Solvent Organization in an Oligonucleotide Crystal

We describe the crystal structure of d(GCGAATTCG) determined by x-ray diffraction at atomic resolution level (0.89 Å). The duplex structure is practically identical to that described at 2.05 Å resolution (Van Meervelt, L., Vlieghe, D., Dautant, A., Gallois, B., Précigoux, G., and Kennard, O. (1995) Nature 374, 742–744), however about half of the phosphate groups show multiple conformations. The crystal has three regions with different solvent structure. One of them contains several ordered Mg+2 ions and can be considered as an ionic crystal. A second region is formed by a network of ordered water molecules with a polygonal organization that binds three duplexes. The third region is formed by channels of solvent in which very few ordered solvent molecules are visible. The less ordered phosphates are found facing this channel. The latter region provides a view of DNA with highly movable charges, both negative phosphates and counterions, without a precise location.

Two periods could be distinguished in the x-ray diffraction studies of DNA: the era of fiber diffraction of polymeric DNA/ polynucleotides and the time of single crystal x-ray structures of short fragments. The data available from fiber diffraction were limited and allowed no detailed analysis. The goal of DNA crystallography is, therefore, the study of detailed DNA structures. However, crystallographic data are also limited in some important aspects of DNA structure. For example, it is well known (1) that the solvent environment plays an important role in the conformational behavior and interactions of DNA. To study this feature in detail, it is necessary to work with x-ray data at atomic resolution level. Until recently, such data were available only for Z-DNA fragments. This situation is now changing. Synchrotron radiation of increasing power, together with better detectors and cryotechniques, make possible a third period of DNA crystallography: the epoch of high resolution DNA structures.
We recently presented (2) a preliminary account of the structure of the B-DNA fragment (GCGAATTCG) solved at atomic resolution (0.89 Å). This structure had already been solved at 2.05-Å resolution (3,4). In our previous analysis we described the water spine in the minor groove and compared it with related structures. Here we present a detailed analysis of the same oligonucleotide, which has multiple conformations in several parts of the phosphodiester backbone. We also describe the organization of the solvent, which in some regions shows well resolved water molecules, whereas in other regions it remains disordered, despite the fact that our crystals have been studied at 120 K. Thus, a frozen sample at atomic resolution, instead of showing a highly ordered duplex, demonstrates multiple conformations and regions of disordered solvent.

MATERIALS AND METHODS
Crystallization-The d(GCGAATTCG) nonamer was crystallized, using a batch method, in sitting drops containing 0.5 mM DNA duplex, 1 mM acridine-(Arg 4 ) drug-peptide aduct, 20 mM sodium cacodylate buffer, pH 7, 100 mM MgCl 2 , and 35% MPD. 1 The crystals grew in approximately 2 months to a typical size of 0.6 x 0.4 x 0.4 mm at 20°C constant temperature. Our original purpose was to study crystals of ordered peptide/DNA complexes, but no peptide was detected in the crystals obtained.
The batch method consists of mixing the sample with the crystallization solvent at a duplex concentration such that supersaturation is instantaneously reached. In this method, the reservoir no longer acts to concentrate the crystallization drop, but only to maintain a constant vapor pressure. Usually, nucleation tends to be too extensive, because it starts from supersaturation, but large crystals can be eventually obtained when working close to the metastable region. In our case, once the nuclei appeared, the formation of suitable crystals was quite fast.
Data Collection-For data collection, crystals were mounted in a fiber loop and immediately flash-cooled at 120 K in a cold nitrogen stream using an Oxford Cryosystems Cryostream. Data were collected using synchrotron radiation at EMBL beamline X11 in Deutsches Elektronen Synchroton Hamburg Outstation on a 345-mm MAR Research imaging plate scanner. Three sets of data were collected at resolution cutoffs of 0.89, 1.5, and 2.64 Å to avoid saturation of the high intensity reflections. The data were processed and reduced with DENZO (5) and SCALEPACK. The overall R merge for all data after scaling and merging was 3.5%, and data were 97.6% complete in the resolution range 30 -0.89 Å.
Refinement-The nonamer structure previously reported (4) at 2.05-Å resolution was used as a starting model. It was refined in XPLOR 3.8 (6) using data between 30 and 1.1 Å. Refinement was carried out against 95% of the measured data (32,430 reflections). The remaining 5% were randomly excluded from the data set and used as a cross-validation test using the free R factor . It converged at R free ϭ 0.248 and R factor ϭ 0.222. Simulated annealing protocols were employed. We inspected the structure with 2F o Ϫ F c and F o Ϫ F c Fourier maps. The DNA structure was updated, and the electron density peaks greater than 4 were considered as water molecules. After some cycles with XPLOR, we switched to SHELXL (7), where anisotropic refinement was carried out with some conjugate-gradient cycles using the maximum resolution. The remaining structure was built manually into 2F o Ϫ F c and F o Ϫ F c electron density maps generated with SHELXPRO after each refinement step, visualized with the TURBO program (8). The R free and R factor dropped to 0.161 and 0.135, respectively, for F Ͼ 4. A final step was carried out using a least square cycle, including all data, converging at R factor ϭ 0.140 for all data between 30 and 0.89 Å (F Ͼ 4).
We detected four phosphate groups in alternative conformations, two of them extending a small disorder into the deoxyribose ring and into adjacent residues as well. The refinement was carried out against parameters of the SHELXL dictionary xdna hr.dic. During refinement, we realized that restraining the planarity of the C1Ј atom with the corresponding nitrogenated base pulled the model away from the best fit to the data. This fact was evident when inspected in the F o Ϫ F c maps. Therefore, we released this restraint from the dictionary, lowering the R factor from 0.148 to 0.135. This restraint release was not introduced in our preliminary model (2).
Modeling the multiple conformation of some phosphates was not straightforward. For simplicity, the phosphates were assumed to have only two conformations. Refinement with SHELXL of the two conformations showed some anomalous values for bond lengths and angles. For example the P-O3Ј bond length was 1.50 Å in one of the conformations of the P2 phosphate and 1.67 Å in one of the P7 phosphates, very far from the average value (1.58 Å). An adequate modeling probably should include multiple conformations, but this problem has to be studied further at even higher resolution. Thus the stereochemical parameters obtained in phosphates with a double conformation are not accurate. In two cases (P2 and P18) only the phosphate group was modeled as a double conformation, whereas in P7 and P11, a double conformation of the deoxyribose, was also considered. In the case of P7 the deoxyribose of residue 6 was also modeled as a double conformation. A further problem was found in the refinement of phosphates 9, 12, and 14. An additional peak of electron density was found at distances of 0.9 -1.4 Å of either the phosphorous or one of its oxygens. An example will be shown below (see Fig. 4). It looked as if the phosphorous atom was pentacoordinated, but such a structure is only found in organic esters and never in aqueous solutions. We refined these peaks as oxygen atoms, which turned out to have an occupancy of 80%. Most likely they are a sign of disorder in these phosphates. These anomalous oxygen atoms have been labeled X and placed at the end of the coordinate file.
A total of seven Mg 2ϩ ions were modeled. The 19, 26, 31, and 38 Mg 2ϩ ions are well ordered and fully hydrated in the usual octahedral fashion. On the other hand, the 44, 49, and 52 Mg 2ϩ ions are partially disordered and not fully hydrated. We assigned them as Mg 2ϩ ions due to several short (about 2 Å) intermolecular distances to neighbor water molecules. In our preliminary analysis (2) we assigned them to water molecules, but the further refinement carried out clearly shows that they correspond to partially ordered Mg 2ϩ ions. An additional disordered Mg 2ϩ ion could correspond to water 178. This molecule shows hydrogen bonds with seven water molecules, three of which are rather short, in the range of 2 to 2.3 Å. Nevertheless, we included it as a water molecule in the coordinate file.
A very clear Cl Ϫ ion was also found near two Mg 2ϩ ions. An electron density peak with a high density was present at this position. In our previous analysis we also described two poorly ordered sodium ions (B factors ϭ 24.1 and 71.6 Å 2 ). They were found near phosphate groups and were tentatively assigned on the basis of several short distances (less than 2.6 Å) to neighbor water molecules. Because they have a low occupancy, we now consider them as partially occupied water sites (waters 161 and 172, respectively). Furthermore, given the low concentration of sodium ions in our crystallization buffer, it is unlikely that these ions should be present as ordered sites in the crystal. 151 water molecules have been located, compared with 86 found in the structure reported at 2.05 Å. Some of them show a clear double conformation (triple in one case). On the other hand, several water molecules have a very poor electron density. To improve the latter sites we released their occupancies in 10 cycles of refinement and then recalculated the improved F o Ϫ F c maps. Finally we classified the 151 water molecules in three categories: 1. full occupancy waters with a single position, 115; 2. waters with well-defined alternative positions whose occupancies add to unity, 14; 3. disordered waters with fractional occupancies, 22.
After this water site assignment we refined all water occupancies. Some of the waters with either alternative positions or fractional occupancies showed short contacts with other water molecules. Hydrogen atoms were included at geometric positions in the final step. Neither MPD nor the drug-peptide complex used in the crystallization was found in the crystal.
The final crystal data and refinement statistics for the structure are listed in Table I. Related data from the 2.05-Å resolution structure (4) are also shown. The results presented here differ from our previous refinement (Nucleic Acid Database code: BD0016) in several features, which have already been discussed. Furthermore, we carried out a more accurate treatment of the disordered regions in backbone and solvent. As a result, two more Mg ϩ2 ions and several additional water molecules were located.
The Parameter File-Given the high resolution obtained in this structure, we decided to compare the stereochemical parameters observed in our final structure with those used for refinement (9) in programs such as X-PLOR (6), CNS (10), or SHELX (7). A table including bond lengths and angles is given as supplementary material. In general, all our values coincide with those of Parkinson et al. (9). The main exceptions are the P-O3Ј and C1Ј-N bonds. We find that the P-O3Ј bond is shorter by about 0.03 Å from the standard value, with an average of 1.577 Å ( ϭ 0.023), whereas Parkinson et al. It should be noted that these small discrepancies with the standard parameters are not unexpected, because Parkinson et al. (9) could only use a limited set of data of di-and trinucleotides in their statistical analysis of the backbone. Nevertheless, further data are necessary to compile a new parameter file based on the new high resolution data that are presently emerging.
The most unexpected feature we found was that, upon refinement, the C1Ј atom was not placed at the central position of the corresponding electron density. We discovered that this result was due to the restraint we had used of assuming the C1Ј atom to be coplanar with the aromatic ring of the base to which it is attached. This restraint should be where ͉F o ͉ and ͉F c ͉ are the observed and calculated structure factor amplitudes respectively, with 5% of the reflections omitted. c R free was calculated using a random set containing 5% of observations that were omitted during refinement. removed from refinement protocols. Upon removing this restraint, about half of the C1Ј atoms moved by 0.1-0.3 Å from the average plane of the base, the other half remained approximately coplanar.
Structure Analysis-The program NEWHELIX93 (courtesy of Prof. R. Dickerson) was used for calculation of helical parameters. The programs TURBO (8) and O (11) were used as graphical displays for model building. Figures were produced using CERIUS (12), SETOR (13), and BOBSCRIPT (14).
Base Pair and Solvent Volume-Given the high resolution of our structure, we expected to localize most of the water molecules. However, we found a channel in the crystal with almost no localized solvent molecules. In ordered regions of the solvent it was also apparent that some water molecules were missing. Therefore we decided to estimate how many solvent molecules should be found in the asymmetric unit.
For an approximate estimate of the volume of base pairs at room temperature, we decided to use the unit cell volume of available structures of mono-and dinucleotides determined at high resolution (15,16). We found considerable differences in volume, up to almost 10%, when different crystal structures were compared. By trial and error we took as approximate values those given in Table II. We estimate a maximum error of 5% in the values given. When more high resolution structures of oligonucleotides become available, these volumes should be recalculated taking into account the van der Waals volume of the base pairs. The Mg 2ϩ volume is considered to be zero, because it induces electrostriction in the surrounding water molecules.
The values given in Table II are in reasonable agreement with those calculated by Chalikian et al. (17) from fiber diffraction models using a different method. They found an average value of 562 Å 3 /base pair at room temperature.
The volume of base pairs at 120 K was calculated by subtracting 5% from the estimated room temperature value, because this is the decrease we found in our structure (see below). The accurate volume of individual water molecules is difficult to ascertain. It has been reported (18) that water associated with DNA has a higher density. On the other hand, if water is ice-like at 120 K, its molecular volume should be greater than at room temperature. So we decided to use the liquid water volume of 30 Å 3 /molecule at all temperatures.
With the values given in Table II, the nonamer volume is 4960 Å 3 . The volume of solvent in the asymmetric unit was found to be 5607 Å 3 , equivalent to 187 water molecules if no MPD is present. Because we localized 151 water molecules, there should be about 36 additional water molecules for each duplex in disordered regions of the crystal.

General Features: Comparison with the Room Temperature
Form-Comparison of the nonamer structure with that previously obtained (4) at 2.05-Å resolution for the same sequence should show greater detail but also changes due to the lower temperature used in the collection of the high resolution data. As shown in Fig. 1, both nonamers present very similar features, with a root mean square deviation of only 0.41 Å between both structures. If the central hexamer sequence is compared, the root mean square decreases to 0.26 Å, demonstrating that the largest differences occur at both ends of the nonamer.
The main difference to be expected between both structures is in the B factors of the atoms, which are represented in Fig. 2. The B factors follow the same trend throughout the structure, with values being about 50% higher in the room temperature model, and show that the local vibration modes of the molecule are the same at both temperatures, although they are more intense at room temperature. An exception is phosphate 7 (as shown in Fig. 2), which not only has a double conformation (to be discussed below) but comparatively higher B factors at low temperature. The anomalous behavior of this phosphate might be due to the fact that it is placed in a region of the crystal that has a highly disordered solvent structure; however, this is not necessarily the main reason, because other phosphates are also placed in regions of solvent disorder and have moderate B factors.
As expected from the overall comparison of the structure (Fig. 1), the torsion angles (Table III) and conformational parameters calculated with NEWHELIX93 do not vary much. Most parameters differ by small quantities, in a way similar to the twist shown in Fig. 3. The exception is the propeller value, as also shown in Fig. 3, which on the average is 36% higher in the room temperature structure. It is not clear whether this difference represents a real structural feature due to the different temperature of the sample or a refinement artifact due to the lower resolution available at room temperature.   Due to the difference in temperature, the overall dimensions of the unit cell are smaller in the low temperature sample. The cell decreases by about 1.4% both in the x and y directions and by 2.6% in the z direction. These changes in the cell dimensions are paralleled by an overall shrinkage of the dimensions of the duplex upon cooling. The external diameter as measured by the average phosphate/phosphate distances in a base pair decrease by about 1%, whereas the distances between C1Ј atoms in a base pair do not change: The phosphodiester backbone moves inward, whereas the base pairs do not change dimensions. In the z direction the duplex also shrinks, the average rise decreases from 3.48 to 3.39 Å, a compression equivalent to the 2.6% decrease of the c dimension of the unit cell. All these changes reflect a decrease in the van der Waals distances among atoms.
Despite all these changes, the conformational angles of the phosphodiester chain do not vary much when both structures are compared. In particular, the ␦ angles, which define the sugar pucker, and the ⑀/ pair, which distinguish the BI/BII conformations (to be discussed below) are quite similar in corresponding residues of both structures. An interesting difference is the ␥ angle, which varies very little at low temperatures throughout the sequence, with a standard deviation of 2.9°, whereas at room temperature the standard deviation increases to 8.6°. In both cases the average value is 47°. This difference in behavior is probably a result of the lower resolution of the room temperature crystal. A similar behavior, but more restricted, is found in the ␣ angle. All other conformational angles show a similar variability in both structures.   Another feature of interest shown in Figs. 2 and 3 is the comparison with the same sequence in the central part of the dodecamer d(CGCGAATTCGCG), which has also been recently crystallized at high resolution (19) in the presence of Mg 2ϩ . Although there are differences in detail, the general trend of the conformational parameters is similar in both cases (Fig. 3), whereas the B factor of the atoms follows a somewhat different trend as shown in Fig. 2.
A peculiar feature of both nonamer and dodecamer structures is the value of the ␦ angle in the central thymine residues of the AATT sequence, which in all cases has a value of around 110°and systematically deviates from the canonical C2Ј-endo conformation of the rest of the residues in the duplexes.
The high resolution of the nonamer structure allowed us also to study the position of the C1Ј atoms. As discussed in the "Materials and Methods," we found that the latter sugar atoms are not coplanar with the bases at which they are bound. In Fig. 4 a plot is presented that shows that there is a moderate correlation with the glycosidic angle , but other factors may have an influence.
Phosphate Conformation-As it was stated in the introduction, one of the conspicuous features of high resolution DNA structures (20,21) is the presence of phosphate groups with a multiple conformation. Some examples are given in Fig. 5. We have found nine phosphates with a single conformation, both of BI and BII types (22), four phosphates with a multiple conformation (2, 7, 11, and 18), and three phosphates (9, 12, and 14) that show additional electron density, which has been interpreted as a sign of conformational disorder, as discussed under "Materials and Methods." Inspection of Table III shows that the double conformations found in some phosphate groups are mainly associated with simultaneous changes in the values of the ␣ and ⑀ angles, changes of which may exceed 50°.
The C3Ј-O3Ј-P conformational angles of all phosphodiester residues, which define the BI/BII conformations, are represented in Fig. 6. There are ten residues with the BI conformation and six with the BII conformation. Equivalent residues in both strands have similar conformations. Those phosphates, which have a double conformation, do not vary the type of conformation: There is no phosphate with alternate BI/BII conformations.
Inspection of Fig. 6 shows that the BI conformation of different residues does not show much change, whereas the BII conformation may span a much larger region of conformational space. Another feature of interest is that the different points do not show any trend to fall onto the ⑀ Ϫ ϭ Ϯ90°lines, which had been suggested as diagnostic of the BII/BI conformations (22). It appears more logical to define such conformations only on the basis of the angle, which is close to Ϫ90°in the BI conformation and to 170°in the BII conformation. The ⑀ angle varies much more in either conformation. No intermediate value of is found in this oligonucleotide, whereas in some FIG. 5. Examples of the 2 F o ؊ F c electron density map of phosphate groups. The stereo maps are contoured at 2. Phosphates 3 and 12 have clear single conformations, but phosphate 12 presents additional density, which has been modeled as an oxygen atom with partial occupancy as discussed under "Materials and Methods." Phosphate 2 shows a clear double conformation, whereas phosphate 11 has a less ordered double conformation, which probably corresponds to multiple conformations. The B factor for the phosphorous atom is given in each case and for the additional oxygen atom in phosphate 12. dodecamer structures there are a few phosphate groups with such values (22,23).
The BI/BII change is like a crankshaft motion with correlated changes in the ␤ and angles, which move the phosphate group toward the interior part of the minor groove. From Table  III it can be calculated that the average value of ␤ is 177°in the BI conformation and decreases to 149°in the BII conformation, in parallel with the changes of mentioned above and represented in Fig. 6.
Crystal Structure-The duplexes are organized in the crystal as layers (shown in Fig. 7, top left). Each duplex is surrounded by another six duplexes, four of which are in close contact, whereas the other two are at greater distance. As a result, channels of solvent are defined along the x axis of the cell. These channels are also visible in the unit cell representation given in Fig. 7 (top right). As we will show below, these channels contain disordered solvent. Each duplex is associated with neighbors above and below so that the unpaired guanines 1 and 10 form minitriplexes with neighbor duplexes (Fig. 7, bottom) and stabilize infinite columns along the z axis of the cell. However, the axes of the duplexes in different layers do not coincide, therefore, the solvent channels occur in different po- sitions in neighbor layers.
Organization of Counterions: an Ionic Crystal Around the Triplexes-Some of the Mg 2ϩ ions have the typical octahedral coordination with associated waters. In other cases the associated waters are much more disordered, as shown in Fig. 8. One chloride and six Mg 2ϩ ions maintain an ionic network throughout the crystal at the level of the region where triplexes are formed. The fact that most Mg 2ϩ ions are found to be located around the minitriplex (Fig. 7, bottom) supports their important role in triplex structure stabilization (24).
Four Mg 2ϩ cations interact with two or three duplexes either directly or through their hydration waters. These interactions stabilize the crystal lattice. In fact, Mg 2ϩ ions may be considered as organized in a hydrated tube, which runs among the crystallized duplexes as shown in Fig. 7 (top left). The crystal may thus be considered as organized in layers, with positive and negative charges covering both ends of the duplexes shown in Fig. 7 (top left). In the latter region there is an excess of positive charges, which are probably neutralized in the crystal by additional chloride ions that have not been detected. The single localized chloride ion interacts with the N4 atom of cytosine 2, but also with the O6 atom of guanine 10 of a neighbor duplex, which is an unusual interaction between two electronegative atoms. Such an interaction is possible, because the negative charge of the chloride ion is probably weakened by the two Mg 2ϩ ions and the amino group that surround it.
There are two magnesium ions, 19 and 49, which only interact with one duplex. They occupy equivalent positions at both ends of the duplex on the major groove side. Magnesium 19 is highly ordered, as shown in Figs. 8 and 9, and has a very low B factor (6.5). It was also found with a low B factor in the room temperature structure (4). The precise interactions shown in Fig. 9 suggest that this is a major groove-specific site for Mg 2ϩ ions at a GA base step, with water/base hydrogen bonds at O6 and N7 of guanine and O4 of thymine. However, inspection of other sequences crystallized in the presence of Mg 2ϩ do not show such an interaction. The G12A13 base step at the other side of the duplex only shows a partially ordered Mg 2ϩ ion (number 49), which is completely absent in the room tempera-ture structure. In conclusion, it is not clear why Mg 2ϩ 19 occupies such a precise position on the duplex with a low B factor and no interactions with other duplexes in the crystal. Perhaps the chloride ion helps to stabilize its position.
A seventh Mg 2ϩ ion, number 38, lies at the edge of the phosphodiester backbone on the major groove side and contributes to cement the crystal lattice at the central region of the duplexes. The hydration waters of Mg 2ϩ 38 interact with phosphates 4, 14, and 15, each from a different duplex. This ion is shown in yellow in Fig. 7. It was found in a region of the crystal different from that occupied by the other Mg 2ϩ ions.
In summary, as a result of all these interactions, each duplex is in contact with 14 well defined Mg 2ϩ ions, 12 of which cross-link with neighbor duplexes. The distribution of such Mg 2ϩ ions is very irregular, as it is clearly apparent from Fig.  7. Additional disordered Mg 2ϩ should be present in the disordered solvent channels.
The Ordered Water Regions-Ninety-seven of the total water molecules, which have been localized, are in contact with one or more DNA atoms. Because some of them cross-link with several duplexes, each duplex is in fact covered by about 120 water molecules. In general, hydration sites correspond to those described by Schneider et al. (25,26). However, the water hydration of different residues is not regular. The base pairs C2⅐G18 and G9⅐C11 involved in the formation of triplexes are less hydrated than the other base pairs, with only 10 -11 waters associated per base pair. This is in part due to the fact that the additional guanine in the triplex satisfies part of the hydrogen bonding potential of the base pairs. Also, the phosphates 6, 7, and 8, which face the poorly ordered solvent region (see below), have only an average of two waters per phosphate, whereas most other phosphates have four to five associated waters.
The rest of the water molecules (54) cross-link other waters and Mg 2ϩ ions and create a network of water molecules placed among neighbor duplexes. Part of this network is shown in Fig.  10. Water structure is not regular; polygons of different sizes are formed. In fact only one third of the water molecules (excluding those coordinated to Mg 2ϩ ) have a tetragonal coordination, as is apparent from Fig. 11 and has been found in other cases (27,28). Thus, although the water network is very well organized, it has no regular structure. Polygons similar to those described by other authors are found (28 -32). Pentagons predominate, but other polygons are also present, some of them clearly puckered, as found in other cases (32). Such a polygonal structure is reminiscent of that found in some forms of ice, although the most stable form of ice consists of six-membered rings of water molecules (33).
The ordered water region we have just described should correspond to a stabilization of the room temperature water/ ionic network, which is not detected at room temperature prob-ably as a result of the molecular mobility being too high. It is unlikely that the polygonal structure might be related to low density amorphous ice (34) or any other structure different from that found at room temperature, because the same structure is found in all the unit cells in the crystal.
In the 2.05-Å resolution structure (4) a partially ordered organization of intermolecular waters is only found in the triplex region. Very few water molecules are visible in the region shown in Fig. 10. Most waters in this structure are directly associated with the duplex. Other waters correspond to some of the Cl Ϫ and Mg 2ϩ ions we have located but do not show additional waters in an octahedral coordination.
The Disordered Solvent Channel-In the solvent channel shown in Fig. 7, very few water molecules were found; practically all of them were directly hydrogen-bonded to DNA atoms. Most of the 36 water molecules missing in the asymmetric unit (as described under "Materials and Methods") should be found in this channel. Six of the phosphates in this region do not have any Mg 2ϩ ion in their neighborhood, as indicated in the figure.
The closest Mg 2ϩ ion is at 8.5 Ϯ 1.5 Å, so there is no possibility of direct contacts of the phosphate oxygens with the coordination waters of Mg 2ϩ . The latter phosphates are also poorly hydrated and have the largest B factors. It is likely that there are disordered Mg 2ϩ ions in the channel that contribute to neutralize the phosphate charges. In fact, charge neutralization in this crystal structure is not simple. In the region shown in Fig. 7 (bottom), positive charges predominate, whereas in the disordered solvent channel phosphate charges are in excess. In total, there are 17 negative ionic charges in the asymmetric unit and only 14 positive ionic charges, so additional disordered Mg 2ϩ and probably chloride ions should be present in the crystal. In other high resolution structures (19,21,35), it is also found that a significant number of counterions are not visible in the x-ray analysis.
It is interesting to note that the well ordered water spine in the minor groove is localized with its greater part precisely facing this disordered solvent channel. The well ordered organization of the water molecules in the water spine may in fact limit their potential to organize in a precise manner other water molecules and ions at the surface of the duplex. In the Mg 2ϩ crystal form of d(CGCGAATTCGCG) (19), it is also found that there are very few ordered water molecules at the surface of the water spine in the minor groove.
In summary, the absence of structure in the disordered water channel probably corresponds more accurately to the structure of DNA in solution, with no precise organization of water molecules and ions. An exception are the tightly bound water molecules in the water spine, which should not be expected to change position easily.
Water Interactions on Hydrophobic Surfaces-Each duplex has clear hydrophobic regions such as the thymine methyl groups and the exposed surface of the terminal guanines. All these groups are covered by a net of hydrogen-bonded waters that lie at van der Waals distances (3.5-4 Å) from the hydrophobic carbon atoms, as shown in Fig. 12. Thus the methyl groups of thymine are covered by an ordered layer of water molecules. The same is true for the surface of guanine 10. In the latter case no sign of hydrogen bonding interaction with the electrons of the base is apparent. An exception of the ordered waters we have described is the equivalent guanine 1, where no water molecules are visible at the surface of the base at distances less than 4 Å. It appears that solvent is disordered in the latter region. DISCUSSION One of the conclusions of this study is that the duplex structure found at high resolution is practically identical to the one determined at room temperature at 2.05-Å resolution. This observation gives confidence to the data deposited in the Nucleic Acid Database (36), which have been mostly determined at resolutions in the 2-to 2.5-Å range. On the other hand, our work shows that the conformation of the phosphodiester backbone may be more variable than expected from the low resolution/room temperature data. Almost half of the phosphates in the duplex show multiple conformations. A similar situation has been found in high resolution structures of proteins, which show multiple side chain conformations (37). Such variability should be interpreted as static disorder at the temperature (120 K) of the experiment. But it does reflect the dynamic disorder found at room temperature: Upon fast cooling the sample provides a snapshot of some of the conformations available at room temperature. Several magnesium ions also show disordered conformations (Fig. 8), which indicate a partial delocalization.
The picture that emerges from this study is that the solvent in the crystal is disorganized in some regions, but very well ordered in other regions. Such different organizations of the solvent in the same crystal have also been found in other cases (28,38). The well ordered ionic region found in our case is shown in Figs. 7 and 10. A complex network of ions and water molecules hold the oligonucleotides in an adequate position and stabilize the crystal. However, no general rules can be derived on the spatial organization of charges in the crystal. It appears that most of the Mg 2ϩ ions are organized as hydrated tubes that run among the oligonucleotide duplexes as shown in Fig. 7. Thus, the DNA surface does not define regions of charge complementarity, counterions are distributed in an apparently irregular manner that contributes to stabilize the crystal lattice.
In another region of the crystal, a channel of disordered solvent is found (Fig. 7). That channel should contain disordered counterions and solvent. The phosphates that face that channel have no apparent Mg 2ϩ ions nearby, as shown in Fig.  7 (top right). They also have comparatively high B factors, as demonstrated in Fig. 13. The oxygen atoms bound at the phosphates, which face the disordered solvent channel, are shown in blue in that figure. It is apparent that they are delocalized. Thus, the negative charge of the phosphate groups is spread over a large surface. Therefore, it is not surprising that solvent and counterions are also poorly organized when placed close to this region of the duplex.
The spine of hydration, which we analyzed in a previous paper (2), is also shown in yellow in Fig. 13. The B factors of the water molecules in the spine are also larger in the region of greater disorder of the phosphates. Nevertheless, these water molecules are clearly apparent in the spine of hydration but do not show further interactions with other solvent molecules. On the other hand, the well ordered water molecules at the lower end of the spine participate in the network of ordered water molecules shown in Fig. 10.
The picture of the duplex shown in Fig. 13 is one with delocalized negative charges in those regions, which do not participate in establishing an ionic crystal as described above. Positive counterions should also show a large extent of disorder and in fact are not visible in the disordered solvent channel. A further contribution to charge delocalization are the water molecules that are associated with phosphate oxygens and Mg 2ϩ ions. Partial charge transfer to water molecules should take place so that electrostatic charges are spread over a considerable volume. A fragment of DNA in the cell nucleus should look more like the blue regions of Fig. 13, with highly spread negative charges. A picture of DNA with precisely localized negative charges on a double helical array does not appear to give a correct picture of its electrostatic nature. This view is in agreement with Manning's theory (39), which presents DNA as a weakly charged polyelectrolyte with a high percentage of positive counterions trapped in a random way close to its surface.