1997). This water model has been validated against many experiments (Levitt et al., 1997; Beck et al., 2003). To collect statistics, we wrote structured query language (SQL) programs to query our Dynameomics database (Simms et al., 2008). In addition, 2351 crystal structures from the Protein Data Bank (PDB) (Berman et al., 2000) were compiled using PISCES (Thanki et al., 1988). For these structures, the resolution was ≤1.7 Å, and the R factor was ≤0.26; both values are consistent with previous surveys of water–protein interactions in the PDB (Thanki et al., 1988; Park and Saven, 2005). For all pairs of proteins in this list, the sequence identity was ≤30%, and every protein was larger than 40 residues. In addition, hydrogen atoms not already present on the protein and/or on water molecules were added using a built-in function in Chimera (Pettersen et al., 2004). Hydrogen coordinates already present in the structure were preserved.

Table I
Summary statistics for the analysis of native MD simulations (native MD), denatured states from MD simulations (denat MD) and crystal structures (XTAL)a

For this study, the [var phi]/ψ conformations were defined as follows: PII: −110° ≤ [var phi] ≤ − 50°; 120° ≤ ψ ≤ 180°; αR: −100° ≤ [var phi] ≤ − 30°; −80° ≤ ψ ≤ − 5°; β: −170° ≤ [var phi] ≤ − 110°; 80° ≤ ψ ≤ 180°, and −170° ≤ [var phi] ≤ − 110°; −180° ≤ ψ ≤ − 170°; αL: 5° ≤ [var phi] ≤ 75°; 25° ≤ ψ ≤ 120°. These definitions are similar to those in our previous MD study of unfolded peptides (Beck et al., 2008a). They were modified slightly in order to be compatible with surveys of loops in crystal structures (Swindells et al., 1995; Jha et al., 2005), which use different boundaries than those for unstructured peptides. For instance, unlike in our previous definition, β does not overlap with PII in this study or in previous crystal structure surveys.

Results

We focused on a subset of water bridges fulfilling these criteria: (i) only backbone protein atoms were involved in the bridge; (ii) the protein atoms in the bridge were ≤2 residues apart; (iii) the bridge contained one or two waters; and (iv) the protein atoms were in loops. Bridges between backbone atoms were analyzed because non-polar residues such as Ala have relatively high PII propensities (Kelly et al., 2001; Beck et al., 2008a). Therefore, if water bridges did promote PII, then water bridges between polar backbone atoms would likely be responsible. The maximum sequence separation between protein atoms in the bridge was two because such local bridges constrain only one or two backbone dihedral angles. Thus, they are the bridges most likely to influence conformational preferences. The bridges contained only one or two waters because such bridges account for over 75% of the bridges in high-resolution crystal structures (Supplementary Figure 1 available at PEDS online). Crystal structures include only a subset of possible water bridges; therefore, bridges with the properties most often seen in crystal structures are expected to be among the most stable. Consequently, bridges with these properties are expected to influence the conformation of the protein backbone. Finally, we only considered protein atoms in loops because loops of folded proteins are often treated as models for the denatured state (Serrano, 1995; Swindells et al., 1995; Smith et al., 1996; Fitzkee et al., 2005; Jha et al., 2005). In simulated denatured states, only loops were considered in order to be consistent with analyses from the other data sets.

Water bridges were analyzed in crystal structures and in native and unfolding simulations. The starting structures for the native MD simulations included 10 395 loop residues (Table I). The simulations were sampled at 100 ps granularity, for a total of 37 599 structures. Over 400 000 water bridges were found; thus, the ratio of loop residues to water bridges was 0.170 ± 0.010. In the 2351 crystal structures, there were 208 253 loop residues and 4393 water bridges. Only 2.1 ± 0.1% of loop residues were affected by a water bridge. The frequency of water bridges was an order of magnitude less in crystal structures than in solvated native MD simulations. In the denatured state, 11.5 ± 0.1% of loop residues were surrounded by a water bridge. The denatured state is defined as the last 10 ns of high temperature (498 K) unfolding trajectories lasting 31 ns. In 498 K simulations, structures after 21 ns tend to lose secondary and tertiary structure, they become expanded and highly dynamic, and in general they become very disrupted. In these denatured, disrupted structures, 77.8 ± 0.7% of the residues are in loops. For comparison, 49.2 ± 1.0% of the residues are in loops in the corresponding native states.

In both MD simulations and crystal structures, water strongly influenced the conformation of the backbone. As an illustration, we chose four bridges, labeled as 0_HO, 1_HH, 1_OO and 2_OH (Fig. 2). These bridge types are expressed as s_ab, where s is the residue separation between the two protein atoms in the bridge, a the N-terminal protein atom and b the C-terminal protein atom. For example, in a 2_OH water bridge, the backbone carbonyl oxygen of the ith residue and the backbone amide hydrogen of the i +2th residue were involved in the bridge. These four bridges were chosen because they influence the [var phi] and ψ dihedral angles for a single residue only. For instance, in the 0_HO bridge, waters formed hydrogen bonds to the amide hydrogen and carbonyl oxygen within the same residue. In native MD and crystal structures, this bridge favored PII and β (Fig. 2). The bridge 1_HH promoted mainly αR but also αL, in both data sets. For both the native MD and crystal structures, the 1_OO bridge constrained the protein backbone to a lesser extent than the others mentioned above. In native MD, it allowed all conformations but β. In crystal structures, i permitted every conformation but β and αL with the γL conformation [where ([var phi], ψ)~(90°, 0°)] permitted instead of αL. For the 2_OH bridge, both native MD and crystal structures sampled PII and β. To ensure that these distributions in the native state were similar to those for unfolded proteins, equivalent plots were made for the simulated denatured state. The distributions are similar, suggesting that the native state loops are a good model for the denatured state in this case.

Fig. 2
The influence of water bridges on the backbone conformation of nearby residues. The notation for water bridges is s_ab, where s is the residue separation between the two protein atoms in the bridge, and a and b are the N- and C- terminal protein atoms, ...

Next, we tested whether the distribution of water bridges was similar in native MD and crystal structures. There was moderate agreement between the simulated and the crystallographic frequencies (Fig. 3). The 1_HH bridge was the most populated HH bridge in both native MD and crystal structures; this bridge comprised 47.1 ± 0.5% and 18.1 ± 1.9% of the local water bridges in native MD and crystal structures, respectively. The 1_OO bridge was slightly more populated in native MD than in crystal structures. In contrast, the most prominent HO and OH bridges were more frequent in crystal structures versus in the simulated native state. The water bridge frequencies for the denatured state were similar to those in the simulated native state.

Fig. 3
Comparison of relative water bridge frequencies in crystal structures (XTAL), native MD and denat MD. The percentage is relative to the counts of all possible water bridges. Thus, the sum of all the percentages shown for crystal structures and MD was ...

The distribution of water bridges and the effect of water bridges on the [var phi]/ψ conformations were similar for native MD and crystal structures. Furthermore, whenever possible, proteins in the library of 298 K simulations have been validated against experiments (Beck et al., 2008b). Also, the force field has been benchmarked for many proteins outside the scope of the Dynameomics project. To augment validation already done, we assessed the ability of the force field to preserve the conformational distribution of loop residues in native state simulations. Thus, for the library of proteins, the conformational frequencies of loop regions at the start of the simulation were compared with the average values over the entire length of the simulation (Table II). The average conformational frequencies in MD were similar to those in the starting structure, which indicates that the simulation did not bias the conformations away from the X-ray or NMR structures. The frequencies of αR and PII at the start of the simulation were not statistically different from their average values. The average frequencies of αL and β in simulation were in reasonable agreement with those at the start of the simulation. The average β frequency was slightly decreased relative to that at the start of the simulation. Overall, the simulations did not significantly perturb the conformational frequencies in the loops.

Table II
The frequencies of β, PII, αR and αL in unfolded regionsa

Next we investigated to what extent water bridges influence the conformations in loops. More specifically, if water bridges were responsible for the predominance of PII in loops, then water bridges would surround PII residues more than other conformations. Of course, water would solvate all conformations, forming hydrogen bonds to backbone donors/acceptors. However, three pairs of nearby polar backbone atoms are arranged closely in space for PII, while two pairs are present for the other conformations (Figs 1 and and2).2). Therefore, more of these first shell waters should connect neighboring polar backbone atoms in PII as opposed to other conformations. In contrast to the expectation, water bridges surrounded residues in PII only 12.1 ± 1.2% and 2.0 ± 0.1% of the time in loops for native MD and crystal structures, respectively (Table III). Out of the four major conformations (αR, αL, PII and β), the frequency of water bridges around PII was lowest in native MD and tied for third lowest in crystal structures. In denatured MD, this frequency was third lowest of the major conformations. These rankings took into account the standard deviations. Water bridges surrounded other conformations more often than PII. As water bridges were not frequent around PII, they do not appear to be a major source of stability for this conformation.

Table III
Percent of water bridges (fwb) around the β, PII, αR and αL conformationsa

Up to this point, we have only tested whether water bridge frequencies were related to the conformational frequencies. We asked whether the highest frequency conformation in loops, PII, also had the highest water bridge frequency. Here, we ask whether water bridges influenced the PII propensities of the different residues. If water bridges are the dominant factor promoting PII, then residues with the largest PII frequencies should also have the highest water bridge frequencies when in PII. We focused on the 0_HO, 1_OO, and 2_OH bridges because these bridges surrounded residues in PII (Fig. 2). Contrary to expectations, the frequencies of PII were not correlated with those for water bridges (Supplementary Figure 2 available at PEDS online). The correlation coefficient (R) was −0.09 in crystal structures, −0.21 in native MD and −0.47 for denatured MD. This analysis was repeated for αR, αL and β, and no correlations were found (Supplementary Figure 2 available at PEDS online). Therefore, water bridges do not explain the residue-based propensities for PII.

Discussion

PII is considered an important component of protein denatured states, and water bridges have been hypothesized to be responsible for the high frequency of PII (Sreerama and Woody, 1999). Recent studies have addressed this water bridge hypothesis using Monte Carlo calculations, MD and analyses of crystal structures; however, no consensus on the role of water bridges has emerged (Robert and Ho, 1995; Sreerama and Woody, 1999; Poon et al., 2000). In this work, we aimed to resolve this issue by using new and larger data sets. This study was the first analysis of water bridges in a library of native and unfolding MD simulations. Furthermore, in this work, the database of crystal structures was an order of magnitude larger than a similar earlier analysis (Robert and Ho, 1995). In previous studies, only one data set was used at a time. Here, we used three data sets: native MD, denatured MD and crystal structures. All possible water bridges are present in native MD, while, presumably, only waters in the most favored bridges are found in crystal structures. Last, unlike in some of the other water bridge studies (Sreerama and Woody, 1999; Mezei et al., 2004), water bridges that surround αR were also included in this analysis.

The validation of water bridge frequencies and conformational distributions in loop regions in native MD simulations is not straightforward. First, crystal structures contain only a subset of the most stable waters, while all waters are observed in simulation. This is a potential problem because the most stable water bridges may have different properties than the set of all water bridges. Second, crystal structures do not typically have hydrogens, a critical component of hydrogen bonds. Therefore, we have added hydrogen bonds to the structures, and we have confidence that the results were not sensitive to the placement of these hydrogen atoms, for the following reason. The crystallographic frequencies of different types of water bridges were similar when the definition of hydrogen bonding was changed from including hydrogen atoms to using a cutoff distance between two heavy atoms (Supplementary Figure 3 available at PEDS online). A third complication is that crystal structures are often solved at low temperatures, while the native state simulations were performed at 298 K, such that the differences in entropy may alter the conformational distributions.

Even given these caveats, we expected moderate agreement between 298 K simulations and crystal structures. Indeed, our force field (Levitt et al., 1995, 1997) has been validated against experiment for unstructured peptides (Beck et al., 2008a). Also, the water model has been benchmarked against a number of experimental parameters, including the oxygen–oxygen radial distribution function and the diffusion constant (Levitt et al., 1997; Beck et al., 2003). In this work, we found that the distributions of conformations seen in the presence of different water bridges were similar in MD (native and denatured) and crystal structures (Fig. 2). In loops, the frequencies of the four major conformations in native simulations also agreed with those in crystal structures. There were a few differences between 298 K simulations and crystal structures, however. For example, the 1_HH and 1_OO bridges occurred more often in the native MD simulations than in crystal structures. Also, bridges often surrounded αR residues in native MD; however, the opposite was true in crystal structures. One possible explanation for this is that the least stable water bridges (seen only in native MD) strongly favor αR, while the most stable water bridges (seen in both crystal structures and native MD) favor β. Overall, the validations of the native simulations listed here augment those already conducted (Beck et al., 2008b).

This study systematically analyzed how four different water bridges constrained loop conformations. For both native MD and crystal structures, if the bridge involved at least one amide hydrogen, then the backbone dihedral angles were restricted to two or fewer major conformations. In contrast, 1_OO, the one bridge without any amide hydrogen atoms, allowed three major conformations in native MD and two plus γL in crystal structures. This bridge was less restrictive because carbonyl oxygen atoms have two lone pairs of electrons.

This work suggests that water bridges are not responsible for the high frequency of PII. The frequency of water bridge formation around residues in PII was lower than the corresponding frequencies for other conformations (Table III). Second, water bridges did not tend to surround the residues with the highest PII propensities (Supplementary Figure 2 available at PEDS online). This conclusion is the same as that obtained from simulations by Mezei et al. (2004) and calculations by Pappu and co-workers (Drozdov et al., 2004). In contrast, based on previous analyses of crystal structures (Bella et al., 1995) and simulations (Sreerama and Woody, 1999), others have argued that water bridges do in fact promote PII. There are possible reasons for the different conclusions between this study and the ones in favor of the water bridge hypothesis. The studies by Bella et al. (1995) on collagen looked specifically at PII; they did not compare water bridge frequencies around PII with those around other conformations. In our native and denatured MD simulations, the water bridge frequencies around αR were significantly higher than those around β and PII (Table III). We note that Holmgren et al. (1998) have also challenged the idea that water bridges contribute to collagen stability (and therefore PII).

In addition, here we explored whether water bridges could account for the residue-based PII propensities in the unfolded state. Such denatured state propensities, or intrinsic propensities, have been the subject of a number of recent investigations (Kentsis et al., 2005; Shi et al., 2005; Beck et al., 2008a; Firestine et al., 2008). In this work, we were not able to rationalize the intrinsic PII propensities based on water bridges.

Funding

Financial support was provided by the NIH (GM50789 to V.D.) and the Human Frontiers of Science Program (to V.D., PI Lynne Regan). These simulations are part of our Dynameomics effort (www.dynameomics.org), which is supported by the External Research Program of Microsoft Research (www.microsoft.com/science) and computer time through the DOE Office of Biological Research as provided by the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the US Department of Energy under contract no. DE-AC02-05CH11231.

Supplementary Material

[Supplementary data]

Acknowledgements

We thank Rudesh Toofanny for technical assistance and Drs Amanda Jonsson, David Beck, Niels Andersen and Gabriele Varani for helpful discussions.

Footnotes

Edited by Lynne Regan

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