Crystal Versus Solution Structures of Thiamine Diphosphate-dependent Enzymes*

The quaternary structures of the thiamine diphosphate-dependent enzymes transketolase (EC 2.2.1.1; from Saccharomyces cerevisiae), pyruvate oxidase (EC1.2.3.3; from Lactobacillus plantarum), and pyruvate decarboxylase (EC 4.1.1.1; from Zymomonas mobilis and brewers' yeast, the latter in the native and pyruvamide-activated forms) were examined by synchrotron x-ray solution scattering. The experimental scattering data were compared with the curves calculated from the crystallographic models of these multisubunit enzymes. For all enzymes noted above, except the very compact pyruvate decarboxylase from Z. mobilis, there were significant differences between the experimental and calculated profiles. The changes in relative positions of the subunits in solution were determined by rigid body refinement. For pyruvate oxidase and transketolase, which have tight intersubunit contacts in the crystal, relatively small modifications of the quaternary structure (root mean square displacements of 0.23 and 0.27 nm, respectively) sufficed to fit the experimental data. For the enzymes with looser contacts (the native and activated forms of yeast pyruvate decarboxylase), large modifications of the crystallographic models (root mean square displacements of 0.58 and 1.53 nm, respectively) were required. A clear correlation was observed between the magnitude of the distortions induced by the crystal environment and the interfacial area between subunits.

Over the past decade, tremendous amounts of high-resolution structural information have been obtained about biological macromolecules using x-ray crystallography and nuclear magnetic resonance. Whereas the application of the latter method is limited to monomeric proteins with molecular masses below 30 kDa, x-ray crystallography yields atomic models of oligomeric macromolecules with high (hundreds of kilodaltons) molecular masses. The question arises nevertheless whether the macromolecular structures under physiological conditions in solution are preserved in the crystal environment. This ques-tion is of special importance for multisubunit enzymes as the mechanisms of their functioning often require conformational changes within or between the subunits (e.g. for opening/closing the active sites). Being noncovalent in nature, interactions between the subunits are expected to be of the same order of magnitude as those between neighboring molecules in the crystal determined by the crystal packing forces. The latter may therefore influence the arrangement of the subunits and distort the quaternary structure of the enzymes in the crystal.
Small-angle x-ray scattering (SAXS) 1 is an effective method to study the low-resolution structure of biological macromolecules under nearly physiological solutions, and it is applicable in a broad range of conditions and sizes of macromolecules (1). As the SAXS curves are sensitive to the overall shape and quaternary structure of the solute particles, comparisons between the experimental scattering profiles and those calculated from the crystal structures have long been used to validate the crystallographic models in solution (2)(3)(4). Recently, methods have been developed to compute solution scattering patterns from atomic coordinates taking into account the influence of the hydration shell (5,6) and to rapidly evaluate scattering from multisubunit complexes (7). These methods were successfully applied to model the solution structures of complex particles by rigid body movements of the structural domains (8 -10). Significant differences between the experimental scattering profiles and those calculated from the crystal structures have been reported for several multisubunit proteins, and rigid body modeling has been used to account for these differences (11,12). In this work, the rigid body refinement approach was used to systematically analyze the quaternary structure of thiamine diphosphate (TDP)-dependent enzymes from different species.
The mechanism of catalysis of TDP-dependent enzymes has been studied for decades with different methods (see Ref. 13 for a review). Recently, the crystal structures of transketolase from the recombinant wild type of Saccharomyces cerevisiae (ScTK) (14,15), pyruvate oxidase from a stabilized mutant of Lactobacillus plantarum (LpPOX) (16,17), pyruvate decarboxylase from brewers' yeast and brewers' yeast strain in native (18,19) and pyruvamide-activated (20) 2 forms (ByPDC forms A and B, respectively), and pyruvate decarboxylase from the recombinant wild type of Zymomonas mobilis (ZmPDC) (21) have become available. All these enzymes consist of identical (or nearly identical) subunits with molecular masses of ϳ60 kDa, and they display the same so-called "V" conformation (22,23) of TDP in the active centers. At the same time, differences in subunit arrangement lead to very different quaternary structures.
The pyruvate decarboxylases from yeast and plants (but not that from the bacterium Z. mobilis) are activated by their substrate, pyruvate (24,25). Tritium-hydrogen exchange studies (26), cross-linking (27), and previous SAXS studies of By-PDC revealed a large conformational change during enzyme activation by the substrate (pyruvate) or its surrogate, pyruvamide. The low-resolution shapes of tetramers of native (form A) and pyruvamide-activated (form B) ByPDCs (28,29) and ZmPDC (30) obtained ab initio from the SAXS data were later confirmed by their crystal structures (18 -21). Moreover, comparison of the experimental and calculated profiles for tetrameric ByPDC suggested that the quaternary structure of the enzyme in solution is more compact than that in the crystal (30). To systematically analyze the influence of crystal packing on the quaternary structure, SAXS experiments on the five enzymes with known crystal structures were performed. The observed differences between the experimental scattering profiles and those computed from the crystallographic models are analyzed in terms of rigid body movements of the subunits.

EXPERIMENTAL PROCEDURES
Enzyme Preparation-Pyruvate decarboxylase from brewers' yeast was isolated as described (31) with some modifications (32,33). Pyruvate decarboxylase from the brewers' yeast strain was isolated as described (20). Pyruvate decarboxylase from the recombinant wild type of Z. mobilis was isolated as described (21). Preparation of transketolase from the recombinant wild type of S. cerevisiae was as described (34). Pyruvate oxidase isolated from a triple mutant from L. plantarum (35) was a gift from the Biochemical Research Centre, Roche Molecular Biochemicals (Penzberg, Germany).
Solution Scattering Experiments and Data Processing-The SAXS data were collected following standard procedures using the X33 camera (36 -38) of the European Molecular Biology Laboratory in HASY-LAB on the storage ring DORIS of the Deutsches Elektronen Synchrotron at Hamburg using multiwire proportional chambers with delay line readout (39). Data were collected at three different camera lengths (1.3, 2.7, and 4 m) to cover the range of momentum transfer: 0.1 Ͻ s Ͻ 5.0 nm Ϫ1 (s ϭ 4sin/, 2 is the scattering angle, and ϭ 0.15 nm is the wavelength). Protein concentrations were 3-15 mg/ml for ZmPDC, 5-30 mg/ml for ByPDC form A, 4 -10 mg/ml for ByPDC form B, 2-10 mg/ml for ScTK, and 4 -20 mg/ml for LpPOX. Buffer and pH conditions during the SAXS measurements were, in all cases, identical to those for crystallization of the enzymes. The experimental data were normalized to the intensity of the incident beam, corrected for the detector response; the buffer scattering was subtracted; and the statistical errors were calculated using the program Sapoko. 3 The data recorded at lower concentrations using longer camera lengths (lower angles) were merged with those recorded at higher concentrations and shorter camera lengths to yield final composite scattering profiles. The latter were processed with the program Gnomoko, a version of the indirect transform package Gnom (40 -42), to obtain the forward scattering intensity (I(0)) and the radius of gyration (R g ). The molecular masses of the solute were calculated by comparison of the I(0) values with those from reference solutions of bovine serum albumin (Sigma).
Rigid Body Modeling-The atomic models of ScTK, LpPOX, ByPDC forms A and B, and ZmPDC were taken from the Protein Data Bank (43), codes 1trk (15), 1pow (16), 1pvd (19), 1ypd (20), and 1zpd (21), respectively. The scattering curves from the crystallographic structures were calculated using the program Crysol (5), which surrounds the macromolecule in solution by a 0.3-nm-thick hydration layer with an adjustable density ( b ). The scattering from a particle in solution is shown in Equation 1, where A a (s) is the scattering amplitude from the particle in vacuo; A s (s) and A b (s) are these from the excluded volume and the hydration layer, respectively, both with unitary density ␦ b ϭ b Ϫ s ; s is the density of the bulk solvent; and ͗ ͘ stands for the spherical average in reciprocal space. Intensity in Equation 1 depends on the average excluded volume per atomic group r a (which changes the excluded particle volume V and thus A s (s)) and on the contrast of the hydration layer ␦ b . Default values for proteins are r a Х 0.161 nm 3 and ␦ b Х 30 e/nm 3 , corresponding to a partial specific volume of 0.73 ml/g and a bound solvent density of 1.1 g/ml (5,6). Given the atomic coordinates, the program either predicts the SAXS profile (e.g. using the default values) or fits the experimental data, if they are available, by minimizing the discrepancy as in Equation 2, where N is the number of experimental points, and I(s), I exp (s), and (s) denote the calculated curve, the experimental intensity, and its standard deviation, respectively. The parameters are adjusted in the range 0.158 Ͻ r a Ͻ 0.165 nm 3 and 0 Ͻ ␦ b Ͻ 0.09 e/nm 3 (5).
For the rigid body refinement of dimeric ScTK, the crystallographic model was oriented so that the 2-fold axis transforming one monomer into the other coincided with the y axis and the line connecting the centers of mass of the monomers coincided with the z axis. The parameters to refine were the Euler angles of rotation (␣, ␤, and ␥) of the first monomer around the center of mass and its shift along the z axis (⌬z). Both rotation and shift of the monomer were performed with respect to its reference position in the crystallographic dimer (in the latter position, ␣ ϭ ␤ ϭ ␥ ϭ ⌬z ϭ 0). The scattering amplitude of the monomer in the reference position was evaluated using Crysol with the default values of r a and ␦ b . The symmetry-related amplitude was generated from an arbitrary set of values (␣, ␤, ␥, and ⌬z) to rapidly compute the intensity from the entire dimer as described (44). An automated search was performed to find the parameters providing the best fit to the experimental scattering data from the dimer. The values of r a and ␦ b were then refined by running Crysol again on the entire dimeric structure corresponding to the optimized positional parameters.
A similar search was performed for the tetrameric proteins (LpPOX, ByPDC forms A and B, and ZmPDC) in terms of the relative positions of the dimers in the tetramer. The scattering amplitudes of the crystallographic dimers were evaluated using Crysol; the dimers were oriented so that the 2-fold axis coincided with the y axis and displaced along the z axis. The fit of the experimental scattering data from the tetramer yielded the positional parameters of the dimers in the entire enzyme. For LpPOX, ByPDC form A, and ZmPDC, the ␤ and ␥ values were fixed to zero to keep 222 the point symmetry of the tetramers observed in the crystal (i.e. only rotations around the z axis were allowed).

Structural Parameters of the TDP Enzymes-
The structural parameters of the enzymes computed from the SAXS data are presented in Table I. The molecular mass estimates from the forward scattering agree well with the theoretical values calculated on the basis of the amino acid sequences deduced from those of the structural genes and indicate that ScTK is dimeric and the others are tetrameric in solution under the experimental conditions.
Solution Structure of ZmPDC-The SAXS data from tetrameric ZmPDC is presented in Fig. 1 (curve 1), and its crystallographic model is shown in Fig. 2. The scattering curve from the atomic structure computed by Crysol fits the experimental data with ϭ 0.88 for a radius of the atomic group r a ϭ 0.164 nm and a contrast of the hydration layer ␦ b ϭ 16 e/nm 3 . The experimental R g ϭ 3.98 Ϯ 0.06 nm agrees well with the calculated value accounting for the solvation shell (3.90 nm). Rigid body modeling yielded no significant improvement of the fit compared with that in Fig. 1 (curve 2), suggesting that the mutual arrangements of the dimers in tetrameric ZmPDC in the crystal and in solution are identical.
Solution Structure of LpPOX-The experimental scattering profile from tetrameric LpPOX is presented in Fig. 3a, and the crystallographic model of the enzyme is shown in Fig. 4A (left). The fit to the experimental data computed by Crysol at r a ϭ 0.163 nm and ␦ b ϭ 44 e/nm 3 yields ϭ 1.62. Although the experimental R g ϭ 4.06 Ϯ 0.03 nm agrees with the calculated value of 4.07 nm, systematic deviations between the experimental data and the curve computed from the crystal structure (Fig. 3a, curves 1 and 2) in the range of the first shoulder (s Х 1 nm Ϫ1 ) point to a difference in the quaternary structure. Rigid body modeling yielded a better fit to the experimental data (Fig. 3a, curve 3) after rotating the crystallographic dimer by ␣ ϭ 3°and increasing the distance between the dimers from 4.22 nm in the crystal structure to 4.56 nm (⌬z ϭ 0.17 nm). The resulting model of LpPOX in solution is presented in Fig. 4A (right) and yields ϭ 1.36 at r a ϭ 0.163 nm and ␦ b ϭ 22 e/nm 3 (R g ϭ 4.06 nm). The root mean square displacement between the atomic coordinates of the crystal and solution models is 0.23 nm, and the main difference between the two structures is a larger separation of the dimers, leading to a less compact arrangement of the dimers than in the crystal.
Solution Structure of ScTK-The crystallographic model of dimeric ScTK is shown in Fig. 4B (left). Fig. 3b presents the experimental scattering data (curve 1) along with the fit ( ϭ 1.77) computed from the crystallographic model by Crysol at r a ϭ 0.165 nm and ␦ b ϭ 38 e/nm 3 (curve 2). The experimental R g ϭ 3.40 Ϯ 0.03 nm is somewhat larger than the calculated value (3.28 nm), and systematic deviations were observed between the experimental and calculated profiles for s Ͼ 1 nm Ϫ1 . The rigid body modeling reduced the discrepancy to ϭ 1.43 for the rotation angles ␣ ϭ 0, ␤ ϭ ␥ ϭ 3°, and ⌬z ϭ 0.21 nm (the distance between the monomers increased from 2.80 to 3.22 nm). The model of ScTK in solution (Fig. 4B, right) yields R g ϭ 3.30 at r a ϭ 0.165 nm and ␦ b ϭ 14 e/nm 3 , and the root mean square displacement between this model and the crystallographic one is 0.27 nm.
Solution Structure of Native ByPDC (Form A)-The SAXS profile from this form of ByPDC in Fig. 3c (curve 1) was recorded at pH 5.3 and corresponds to a tetrameric enzyme (28). The crystallographic model of the native tetrameric ByPDC is displayed in Fig. 4C (left), and the theoretical curve computed from this model by Crysol (r a ϭ 0.161 nm and ␦ b ϭ 0) deviates significantly from the experimental data (Fig. 3c, curves 2 and  1, respectively; ϭ 1.68). The experimental value of R g ϭ 3.97 Ϯ 0.03 nm is smaller than that computed from the crystallographic model (4.13 nm). This indicates that the structure in solution is more compact than that in the crystal, in agreement with earlier results (30). Rigid body modeling provided the fit in Fig. 3c (curve 3) by reducing the distance between the centers of the dimers from 5.50 to 4.74 nm (⌬z ϭ Ϫ0.38 nm) at ␣ ϭ Ϫ11°. The resulting solution structure in Fig. 4C (right) has a root mean square displacement of 0.58 nm with respect to the crystallographic model and provides a good overall fit to the experimental data with ϭ 0.94 (r a ϭ 0.165 nm, ␦ b ϭ 6 e/nm 3 , and R g ϭ 3.94 nm). Comparison of the crystal and solution models in Fig. 4C indicates that the tilt of the dimers in combination with the smaller separation between their centers leads to an essentially more compact model of native ByPDC in solution.
Solution Structure of Pyruvamide-activated ByPDC (Form B)-The experimental scattering profile from tetrameric By-TABLE I Structural parameters of the crystallographic models and of those obtained by rigid body refinement MM calc and MM SAXS are the molecular masses calculated from the amino acid sequences corresponding to the structural genes and from the scattering data, respectively. Res. is the resolution of the crystallographic model. S is the interaction area between the two monomers for ScTK (15) or between the functional dimers for the other enzymes (21). cryst and sol are the discrepancy in the fits to the experimental data computed from the crystallographic and solution models, respectively. ␣, ␤, and ␥ and 2⌬z are Euler angles of rotation and shift along the z axis of the subunit in the crystallographic model, respectively. r.m.s.d. is the root mean square displacement between the atomic coordinates of the crystallographic and solution models.  Fig. 2  (curve 2). The ordinate axis is labeled as lg I, relative to indicate that the fit is presented in relative units on a logarithmic scale.  Fig. 3d (curve 1) was collected under the same conditions as that of native ByPDC (except for the addition of 0.3 M pyruvamide to the former). The scattering curve calculated from the crystallographic model in Fig. 4D (left) at r a ϭ 0.161 nm and ␦ b ϭ 4 e/nm 3 displays a poor ( ϭ 3.45) agreement with the experimental data in the entire angular range (Fig. 3d, curve 2). The R g ϭ 3.97 nm computed from this model is smaller than that of the crystallographic model of native ByPDC (i.e. the former model is more compact than the latter). Comparison of the experimental values suggests the opposite, namely, that activated ByPDC in solution (experimental R g ϭ 4.20 Ϯ 0.03 nm) should be less compact than the native enzyme (45). Interestingly, the crystallographic structure of native By-PDC (form A) provides a somewhat better fit with ϭ 2.02 (data not shown) to the experimental scattering data of ByPDC form B. The latter profile can be neatly fitted ( ϭ 1.38) by rotating the crystallographic dimer of form B by ␣ ϭ 108°, ␤ ϭ 9°, and ␥ ϭ 52°at ⌬z ϭ 0.35 nm to increase the distance between the dimers from 4.68 to 5.38 nm. The resulting structure (Fig. 4D, right) has R g ϭ 4.16 nm at r a ϭ 0.165 nm and ␦ b ϭ 22 e/nm 3 . Despite a very large root mean square displacement of 1.53 nm with respect to the crystallographic model of  ByPDC form A (c), and ByPDC form B (d) by rigid body refinement. Curve 1, experimental scattering data; curves 2 and 3, scattering curves computed from the models in the crystal presented in Fig. 4 (left orientations) and from the refined models in solution (Fig. 4, right orientations), respectively. The ordinate axes are labeled as lg I, relative to indicate that the fit is presented in relative units on a logarithmic scale.

PDC form B in
ByPDC form B, the arrangement of dimers in the solution model is qualitatively closer to the crystallographic structure of form B than to that of form A in Fig. 3c. Indeed, the long axes of the dimers in the solution model form an angle of 42 o in the plane of Fig. 4D (bottom orientations), close to 30.1 o observed for form B in the crystal, but differing remarkably from a nearly parallel orientation in the crystal structure of native ByPDC (form A).

DISCUSSION
Solution scattering is sensitive to the quaternary structure of the solute particles, and movements of large structural domains as rigid bodies result in noticeable changes in the scattering profiles. This permits the establishment of the mutual positions and orientations of the subunits in multisubunit enzymes by rigid body refinement of the high-resolution crystallographic models against the SAXS data. This modeling requires variation of a few positional parameters only. In keeping with the low information content of the scattering data, no attempt was made to account for possible changes in the tertiary structure of the enzymes. The latter changes would also have had relatively little impact on the discrepancy between the experimental and calculated scattering profiles (Equation 2) dominated by the strong scattering at low angles.
It is remarkable that significant differences between the experimental scattering data and the curves computed from the crystallographic models would have been found for all investigated enzymes but one (ZmPDC). Minor modifications of the crystallographic models were sufficient to significantly improve the fit to the experimental data from LpPOX and ScTK. In contrast, fitting the scattering data from both the A and B forms of ByPDC required large movements of subunits. There is a clear correlation between the intersubunit interaction areas in Table I and the differences observed between the crystal and solution structures. Tetrameric ZmPDC is formed by tightly packed dimers (Fig. 2), and the intersubunit contacts seem to be sufficiently strong not to be disturbed by the crystal packing forces. The situation is similar for the rather compact LpPOX tetramer and ScTK dimer (Fig. 4, A and B), and only minor subunit displacements are observed in the crystal. The enzymes with looser subunit packing (ByPDC forms A and B) (Fig. 4, C and D) are, on the contrary, susceptible to the influence of the packing forces, and their solution models differ significantly from the crystal structures. A similar correlation has recently been found for two crystal forms of the allosteric enzyme aspartate transcarbamylase (11). The quaternary structure of the compact T-state of the enzyme is preserved in solution, whereas there are large differences between the solution and crystal models of a looser R-state. These results support the hypothesis that differences between the quaternary structures in the crystal and in solution are caused by the crystal environment distorting the arrangement of the subunits. The influence of the chemical environment as a cause of the difference can be excluded as the scattering experiments in this study were performed in the crystallization buffers of each enzyme.
In all cases, rigid body modeling enabled us to significantly reduce the systematic deviations between the experimental and calculated data. In other words, the crystallographic models could be reconciled with the observed SAXS profiles by movements of dimers in the case of tetrameric enzymes and of monomers in the case of dimeric ScTK. The residual deviations at higher angles for ScTK (Fig. 3b) are at the limit of the experimental precision as the data are extremely sensitive to background subtraction in this range. It is also worth noting that the contrast of the bound water in the hydration shell was found to be positive for all the enzymes studied (6 Ͻ ␦ b Ͻ 22 e/nm 3 corresponding to a bound water density between 1.02 and 1.07 g/ml). When the hydration shell was not taken into account, the fits to the experimental data were significantly worse. This corroborates the earlier finding (5, 6) that the density of the bound water around proteins is higher than that of the bulk.
Most of the enzymes studied (LpPOX, ScTK, and ByPDC form B) appear less compact in solution than the corresponding crystallographic models, and higher flexibility of the enzymes in solution may be necessary for catalytic activity. Native By-PDC (form A) is the only enzyme that is more compact in solution than in the crystal. A rather open form of this enzyme in the crystal has long been the subject of controversy, leading even to the hypothesis that this structure may in fact correspond to an activated enzyme (46). According to our analysis, the unusual openness of native ByPDC should be attributed solely to the influence of the crystal packing forces. The model of native ByPDC in solution in Fig. 4C nearly coincides with that of the pyruvate decarboxylase from the recombinant wild type of S. cerevisiae obtained earlier by rigid body refinement (30).
The most pronounced changes were observed for ByPDC activated with pyruvamide (form B). This can be expected as activation leads to opposite effects in the crystal (higher compactness) (20) and in solution (loosening of the quaternary structure) (45). It has been argued that the active sites must be closed to ensure catalysis (47,48). In the crystallographic model of native ByPDC (form A) (18,19), the dimers assemble into a loose tetramer with approximate 222 symmetry. The active sites are rather open and accessible to solvent because of disordered loop regions (residues 104 -113 and 290 -304). In the crystallographic model of pyruvamide-activated ByPDC (form B), two of the four active sites are closed, and the abovementioned loop regions are well ordered and shield the two closed active sites from the solvent. This large conformational change is achieved by an asymmetric distortion of the tetramer (rotation of one of the dimers by 30.1°around the x axis in Fig.  4D, bottom left orientation) that breaks the 222 symmetry. The structures of the dimers of both ByPDC forms are almost identical up to a small rotation of the middle R-domain (20). This means that the dimer arrangement of ByPDC has to be rather flexible for the conformational change accompanying substrate activation to be possible. The crystallographic model of pyruvamide-activated ByPDC shown in Fig. 4D (left) may reflect only one possible conformation adopted by the enzyme during crystallization. Another possible conformation is provided by the crystallographic model of ketomalonate-activated ByPDC (49), which displays a similar dimer-dimer arrangement lacking the 222 symmetry with a 24°distortion angle. Granted that different configurations are possible, the solution model probably yields an average position of dimers in the fully activated tetramer. It is interesting to note that both the crystallographic and solution models of ByPDC form B show two active sites closed (Fig. 4D, right). High flexibility of the ByPDC tetramers may also be the reason why the crystals of both forms diffract to lower resolution compared with the crystals of the other enzymes (Table I). CONCLUSION Despite limited resolution, solution scattering studies can usefully complement the picture of proteins provided by crystallographic snapshots. The results obtained here for the four TDP-dependent enzymes clearly demonstrate that the crystal packing forces significantly affect the architecture of multisubunit enzymes. There is a clear correlation between the magnitude of these effects and the interfacial area between the subunits. The solution models of most of the enzymes studied appear less compact than the crystallographic models, pointing to a higher flexibility of the enzymes in solution, which may be necessary for catalysis.