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When proteins are completely hydrated in crystals
International Journal of Biological Macromolecules 89 (2016) 137–143
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When proteins are completely hydrated in crystals Oliviero Carugo ∗ Department of Chemistry, University of Pavia, Pavia, Italy and Department of Structural and Computational Biology, Vienna University, Vienna, Austria
a r t i c l e
i n f o
Article history: Received 22 January 2016 Received in revised form 15 March 2016 Accepted 21 April 2016 Available online 22 April 2016 Keywords: Crsytallographic resolution Crystallography Hydration Protein data bank Protein structure Solvent Water
a b s t r a c t In the crystalline state, protein surface patches that do not form crystal packing contacts are exposed to the solvent and one or more layers of hydration water molecules can be observed. It is well known that these water molecules cannot be observed at very low resolution, when the scarcity of experimental information precludes the observation of several parts of the protein molecule, like for example sidechains at the protein surface. On the contrary, more details are observable at high resolution. Here it is shown that it is necessary to reach a resolution of about 1.5–1.6 Å to observe a continuous hydration layer at the protein surface. This contrasts previous estimations, which were more tolerant and according to which a resolution of 2.5 Å was sufficient to describe at the atomic level the structure of the hydration layer. These results should prove useful in guiding a more rigorous selection of structural data to study protein hydration and in interpreting new crystal structures. © 2016 Elsevier B.V. All rights reserved.
1. Introduction In physiological conditions, globular proteins are surrounded by water molecules and cannot perform their chemical and biological roles in the absence of at least one hydration layer [29]. Consequently, protein hydration has been extensively studied with both experimental and computational methods [1]. Most of the information on hydration structure has been obtained with crystallographic studies. Several statistical analyses have been published, based on room temperature crystal structures [30–32,22,34,14,19]. More recently, structural analyses are routinely performed at low temperature (typically 100 K), to minimize radiation damage due to bright synchrotron sources [18,17,7]. New statistical surveys of the structures determined with cryocrystallography have also been published. It arose that more water molecules are detectable at low temperature, though previous observations at room temperature have been generally confirmed [25,27,28,23]. Interestingly, the growth of water molecule numbers at low temperature was not detected in a previous analysis, where few low temperature crystal structures (only 33 compared to 873 room temperature structures) were compared though linear multiple regression [6].
∗ Correspondence to: Department of Structural and Computational Biology, Vienna University, Campus Vienna Biocenter 5, 1030 Vienna, Austria. E-mail address: [email protected] http://dx.doi.org/10.1016/j.ijbiomac.2016.04.061 0141-8130/© 2016 Elsevier B.V. All rights reserved.
The effects of lowering the temperature of protein crystals on the structures have been examined extensively [16,15,33,21,35]. It emerged that low temperature structures are systematically different from room temperature structures, though many differences are relatively minor. At low temperature, the crystal volume diminishes slightly, inter-atomic contacts between symmetry related molecules are more numerous, and the conformational disorder of some side chains is different. More water molecules are detected in low temperature crystal structures, especially in the second hydration sphere [13]. However, cryo-crystallography became a routine technique and nearly all new protein crystal structures deposited in the Protein Data Bank [2,3] are determined at temperature close to 100 K. Therefore, given that the positions of the hydration water molecules do not change by lowering the temperature, [24] and although these data might provide a partially biased view of protein flexibility, it is obviously necessary to mine this enormous amount of experimental information in order to detect interesting structural trends. Several issues must be addressed in data mining the Protein Data Bank [11]. It is mandatory to define the criteria for the selection of the protein crystal structures. The latter ones must be reasonably well hydrated if one is looking for realistic statistical trends. For example, it is probable better to exclude structures refined at very low crystallographic resolution, where few water molecules are detectable in the electron density maps. Crystallographic resolution is by far the most used quality indicator in statistical surveys of protein structures. For example, only
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crystal structures refined at resolution better than 1.5 Å have been considered in a detailed analysis of water molecules buried in the protein core [5]. A threshold of 2.0 Å was used in the analysis of buried chlorides [4]. Other threshold values have been used too and the selection of the threshold is a compromise between the need of accuracy, which improves with smaller and more stringent values, and the need of large datasets, which enlarge with higher and less severe threshold values. It must be admitted, however, that threshold values are often quite arbitrary. When dealing with the analysis of protein hydration, it is necessary to identify the most correct value of resolution, in order to include (nearly) only crystal structures of proteins that have well hydrated surfaces and to exclude proteins that have an incomplete hydration layer. This problem is addressed in the present communication by computing several figures of merit, which monitor the hydration degree, at various resolution levels. 2. Methods All protein crystal structures were downloaded from the Protein Data Bank [2,3] according to the following criteria: (i) entries with nucleic acids were discarded, (ii) only crystal structures determined at low temperature (80–120 K) were considered; (ii) only monomers with one molecule per asymmetric unit were retained. I imposed the restriction on the data collection temperature since the hydration degree may depend on temperature [13]. I analyzed only monomers, since the reduction of sequence redundancy is obviously simpler and more effective, if oligomeric assemblies are discarded. Sequence redundancy was limited to pairwise 30% sequence identity. I removed incomplete structures, lacking atoms and residues or with zero occupancy atoms, since these residues and atoms are very often at the surface of the protein and are therefore crucial for the detection of hydration water molecules. For similar reasons, I discarded structures where protein atoms had B-factors larger than 70 Å or larger than five times the average B-factor of the protein atoms. These thresholds on the B-factors are necessary, since the hydration of structures with large flexible moieties is unreliable. In particular, an atom with a B-factor of 70 Å2 has a mean displacement amplitude from its average position larger than 0.94 Å, which is closer to the shortest covalent bond distance (C H). I also rejected proteins shorter than 50 amino acids. Structures were classified into 22 groups according to their resolution. The first group included only structures refined at a resolution equal to or better than 1.0 Å The last group was formed only by structures refined at a resolution lower than 3.0 Å. The other groups comprised structures in 0.1 large resolution ranges ranging from 1.0 to 3.0 Å. The largest group, 129 structures, was in the 1.70–1.80 Å resolution range. The smallest group, 3 structures, included structures refined at a resolution lower than 3.0 Å. The average dimension of the groups was 51 (standard error = 9). Residues involved in crystal packing contacts were identified with the program CPC [10] and solvent accessible surface areas were computed with NACCESS [20]. A protein atom located at the protein surface and not involved in crystal packing contacts was considered to be close to a hydration water molecule if their interatomic distance was minor than 4.5 Å. A residue was considered to be hydrated if at least one of its atoms was close to at least one water molecule. I computed the propensities of the solvent accessible residues to be close to water molecules according to the following equation: propensity =
nr,w ⁄nw nr ⁄n
(1)
where nr,w is the number of residues of type “r” that are close to water molecules, nw is the total number of residues that are close
Fig. 1. Relationship between resolution and percentage of residues that are solvent accessible and close to a water molecule. Vertical bars indicate estimated standard errors.
to water molecules, nr is the total number of residues of type “r”, and n is the total number of residues. Consequently, an amino acid with a propensity values larger than 1 tend to be close to a water molecules, while an amino acid with a propensity lower than 1 does not tend to be close to a water molecule. 3. Results First, it is mandatory to identify which are the residues that are really exposed to the solvent in the crystal structure. Some of the residues that are at the protein surface are not exposed to the solvent, since they are at the interface between two proteins related by a symmetry operation. In other words, they are buried in crystal packing contacts. I used the program CPC, which has been used in other studies [8,9,36], to identify residues that are at the surface of the proteins and that are buried in crystal packing contacts and that are, therefore, not accessible to the solvent. I considered accessible to the solvent all the other residues that are at the surface of the protein and are not involved in crystal packing interactions. Then, I computed for each protein crystal structure the percentage of amino acids that are really solvent accessible and close to a water molecule. The average percentages for all residues are shown in Table 1 and plotted in Fig. 1, for various resolution ranges. Fig. 2 shows the average percentages for each amino acid type. Table 1 and Fig. 1 show that at very high resolution, most of the residues are close to water molecules. If resolution decreases, the percentage of residues close to water molecules is nearly constant, slightly above 90%, until resolution of 1.5–1.6 Å. Then it decreases slowly up to 2.3–2.4 Å resolution and it fall steeply at lower resolution. The points of Fig. 1 can be fitted very well (Pearson correlation coefficient = 0.996) by a sigmoid function: y = −281.0 +
90.4 + 281.0 1+
x 7.15 3.6
.
(2)
This indicates that the maximum percentage of amino acids that are really solvent accessible and are close to a water molecule is equal to 90.4 and that this percentage decreases very little when resolution diminishes to 1.5 Å (89.7). The same percentage diminishes considerably when resolution decreases to 2.4 Å (71.1), falls steeply at worse resolution and reaches a value of 0 at resolution larger than 3 Å. It must be observed that this function cannot be used to predict the percentage of amino acids that are really solvent accessible and are close to a water molecule outside the resolution
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Fig. 2. Relationship between resolution and percentage of residues that are solvent accessible and close to a water molecule for all the 20 amino acid types. Vertical bars indicate estimated standard errors. Table 1 Dependence on resolution of the percentage of residues that are solvent accessible, not involved in crystal packing contacts and close to water molecules (standard errors in parentheses). Resolution (Å)
%
< 1.0 1.0–1.1 1.1–1.2 1.2–1.3 1.3–1.4 1.4–1.5 1.5–1.6 1.6–1.7 1.7–1.8 1.8–1.9 1.9–2.0 2.0–2.1 2.1–2.2 2.2–2.3 2.3–2.4 2.4–2.5 2.5–2.6 2.6–2.7 2.7–2.8 2.8–2.9 2.9–3.0 >3.0
91.2 (2.1) 89.3 (3.1) 92.0 (0.8) 92.4 (1.0) 91.2 (0.9) 90.3 (0.7) 90.4 (0.6) 88.9 (0.6) 87.6 (0.7) 86.7 (0.7) 84.3 (0.8) 83.0 (1.0) 80.7 (2.0) 78.3 (1.8) 78.9 (2.0) 73.8 (5.8) 66.0 (5.5) 54.3 (14.3) 45.1 (12.3) 33.2 (8.7) 23.9 (6.2) 12.3 (5.1)
range that is examined here. It is therefore impossible to predict the percentage at resolution increasing much more than 1 Å. Each of the 20 types of amino acids shows a closely similar trend (Fig. 2). In general, at very low resolution, the percentage of residues close to water molecules tends to be a bit larger for polar residues, like Asn or His, than for apolar residues, like Ala or Ile. This suggests that in low resolution protein structures it is possible to detect and locate better the water molecules that interact with polar residues. At very high resolution, close to 1 Å, the percentage of residues close to water molecules is nearly equal to 100 for polar residues, like Arg or Lys, and slightly smaller for apolar residues, like Leu or Ile. This implies that even at very high resolution, it is sometime impossible to detect and localize water molecules close to apolar residues. For all the 20 types of amino acids, the percentage of residues close to
Fig. 3. Relationship between resolution and the average absolute difference from 1 of the propensities to be close to water molecules of the residues that are solvent accessible.
water molecules does not change much at resolution better than 1.5–1.6 Å Another way to monitor the degree of hydration of the protein surface is the computation of the intrinsic propensities of each type of amino acid to be close to a water molecule (Table 2). At low resolution, only polar residues have propensities larger than 1 to be close to water molecules. This indicates that they are often observed near water molecules. Apolar residues have propensities lower than one at low resolution, suggesting that water molecules are rarely detected and positioned close to them. On the contrary, at high resolution, all the propensity values tend to 1 and small differences are observed amongst the 20 types of residues. Fig. 3 and Table 3 show the average absolute deviations from 1 of the propensities as a function of the resolution. If the resolution is lower than 3.0 Å, the average deviation of the propensities from 1 is equal to 0.416; and if the resolution is better than 1.0 Å, the average deviation of the propensities from 1 is equal to 0.048. This average
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Amino Resolution (Å) acid 1.0–1.1 >1.0
1.1–1.2
1.2–1.3
1.3–1.4
1.4–1.5
1.5–1.6
1.6–1.7
1.7–1.8
1.8–1.9
1.9–2.0
2.0–2.1
2.1–2.2
2.2–2.3
2.3–2.4
2.4–2.5
2.5–2.6
2.6–2.7
2.7–2.8
2.8–2.9
2.9–3.0
> 3.0
ALA ARG ASN ASP CYS GLN GLU GLY HIS ILE LEU LYS MET PHE PRO SER THR TRP TYR VAL
0.958 1.082 1.063 1.058 1.005 1.059 1.058 1.034 1.021 0.864 0.868 1.088 0.811 0.971 1.055 1.019 1.021 1.011 1.037 0.917
0.934 1.062 1.034 1.054 0.980 1.079 1.056 1.019 1.038 0.887 0.883 1.092 0.842 0.946 1.058 1.023 1.065 1.025 1.013 0.911
0.936 1.062 1.035 1.067 1.020 1.055 1.052 1.008 1.069 0.873 0.849 1.088 0.865 0.891 1.056 1.038 1.049 1.027 1.037 0.922
0.967 1.077 1.075 1.068 0.986 1.049 1.074 1.003 1.028 0.867 0.860 1.100 0.900 0.891 1.040 1.029 1.021 1.017 1.048 0.899
0.979 1.087 1.060 1.060 0.952 1.054 1.068 1.022 1.048 0.881 0.852 1.092 0.894 0.896 1.052 1.035 1.021 1.027 1.018 0.897
0.968 1.096 1.063 1.069 0.962 1.040 1.045 1.009 1.053 0.863 0.872 1.079 0.899 0.883 1.040 1.044 1.030 1.052 1.033 0.899
0.966 1.101 1.067 1.084 0.962 1.034 1.049 1.013 1.038 0.848 0.859 1.105 0.877 0.903 1.057 1.046 1.023 1.033 1.039 0.897
0.966 1.092 1.060 1.078 0.977 1.050 1.052 1.009 1.044 0.854 0.855 1.097 0.921 0.911 1.049 1.011 1.011 1.047 1.043 0.873
0.981 1.116 1.046 1.069 0.935 1.081 1.088 1.009 1.057 0.865 0.857 1.091 0.875 0.896 1.055 0.999 1.039 1.033 1.038 0.869
0.967 1.134 1.084 1.058 0.908 1.085 1.081 1.028 1.046 0.859 0.847 1.103 0.881 0.889 1.058 1.016 1.017 1.051 1.021 0.867
0.948 1.119 1.084 1.099 1.032 1.091 1.093 0.997 1.067 0.813 0.797 1.141 0.808 0.952 1.040 1.008 1.041 1.006 0.996 0.867
0.879 1.178 1.070 1.097 0.995 1.066 1.086 0.968 1.089 0.818 0.826 1.121 0.820 0.937 1.039 0.989 1.026 1.049 1.034 0.914
0.892 1.153 1.080 1.055 0.999 1.096 1.095 0.972 1.056 0.796 0.849 1.090 0.877 0.966 1.059 1.021 1.027 1.004 1.034 0.879
0.898 1.199 1.056 1.031 1.190 1.109 1.110 0.954 1.093 0.773 0.843 1.088 0.824 0.969 1.022 1.037 1.055 0.897 0.990 0.862
0.942 1.151 1.139 1.127 1.082 1.058 1.093 0.954 1.055 0.738 0.816 1.165 0.732 0.878 1.008 1.068 1.046 1.027 1.016 0.907
1.049 1.117 1.376 1.212 0.824 1.122 0.675 0.981 0.952 0.723 0.702 0.989 0.732 0.812 1.116 1.220 1.132 1.133 1.259 0.875
0.703 1.155 0.945 1.257 0.520 1.312 1.102 1.051 1.249 0.855 0.965 0.994 1.166 1.013 1.204 0.958 1.033 0.671 0.964 0.883
0.761 1.143 0.846 1.330 0.789 1.070 1.349 0.976 1.381 0.710 0.907 1.302 1.169 1.152 1.041 0.924 0.953 0.516 0.840 0.842
0.820 1.299 1.479 1.345 0.701 0.783 1.578 0.888 1.566 0.677 0.931 1.836 0.888 0.777 0.799 0.812 0.965 0.634 0.569 0.655
0.652 0.913 2.392 2.004 0.963 0.676 0.913 0.963 1.177 0.605 0.713 0.536 0.378 1.101 0.258 0.576 1.816 1.472 0.695 1.194
0.952 1.090 1.051 1.038 0.988 1.026 1.032 1.022 1.004 0.958 0.922 1.070 0.985 0.819 1.050 1.056 1.015 1.029 1.001 0.893
0.913 1.122 1.067 1.030 1.033 1.002 1.037 1.039 1.062 0.876 0.862 0.992 0.911 0.957 1.024 1.048 1.027 1.027 1.047 0.923
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Table 2 Propensities of the residues (that are solvent accessible and that are not involved in crystal packing contacts) to be close to water molecules in various resolution ranges.
O. Carugo / International Journal of Biological Macromolecules 89 (2016) 137–143 Table 3 Dependence on resolution of average absolute deviation from 1 of the propensities residues to close to water molecules of the residues that are solvent accessible and not involved in crystal packing. (standard errors in parentheses). Resolution (Å)
propensity
<1.0 1.0–1.1 1.1–1.2 1.2–1.3 1.3–1.4 1.4–1.5 1.5–1.6 1.6–1.7 1.7–1.8 1.8–1.9 1.9–2.0 2.0–2.1 2.1–2.2 2.2–2.3 2.3–2.4 2.4–2.5 2.5–2.6 2.6–2.7 2.7–2.8 2.8–2.9 2.9–3.0 >3.0
0.05 (0.01) 0.06 (0.01) 0.06 (0.01) 0.06 (0.01) 0.06 (0.01) 0.06 (0.01) 0.06 (0.01) 0.06 (0.01) 0.06 (0.02) 0.07 (0.01) 0.07 (0.02) 0.08 (0.02) 0.08 (0.02) 0.08 (0.02) 0.08 (0.02) 0.10 (0.02) 0.10 (0.02) 0.17 (0.04) 0.15 (0.03) 0.19 (0.04) 0.31 (0.07) 0.42 (0.09)
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Table 4 Dependence on resolution of percentage of residues that are solvent accessible and not involved in crystal packing contacts, the SASA of which diminished because of the present of water molecules (standard errors in parentheses). Resolution (Å)
%
<1.0 1.0–1.1 1.1–1.2 1.2–1.3 1.3–1.4 1.4–1.5 1.5–1.6 1.6–1.7 1.7–1.8 1.8–1.9 1.9–1.0 2.0–2.1 2.1–2.2 2.2–2.3 2.3–2.4 2.4–2.5 2.5–2.6 2.6–2.7 2.7–2.8 2.8–2.9 2.9–3.0 >3.0
94.1 (1.2) 93.9 (0.9) 92.5 (0.8) 94.2 (0.8) 92.4 (0.9) 92.7 (0.7) 92.7 (0.5) 91.7 (0.5) 91.5 (0.6) 90.8 (0.6) 89.2 (0.7) 89.0 (0.9) 88.3 (1.8) 86.3 (1.5) 86.2 (1.8) 85.4 (3.8) 78.4 (4.7) 79.3 (4.7) 64.5 (6.4) 45.8 (8.7) 33.4 (8.4) 23.6 (9.1)
The points of Fig. 4 can be fitted very well (Pearson correlation coefficient = 0.993) by a sigmoid function: deviation from 1 grows slowly up to 2.5 Å resolution and increases with a much larger slope at lower resolution. The points of Fig. 3 can be fitted very well (Pearson correlation coefficient = 0.990) by the following function: y = 0.065 + 8.7 × 10−7 × x11.56
(3)
This indicates that the average absolute deviations from 1 of the propensities tends to 0.065 at the highest resolution and increases when resolution decreases. At 1.5 Å it is still equal to 0.065 but at 2.4 Å resolution it is considerably larger 0.087 and it increases very steeply if resolution continues to decrease. A further approach to evaluate the degree of hydration of the protein surface is the calculation of the fraction of residues, the solvent accessible surface area (SASA) of which diminishes because of the presence of water molecules at the protein surface. This is performed by computing first the SASA in the absence of the water molecules and then by considering the presence of the water molecules. Table 4 and Fig. 4 show the percentage of residues with diminished SASA as a function of the crystallographic resolution. At very low resolution, the SASA of only 20–30% of the residues diminishes because of the water molecules. At very high resolution, more than 95% of the residues have SASA values that diminish because of the water molecules. Similar trends are observed by analyzing separately the 20 amino acid types (Fig. 5). However, there are small differences between polar and apolar residues. Nearly all the polar residues have diminished SASA because of the water molecules at high resolution, while only 80–90% of the apolar residues have SASA values influenced by water molecule at high resolution. Also at low resolution, the fraction of residues with SASA values affected by the water molecules tends to be higher for polar residues than for apolar residues. The percentage of residues with SASA affected by hydration is nearly constant for resolution values smaller than 1.6 Å, it decreases slightly from 1.6 to 2.4 Å, and it falls abruptly at lower resolution values.
y = −6.8 +
93.4 + 6.8 1+
x 16.90 2.9
.
(4)
This suggests that the maximum percentage of residues with diminished SASA is equal to 93.4 and that this percentage decreases very little when resolution diminishes to 1.5 Å. This percentage diminishes considerably when resolution decreases to 2.4 Å (89.5), falls steeply at worse resolution and reaches a value of 0 at resolution larger than 3.3 Å. It is necessary to observe that this function cannot be used to predict the percentage of residues with diminished SASA outside the resolution range that is examined here. It is therefore impossible to predict the percentage at resolution approaching 0 Å. 4. Discussion The degree of protein hydration has been monitored with three approaches. First, I computed the percentage of residues, which reside on the protein surface and are not involved in crystal packing interactions and which are close to water molecules. Then, I computed their propensities to be close to water molecules. Eventually, I computed the percentage of residues that have a diminished accessibility to the bulk solvent because of the presence of hydration water molecules. As expected, at higher resolution more residues are close to water molecules and have SASA values diminished because of the presence of water molecules; and the contrary occurs at lower resolution. At higher resolution, all the 20 types of amino acids have nearly the same propensity (equal to 1) to be close to water molecules; at lower resolution, the propensities are very variable, being larger than 1 for polar residues and smaller than one for apolar residues. This agrees perfectly with the expectations. At low resolution, fewer water molecules are detectable and localizable at the protein surface and those that are visible tend to interact with polar amino acids. On the contrary, at very high resolution, water molecules cover nearly all the protein surface that is not involved in crystal packing interactions.
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Fig. 4. Relationship between resolution and percentage of residues, the SASA of which diminished because of the presence of water molecules. Vertical bars indicate estimated standard errors.
Fig. 5. Relationships between resolution and percentage of the 20 types of residues, the SASA of which diminished because of the presence of water molecules. Vertical bars indicate estimated standard errors.
It is obviously impossible to identify a resolution threshold that divides completely hydrated from partially hydrated crystal structures. However, it is possible to make interesting observations. Both Figs. 1 and 4 and Tables 1 and 3 show a plateau at resolution smaller than 1.5–1.6 Å, a linear and moderate decrease of the ordinate (the variable y) up to 2.4–2.5 Å, and an abrupt diminution at lower resolution. This is partially confirmed by the analysis of the propensities to be close to water molecules (Fig. 3), where there is only a sharp slope change at 2.5–2.6 Å. In conclusion, these data reinforce the hypotheses that only crystal structures refined at a resolution equal to or better than 2.4–2.5 Å can be used to analyze the stereochemistry of protein hydration, at least for what concerns the first hydration layer [26]. Moreover, we can extract a new information from these data. A more stringent threshold of 1.5–1.6 Å might be preferable to ensure that protein hydration is complete. In fact, at resolution equal to or better than 1.5–1.6 Å, nothing or nearly nothing changes in the three figures of merit that I used to monitor the hydration degree.
This is shown also by the fitting functions (2)–(4). The selection of a more stringent threshold value is justified also by the observation that even at extremely high resolution, no hydration water molecules are observed near few apolar residues. Because of the paucity of the data, the standard errors are large at high and low resolution, with the consequence that statistical analyses might be misleading and larger datasets should be analyzed in this perspective. Regrettably, too few crystal structures have been refined at extremely high resolution and most of the crystal structures refined at low resolution are incomplete, since several residues at the protein surface were “invisible” in the electron density maps [12]. I observe that a threshold of 1.5–1.6 Å is considerable more strict than one at 2.4–2.5 Å. This implies the loss of a substantial amount of data. Roughly speaking, while about 80% of the PDB structures have been refined at a resolution equal to or better than 2.5 Å, only 10% of them have been refined at a resolution equal to or better than 1.5 Å. There is an eight-fold loss of data. However, a great sac-
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International Journal of Biological Macromolecules journal homepage: www.elsevier.com/locate/ijbiomac
When proteins are completely hydrated in crystals Oliviero Carugo ∗ Department of Chemistry, University of Pavia, Pavia, Italy and Department of Structural and Computational Biology, Vienna University, Vienna, Austria
a r t i c l e
i n f o
Article history: Received 22 January 2016 Received in revised form 15 March 2016 Accepted 21 April 2016 Available online 22 April 2016 Keywords: Crsytallographic resolution Crystallography Hydration Protein data bank Protein structure Solvent Water
a b s t r a c t In the crystalline state, protein surface patches that do not form crystal packing contacts are exposed to the solvent and one or more layers of hydration water molecules can be observed. It is well known that these water molecules cannot be observed at very low resolution, when the scarcity of experimental information precludes the observation of several parts of the protein molecule, like for example sidechains at the protein surface. On the contrary, more details are observable at high resolution. Here it is shown that it is necessary to reach a resolution of about 1.5–1.6 Å to observe a continuous hydration layer at the protein surface. This contrasts previous estimations, which were more tolerant and according to which a resolution of 2.5 Å was sufficient to describe at the atomic level the structure of the hydration layer. These results should prove useful in guiding a more rigorous selection of structural data to study protein hydration and in interpreting new crystal structures. © 2016 Elsevier B.V. All rights reserved.
1. Introduction In physiological conditions, globular proteins are surrounded by water molecules and cannot perform their chemical and biological roles in the absence of at least one hydration layer [29]. Consequently, protein hydration has been extensively studied with both experimental and computational methods [1]. Most of the information on hydration structure has been obtained with crystallographic studies. Several statistical analyses have been published, based on room temperature crystal structures [30–32,22,34,14,19]. More recently, structural analyses are routinely performed at low temperature (typically 100 K), to minimize radiation damage due to bright synchrotron sources [18,17,7]. New statistical surveys of the structures determined with cryocrystallography have also been published. It arose that more water molecules are detectable at low temperature, though previous observations at room temperature have been generally confirmed [25,27,28,23]. Interestingly, the growth of water molecule numbers at low temperature was not detected in a previous analysis, where few low temperature crystal structures (only 33 compared to 873 room temperature structures) were compared though linear multiple regression [6].
∗ Correspondence to: Department of Structural and Computational Biology, Vienna University, Campus Vienna Biocenter 5, 1030 Vienna, Austria. E-mail address: [email protected] http://dx.doi.org/10.1016/j.ijbiomac.2016.04.061 0141-8130/© 2016 Elsevier B.V. All rights reserved.
The effects of lowering the temperature of protein crystals on the structures have been examined extensively [16,15,33,21,35]. It emerged that low temperature structures are systematically different from room temperature structures, though many differences are relatively minor. At low temperature, the crystal volume diminishes slightly, inter-atomic contacts between symmetry related molecules are more numerous, and the conformational disorder of some side chains is different. More water molecules are detected in low temperature crystal structures, especially in the second hydration sphere [13]. However, cryo-crystallography became a routine technique and nearly all new protein crystal structures deposited in the Protein Data Bank [2,3] are determined at temperature close to 100 K. Therefore, given that the positions of the hydration water molecules do not change by lowering the temperature, [24] and although these data might provide a partially biased view of protein flexibility, it is obviously necessary to mine this enormous amount of experimental information in order to detect interesting structural trends. Several issues must be addressed in data mining the Protein Data Bank [11]. It is mandatory to define the criteria for the selection of the protein crystal structures. The latter ones must be reasonably well hydrated if one is looking for realistic statistical trends. For example, it is probable better to exclude structures refined at very low crystallographic resolution, where few water molecules are detectable in the electron density maps. Crystallographic resolution is by far the most used quality indicator in statistical surveys of protein structures. For example, only
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crystal structures refined at resolution better than 1.5 Å have been considered in a detailed analysis of water molecules buried in the protein core [5]. A threshold of 2.0 Å was used in the analysis of buried chlorides [4]. Other threshold values have been used too and the selection of the threshold is a compromise between the need of accuracy, which improves with smaller and more stringent values, and the need of large datasets, which enlarge with higher and less severe threshold values. It must be admitted, however, that threshold values are often quite arbitrary. When dealing with the analysis of protein hydration, it is necessary to identify the most correct value of resolution, in order to include (nearly) only crystal structures of proteins that have well hydrated surfaces and to exclude proteins that have an incomplete hydration layer. This problem is addressed in the present communication by computing several figures of merit, which monitor the hydration degree, at various resolution levels. 2. Methods All protein crystal structures were downloaded from the Protein Data Bank [2,3] according to the following criteria: (i) entries with nucleic acids were discarded, (ii) only crystal structures determined at low temperature (80–120 K) were considered; (ii) only monomers with one molecule per asymmetric unit were retained. I imposed the restriction on the data collection temperature since the hydration degree may depend on temperature [13]. I analyzed only monomers, since the reduction of sequence redundancy is obviously simpler and more effective, if oligomeric assemblies are discarded. Sequence redundancy was limited to pairwise 30% sequence identity. I removed incomplete structures, lacking atoms and residues or with zero occupancy atoms, since these residues and atoms are very often at the surface of the protein and are therefore crucial for the detection of hydration water molecules. For similar reasons, I discarded structures where protein atoms had B-factors larger than 70 Å or larger than five times the average B-factor of the protein atoms. These thresholds on the B-factors are necessary, since the hydration of structures with large flexible moieties is unreliable. In particular, an atom with a B-factor of 70 Å2 has a mean displacement amplitude from its average position larger than 0.94 Å, which is closer to the shortest covalent bond distance (C H). I also rejected proteins shorter than 50 amino acids. Structures were classified into 22 groups according to their resolution. The first group included only structures refined at a resolution equal to or better than 1.0 Å The last group was formed only by structures refined at a resolution lower than 3.0 Å. The other groups comprised structures in 0.1 large resolution ranges ranging from 1.0 to 3.0 Å. The largest group, 129 structures, was in the 1.70–1.80 Å resolution range. The smallest group, 3 structures, included structures refined at a resolution lower than 3.0 Å. The average dimension of the groups was 51 (standard error = 9). Residues involved in crystal packing contacts were identified with the program CPC [10] and solvent accessible surface areas were computed with NACCESS [20]. A protein atom located at the protein surface and not involved in crystal packing contacts was considered to be close to a hydration water molecule if their interatomic distance was minor than 4.5 Å. A residue was considered to be hydrated if at least one of its atoms was close to at least one water molecule. I computed the propensities of the solvent accessible residues to be close to water molecules according to the following equation: propensity =
nr,w ⁄nw nr ⁄n
(1)
where nr,w is the number of residues of type “r” that are close to water molecules, nw is the total number of residues that are close
Fig. 1. Relationship between resolution and percentage of residues that are solvent accessible and close to a water molecule. Vertical bars indicate estimated standard errors.
to water molecules, nr is the total number of residues of type “r”, and n is the total number of residues. Consequently, an amino acid with a propensity values larger than 1 tend to be close to a water molecules, while an amino acid with a propensity lower than 1 does not tend to be close to a water molecule. 3. Results First, it is mandatory to identify which are the residues that are really exposed to the solvent in the crystal structure. Some of the residues that are at the protein surface are not exposed to the solvent, since they are at the interface between two proteins related by a symmetry operation. In other words, they are buried in crystal packing contacts. I used the program CPC, which has been used in other studies [8,9,36], to identify residues that are at the surface of the proteins and that are buried in crystal packing contacts and that are, therefore, not accessible to the solvent. I considered accessible to the solvent all the other residues that are at the surface of the protein and are not involved in crystal packing interactions. Then, I computed for each protein crystal structure the percentage of amino acids that are really solvent accessible and close to a water molecule. The average percentages for all residues are shown in Table 1 and plotted in Fig. 1, for various resolution ranges. Fig. 2 shows the average percentages for each amino acid type. Table 1 and Fig. 1 show that at very high resolution, most of the residues are close to water molecules. If resolution decreases, the percentage of residues close to water molecules is nearly constant, slightly above 90%, until resolution of 1.5–1.6 Å. Then it decreases slowly up to 2.3–2.4 Å resolution and it fall steeply at lower resolution. The points of Fig. 1 can be fitted very well (Pearson correlation coefficient = 0.996) by a sigmoid function: y = −281.0 +
90.4 + 281.0 1+
x 7.15 3.6
.
(2)
This indicates that the maximum percentage of amino acids that are really solvent accessible and are close to a water molecule is equal to 90.4 and that this percentage decreases very little when resolution diminishes to 1.5 Å (89.7). The same percentage diminishes considerably when resolution decreases to 2.4 Å (71.1), falls steeply at worse resolution and reaches a value of 0 at resolution larger than 3 Å. It must be observed that this function cannot be used to predict the percentage of amino acids that are really solvent accessible and are close to a water molecule outside the resolution
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Fig. 2. Relationship between resolution and percentage of residues that are solvent accessible and close to a water molecule for all the 20 amino acid types. Vertical bars indicate estimated standard errors. Table 1 Dependence on resolution of the percentage of residues that are solvent accessible, not involved in crystal packing contacts and close to water molecules (standard errors in parentheses). Resolution (Å)
%
< 1.0 1.0–1.1 1.1–1.2 1.2–1.3 1.3–1.4 1.4–1.5 1.5–1.6 1.6–1.7 1.7–1.8 1.8–1.9 1.9–2.0 2.0–2.1 2.1–2.2 2.2–2.3 2.3–2.4 2.4–2.5 2.5–2.6 2.6–2.7 2.7–2.8 2.8–2.9 2.9–3.0 >3.0
91.2 (2.1) 89.3 (3.1) 92.0 (0.8) 92.4 (1.0) 91.2 (0.9) 90.3 (0.7) 90.4 (0.6) 88.9 (0.6) 87.6 (0.7) 86.7 (0.7) 84.3 (0.8) 83.0 (1.0) 80.7 (2.0) 78.3 (1.8) 78.9 (2.0) 73.8 (5.8) 66.0 (5.5) 54.3 (14.3) 45.1 (12.3) 33.2 (8.7) 23.9 (6.2) 12.3 (5.1)
range that is examined here. It is therefore impossible to predict the percentage at resolution increasing much more than 1 Å. Each of the 20 types of amino acids shows a closely similar trend (Fig. 2). In general, at very low resolution, the percentage of residues close to water molecules tends to be a bit larger for polar residues, like Asn or His, than for apolar residues, like Ala or Ile. This suggests that in low resolution protein structures it is possible to detect and locate better the water molecules that interact with polar residues. At very high resolution, close to 1 Å, the percentage of residues close to water molecules is nearly equal to 100 for polar residues, like Arg or Lys, and slightly smaller for apolar residues, like Leu or Ile. This implies that even at very high resolution, it is sometime impossible to detect and localize water molecules close to apolar residues. For all the 20 types of amino acids, the percentage of residues close to
Fig. 3. Relationship between resolution and the average absolute difference from 1 of the propensities to be close to water molecules of the residues that are solvent accessible.
water molecules does not change much at resolution better than 1.5–1.6 Å Another way to monitor the degree of hydration of the protein surface is the computation of the intrinsic propensities of each type of amino acid to be close to a water molecule (Table 2). At low resolution, only polar residues have propensities larger than 1 to be close to water molecules. This indicates that they are often observed near water molecules. Apolar residues have propensities lower than one at low resolution, suggesting that water molecules are rarely detected and positioned close to them. On the contrary, at high resolution, all the propensity values tend to 1 and small differences are observed amongst the 20 types of residues. Fig. 3 and Table 3 show the average absolute deviations from 1 of the propensities as a function of the resolution. If the resolution is lower than 3.0 Å, the average deviation of the propensities from 1 is equal to 0.416; and if the resolution is better than 1.0 Å, the average deviation of the propensities from 1 is equal to 0.048. This average
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Amino Resolution (Å) acid 1.0–1.1 >1.0
1.1–1.2
1.2–1.3
1.3–1.4
1.4–1.5
1.5–1.6
1.6–1.7
1.7–1.8
1.8–1.9
1.9–2.0
2.0–2.1
2.1–2.2
2.2–2.3
2.3–2.4
2.4–2.5
2.5–2.6
2.6–2.7
2.7–2.8
2.8–2.9
2.9–3.0
> 3.0
ALA ARG ASN ASP CYS GLN GLU GLY HIS ILE LEU LYS MET PHE PRO SER THR TRP TYR VAL
0.958 1.082 1.063 1.058 1.005 1.059 1.058 1.034 1.021 0.864 0.868 1.088 0.811 0.971 1.055 1.019 1.021 1.011 1.037 0.917
0.934 1.062 1.034 1.054 0.980 1.079 1.056 1.019 1.038 0.887 0.883 1.092 0.842 0.946 1.058 1.023 1.065 1.025 1.013 0.911
0.936 1.062 1.035 1.067 1.020 1.055 1.052 1.008 1.069 0.873 0.849 1.088 0.865 0.891 1.056 1.038 1.049 1.027 1.037 0.922
0.967 1.077 1.075 1.068 0.986 1.049 1.074 1.003 1.028 0.867 0.860 1.100 0.900 0.891 1.040 1.029 1.021 1.017 1.048 0.899
0.979 1.087 1.060 1.060 0.952 1.054 1.068 1.022 1.048 0.881 0.852 1.092 0.894 0.896 1.052 1.035 1.021 1.027 1.018 0.897
0.968 1.096 1.063 1.069 0.962 1.040 1.045 1.009 1.053 0.863 0.872 1.079 0.899 0.883 1.040 1.044 1.030 1.052 1.033 0.899
0.966 1.101 1.067 1.084 0.962 1.034 1.049 1.013 1.038 0.848 0.859 1.105 0.877 0.903 1.057 1.046 1.023 1.033 1.039 0.897
0.966 1.092 1.060 1.078 0.977 1.050 1.052 1.009 1.044 0.854 0.855 1.097 0.921 0.911 1.049 1.011 1.011 1.047 1.043 0.873
0.981 1.116 1.046 1.069 0.935 1.081 1.088 1.009 1.057 0.865 0.857 1.091 0.875 0.896 1.055 0.999 1.039 1.033 1.038 0.869
0.967 1.134 1.084 1.058 0.908 1.085 1.081 1.028 1.046 0.859 0.847 1.103 0.881 0.889 1.058 1.016 1.017 1.051 1.021 0.867
0.948 1.119 1.084 1.099 1.032 1.091 1.093 0.997 1.067 0.813 0.797 1.141 0.808 0.952 1.040 1.008 1.041 1.006 0.996 0.867
0.879 1.178 1.070 1.097 0.995 1.066 1.086 0.968 1.089 0.818 0.826 1.121 0.820 0.937 1.039 0.989 1.026 1.049 1.034 0.914
0.892 1.153 1.080 1.055 0.999 1.096 1.095 0.972 1.056 0.796 0.849 1.090 0.877 0.966 1.059 1.021 1.027 1.004 1.034 0.879
0.898 1.199 1.056 1.031 1.190 1.109 1.110 0.954 1.093 0.773 0.843 1.088 0.824 0.969 1.022 1.037 1.055 0.897 0.990 0.862
0.942 1.151 1.139 1.127 1.082 1.058 1.093 0.954 1.055 0.738 0.816 1.165 0.732 0.878 1.008 1.068 1.046 1.027 1.016 0.907
1.049 1.117 1.376 1.212 0.824 1.122 0.675 0.981 0.952 0.723 0.702 0.989 0.732 0.812 1.116 1.220 1.132 1.133 1.259 0.875
0.703 1.155 0.945 1.257 0.520 1.312 1.102 1.051 1.249 0.855 0.965 0.994 1.166 1.013 1.204 0.958 1.033 0.671 0.964 0.883
0.761 1.143 0.846 1.330 0.789 1.070 1.349 0.976 1.381 0.710 0.907 1.302 1.169 1.152 1.041 0.924 0.953 0.516 0.840 0.842
0.820 1.299 1.479 1.345 0.701 0.783 1.578 0.888 1.566 0.677 0.931 1.836 0.888 0.777 0.799 0.812 0.965 0.634 0.569 0.655
0.652 0.913 2.392 2.004 0.963 0.676 0.913 0.963 1.177 0.605 0.713 0.536 0.378 1.101 0.258 0.576 1.816 1.472 0.695 1.194
0.952 1.090 1.051 1.038 0.988 1.026 1.032 1.022 1.004 0.958 0.922 1.070 0.985 0.819 1.050 1.056 1.015 1.029 1.001 0.893
0.913 1.122 1.067 1.030 1.033 1.002 1.037 1.039 1.062 0.876 0.862 0.992 0.911 0.957 1.024 1.048 1.027 1.027 1.047 0.923
O. Carugo / International Journal of Biological Macromolecules 89 (2016) 137–143
Table 2 Propensities of the residues (that are solvent accessible and that are not involved in crystal packing contacts) to be close to water molecules in various resolution ranges.
O. Carugo / International Journal of Biological Macromolecules 89 (2016) 137–143 Table 3 Dependence on resolution of average absolute deviation from 1 of the propensities residues to close to water molecules of the residues that are solvent accessible and not involved in crystal packing. (standard errors in parentheses). Resolution (Å)
propensity
<1.0 1.0–1.1 1.1–1.2 1.2–1.3 1.3–1.4 1.4–1.5 1.5–1.6 1.6–1.7 1.7–1.8 1.8–1.9 1.9–2.0 2.0–2.1 2.1–2.2 2.2–2.3 2.3–2.4 2.4–2.5 2.5–2.6 2.6–2.7 2.7–2.8 2.8–2.9 2.9–3.0 >3.0
0.05 (0.01) 0.06 (0.01) 0.06 (0.01) 0.06 (0.01) 0.06 (0.01) 0.06 (0.01) 0.06 (0.01) 0.06 (0.01) 0.06 (0.02) 0.07 (0.01) 0.07 (0.02) 0.08 (0.02) 0.08 (0.02) 0.08 (0.02) 0.08 (0.02) 0.10 (0.02) 0.10 (0.02) 0.17 (0.04) 0.15 (0.03) 0.19 (0.04) 0.31 (0.07) 0.42 (0.09)
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Table 4 Dependence on resolution of percentage of residues that are solvent accessible and not involved in crystal packing contacts, the SASA of which diminished because of the present of water molecules (standard errors in parentheses). Resolution (Å)
%
<1.0 1.0–1.1 1.1–1.2 1.2–1.3 1.3–1.4 1.4–1.5 1.5–1.6 1.6–1.7 1.7–1.8 1.8–1.9 1.9–1.0 2.0–2.1 2.1–2.2 2.2–2.3 2.3–2.4 2.4–2.5 2.5–2.6 2.6–2.7 2.7–2.8 2.8–2.9 2.9–3.0 >3.0
94.1 (1.2) 93.9 (0.9) 92.5 (0.8) 94.2 (0.8) 92.4 (0.9) 92.7 (0.7) 92.7 (0.5) 91.7 (0.5) 91.5 (0.6) 90.8 (0.6) 89.2 (0.7) 89.0 (0.9) 88.3 (1.8) 86.3 (1.5) 86.2 (1.8) 85.4 (3.8) 78.4 (4.7) 79.3 (4.7) 64.5 (6.4) 45.8 (8.7) 33.4 (8.4) 23.6 (9.1)
The points of Fig. 4 can be fitted very well (Pearson correlation coefficient = 0.993) by a sigmoid function: deviation from 1 grows slowly up to 2.5 Å resolution and increases with a much larger slope at lower resolution. The points of Fig. 3 can be fitted very well (Pearson correlation coefficient = 0.990) by the following function: y = 0.065 + 8.7 × 10−7 × x11.56
(3)
This indicates that the average absolute deviations from 1 of the propensities tends to 0.065 at the highest resolution and increases when resolution decreases. At 1.5 Å it is still equal to 0.065 but at 2.4 Å resolution it is considerably larger 0.087 and it increases very steeply if resolution continues to decrease. A further approach to evaluate the degree of hydration of the protein surface is the calculation of the fraction of residues, the solvent accessible surface area (SASA) of which diminishes because of the presence of water molecules at the protein surface. This is performed by computing first the SASA in the absence of the water molecules and then by considering the presence of the water molecules. Table 4 and Fig. 4 show the percentage of residues with diminished SASA as a function of the crystallographic resolution. At very low resolution, the SASA of only 20–30% of the residues diminishes because of the water molecules. At very high resolution, more than 95% of the residues have SASA values that diminish because of the water molecules. Similar trends are observed by analyzing separately the 20 amino acid types (Fig. 5). However, there are small differences between polar and apolar residues. Nearly all the polar residues have diminished SASA because of the water molecules at high resolution, while only 80–90% of the apolar residues have SASA values influenced by water molecule at high resolution. Also at low resolution, the fraction of residues with SASA values affected by the water molecules tends to be higher for polar residues than for apolar residues. The percentage of residues with SASA affected by hydration is nearly constant for resolution values smaller than 1.6 Å, it decreases slightly from 1.6 to 2.4 Å, and it falls abruptly at lower resolution values.
y = −6.8 +
93.4 + 6.8 1+
x 16.90 2.9
.
(4)
This suggests that the maximum percentage of residues with diminished SASA is equal to 93.4 and that this percentage decreases very little when resolution diminishes to 1.5 Å. This percentage diminishes considerably when resolution decreases to 2.4 Å (89.5), falls steeply at worse resolution and reaches a value of 0 at resolution larger than 3.3 Å. It is necessary to observe that this function cannot be used to predict the percentage of residues with diminished SASA outside the resolution range that is examined here. It is therefore impossible to predict the percentage at resolution approaching 0 Å. 4. Discussion The degree of protein hydration has been monitored with three approaches. First, I computed the percentage of residues, which reside on the protein surface and are not involved in crystal packing interactions and which are close to water molecules. Then, I computed their propensities to be close to water molecules. Eventually, I computed the percentage of residues that have a diminished accessibility to the bulk solvent because of the presence of hydration water molecules. As expected, at higher resolution more residues are close to water molecules and have SASA values diminished because of the presence of water molecules; and the contrary occurs at lower resolution. At higher resolution, all the 20 types of amino acids have nearly the same propensity (equal to 1) to be close to water molecules; at lower resolution, the propensities are very variable, being larger than 1 for polar residues and smaller than one for apolar residues. This agrees perfectly with the expectations. At low resolution, fewer water molecules are detectable and localizable at the protein surface and those that are visible tend to interact with polar amino acids. On the contrary, at very high resolution, water molecules cover nearly all the protein surface that is not involved in crystal packing interactions.
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Fig. 4. Relationship between resolution and percentage of residues, the SASA of which diminished because of the presence of water molecules. Vertical bars indicate estimated standard errors.
Fig. 5. Relationships between resolution and percentage of the 20 types of residues, the SASA of which diminished because of the presence of water molecules. Vertical bars indicate estimated standard errors.
It is obviously impossible to identify a resolution threshold that divides completely hydrated from partially hydrated crystal structures. However, it is possible to make interesting observations. Both Figs. 1 and 4 and Tables 1 and 3 show a plateau at resolution smaller than 1.5–1.6 Å, a linear and moderate decrease of the ordinate (the variable y) up to 2.4–2.5 Å, and an abrupt diminution at lower resolution. This is partially confirmed by the analysis of the propensities to be close to water molecules (Fig. 3), where there is only a sharp slope change at 2.5–2.6 Å. In conclusion, these data reinforce the hypotheses that only crystal structures refined at a resolution equal to or better than 2.4–2.5 Å can be used to analyze the stereochemistry of protein hydration, at least for what concerns the first hydration layer [26]. Moreover, we can extract a new information from these data. A more stringent threshold of 1.5–1.6 Å might be preferable to ensure that protein hydration is complete. In fact, at resolution equal to or better than 1.5–1.6 Å, nothing or nearly nothing changes in the three figures of merit that I used to monitor the hydration degree.
This is shown also by the fitting functions (2)–(4). The selection of a more stringent threshold value is justified also by the observation that even at extremely high resolution, no hydration water molecules are observed near few apolar residues. Because of the paucity of the data, the standard errors are large at high and low resolution, with the consequence that statistical analyses might be misleading and larger datasets should be analyzed in this perspective. Regrettably, too few crystal structures have been refined at extremely high resolution and most of the crystal structures refined at low resolution are incomplete, since several residues at the protein surface were “invisible” in the electron density maps [12]. I observe that a threshold of 1.5–1.6 Å is considerable more strict than one at 2.4–2.5 Å. This implies the loss of a substantial amount of data. Roughly speaking, while about 80% of the PDB structures have been refined at a resolution equal to or better than 2.5 Å, only 10% of them have been refined at a resolution equal to or better than 1.5 Å. There is an eight-fold loss of data. However, a great sac-
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