Filtering of the solution NMR restraints
The generation of oligomer conformations requires the use of intra-monomer restraints, and an objective method was used to filter among the solution NMR restraints observed for the Crh monomer, those still valid in the oligomer state observed by ssNMR. The filtering is based on ssNMR chemical shifts and provides restraints valid for microcrystalline as well as for precipitate states of Crh, as the same ssNMR spectrum was observed for both states.41
The possible interaction between β1 and β4 strands is formed very early during the protein oligomerization and crystallization, as it was observed from solution NMR chemical shifts.10
Interactions between strands β1 and β4 were thus imposed through distance restraints corresponding to hydrogen bonds between the β strands, extracted from the X-ray crystallographic structure of Crh. Equivalent information about interaction interfaces could be obtained by mutational studies,42
or molecular dynamics simulations.44
An iterative ARIA calculation was performed on a symmetric homodimer to filter among the monomer NMR distance restraints, those still verified in the dimer structure. The inputs were: (i) the ssNMR sequential assignment of the Crh dimer,21
(ii) the dihedral and intra-monomer hydrogen bond restraints deduced from the TALOS analysis of the ssNMR chemical shifts, (iii) the synthetic peak list built from the solution NMR distance restraints recorded on the residues 16–85. The synthetic peak list was submitted to ARIA along with the monomeric assignments in order to limit the number of restraint contributions and to consequently reduce the combinatorial analysis during the NOE assignment. The iterative ARIA run produced the mono_aria set of restraints. The contact map obtained from restraints mono_aria (, lower triangle) is quite similar to the contact map of the restraints mono_xray obtained by filtering the 1k1c restraints directly on the crystallographic structure 1mo1 (, upper triangle). The restraints mono_xray and mono_aria will be used as intra-monomer restraints during the ARIA calculations described below.
Figure 3 Comparison of the contact map obtained by filtering on the X-ray structure 1mo1 (upper triangle, empty circles) and of the contact map (restraints mono_aria) obtained by filtering monomer peak list using ssNMR chemical shifts (lower triangle, crosses). (more ...)
Presentation of ARIA calculations
Input restraints () include mono_aria and the TALOS restraints, described above, as well as the following inter-monomer restraints. Exact distances, measured on the structure 1mo1, for the inter-monomer peaks assigned on the spectrum NHHC,23
produce the restraints NHHC_xray. The NMR restraints NHHC_ssnmr are built from the NHHC peaks, using invariant bounds 2.5–4.5 Å. Additional inter-monomer restraints between the strands β1 and β4 were applied using hydrogen bond restraints (hbonds_B1B4) or using restraints 4.5–5.5 Å between Cα (CA B1B4), determined from 1mo1. Ambiguous inter-monomer restraints (AIR_inter) similar to the one used in HADDOCK33
were applied between all residues assigned to the dimer interface by chemical shift perturbation in solution.10
Three sets of ARIA conformers were generated (). The restraints used in the first conformer set (exact_xray
) were: mono_xray, NHHC_xray, TALOS and hbonds_B1B4, based on exact crystallographic distances. This calculation was followed by a water refinement step (w_exact_xray
). The second conformer set (nmr_xray
) was obtained using a mixed set of ssNMR and crystallographic restraints: mono_xray, NHHC_ssnmr, TALOS and hbonds_B1B4, in order to explore the conformational landscape in presence of restraints close to those observed in the crystal. Finally, the third conformer set (nmr
) was only based on NMR restraints (mono_aria, NHHC_ssnmr, TALOS) and on the information on dimerisation interface already observed in solution (CA_B1B4 and AIR_inter). This last conformer set intended to sample the conformational landscape of the Crh dimer of dimers during oligomerization and crystal formation. As no significant changes are observed between ssNMR spectra recorded on Crh micro-crystals and precipitates,41
it is possible to assume that ssNMR restraints give information about the Crh oligomer architecture in the crystal as well as in the precipitate.
The study of Crh by NMR in solution10
has shown that two modes of association are possible for the dimer, one arising via the swapping of the β1 strand. The crystallographic structure then gave the exact topology of the position of the strand β1.16
The hypothesis made in the present work that the dimeric state of Crh represent an initial stage of the crystal formation, implies that the hydrogen bonds between β1 and β4, are formed early in the oligomerization process. The associated restraints, hydrogen bonds or restraints between the Cα bring a determinant information for the convergence of the relative monomer positions in the dimer.
The dimer conformations obtained from the sets nmr_xray and nmr were further refined using additional non-crystallographic symmetry (NCS) restraints in geometric force field, to produce the sets NCS_nmr_xray and NCS_nmr. The application of non-crystallographic symmetry (NCS) restraints represents only a qualitative short-range modeling of the crystal or precipitate order. An additional water refinement step was finally performed on a conformations cluster extracted from NCS_nmr_xray and on two clusters extracted from NCS_nmr, to produce the sets wNCS_nmr_ xray, wNCS_nmrI and wNCS_nmrII. The sets wNCS_nmrI and wNCS_nmrII will be described more precisely in the section “Convergence of the calculation and fit to the NMR restraints”.
Convergence of the calculation and fit to the NMR restraints
Clustering-I, described in Materials and Methods was performed on the 50 lowest-energy conformers calculated in the geometric force field (exact_xray, nmr_xray and nmr), and for the conformations of NCS_nmr_xray and NCS_nmr, calculated using NCS restraints. The number of clusters, the cluster sizes, the backbone precision inside the clusters and the accuracy to the X-ray structure 1mu4, were analyzed in . The six clusters detected for exact_xray and their larger sizes in the 38–45 range prove the calculation convergence. The slight decrease of the coordinate precision inside the clusters and of the accuracy to the structure 1mu4, as well as the appearance of 5-members clusters, reveal a decrease of the convergence in nmr_xray. Nevertheless, more than 9 clusters are larger than 30 members, and the lower bounds of the RMSD are similar to those observed for exact_xray. The application of the NCS restraints to the nmr_xray conformers (NCS_nmr_xray), induces convergence and accuracy close to the ones observed for exact_xray. Indeed, the number of clusters is four and their sizes are in the range 41–45, these parameters displaying a similar order of value than in exact_xray. In nmr, a poor accuracy with respect to 1mu4 is obtained, as the coordinates RMSD to 1mu4 increased twofold with respect to other sets, the number of clusters is doubled, and the maximum cluster size is divided by two with respect to exact_xray. The application of NCS restraints (NCS_nmr) does not modify much this situation, which may be due to the relatively local symmetry applied.
Table 2 Results of the clustering-I performed on the 50 best-energy conformers generated in geometric force field (exact_xray, nmr_xray, nmr), and performed on the 50 conformers obtained after a refinement in presence of NCS restraints (NCS_nmr_xray, NCS_nmr (more ...)
The hierarchical clustering-II method, applied on clusters of conformations previously obtained, detected one group of conformers in nmr_xray and NCS_nmr_xray, and two groups in NCS_nmr. The following conformers sets were finally extracted from exact_xray, NCS_nmr_xray and NCS_nmr: (i) for exact_xray, the 38 best-energy conformers, (ii) for NCS_nmr_xray, 41 conformers obtained by clustering-I and closest to the structure 1mu4, (iii) for NCS_nmr, the 12-members cluster (NCS_nmr_I) closest to 1mu4, and a 22-members cluster (NCS_nmr_II), were extracted from the two groups detected by clustering-II. The four conformations sets were then refined in water and, for (ii) and (iii), in the presence of NCS restraints, to provide the sets w_exact_xray, wNCS_nmr_xray, wNCS_nmrI and wNCS_nmrII, which will be analyzed in more details below.
Conformers convergence, quality and accuracy
The Crh monomer convergence is good for all sets (), with coordinate RMSD values in the 0.6–0.9 Å range, close to the value of 0.8 Å obtained on the ssNMR structure 2rlz.17
The small number of restraint violations larger than 0.5 Å in all clusters, along with violation RMS in the 0.11–0.15 Å range prove the good fit of the conformations to the restraints. The conformer local RMSD along the sequence () qualitatively resembles to the fluctuations by residues in MD simulations () and to the B factors in 1mo1 (), with local maxima located in the same protein regions (residues 27, 40, 57, 60, 67).
Quality, restraint fitting and convergence of the ARIA conformers refined in presence of NCS restraints and water (w_exact_xray, wNCS_nmr_xray, wNCS_nmrI, wNCS_nmrII)
Figure 4 Comparison of the A) fluctuations by residues in MD simulations (cryst_tetra: solid, sol_tetra: dotted), of B) the mean local RMSD among ARIA conformers (geometric force field: solid, water and NCS refinements: dotted) plotted along the sequence, and (more ...)
The atomic fluctuations by residues measured along the MD trajectory sol_dimer
(data not shown) are very similar to those observed for the dimer of dimers in trajectory sol_tetra
(). These two sets of fluctuations give a picture of the Crh internal dynamics in qualitative agreement with the observations made by NMR relaxation on Crh in solution. 10
Indeed, the helix α1 (residues 17–28) and the strands β2 (residues 31–37), β3 (residues 40–43) and β4 (residues 60–67), which were shown to have large S2 values by NMR relaxation, display also smaller fluctuations by residues. Also, the residues 37–39 located in the turn between β2 and β3, and the residues 48–54 in helix α2, which were shown to be flexible by NMR relaxation, display larger fluctuations. On the other hand, in the simulations, the helix α3 (residues 70–80) and the strand β1 (residues 4–9) which were rigid according to NMR relaxation measurements, display more flexibility than the rigid protein regions described above.
The clustering simplifies the description of the Crh conformational landscape, with respect to the description obtained with the geometric force field. Indeed, the use of NCS restraints improves the structure precision of more than 1 Å, and the structure accuracy of about 1.0 Å for all sets except for nmr
(data not shown). Along with clustering techniques, the NCS allows to detect sets of conformers (w_exact_xray
) displaying precisions () similar to the precision (1.3 Å) of the ssNMR structure of Crh.17
The accuracy with respect to 1mu4, observed in all sets except wNCS_nmrII
, compares well to the results obtained on the Crh dimer structure 2rlz calculated from ssNMR restraints,17
for which the accuracy on the monomer is 1.6 Å, on the dimer 2.9 Å. Nevertheless, in wNCS_nmrII
, the RMSD to 1mu4 displays a 3-fold increase.
The PROCHECK and WHATIF analyses () determined quality parameters in the range admitted for NMR solution structures. For all runs, more than 86% of the residues are located in the core PROCHECK Ramachandran diagram. Similarly, the WHATIF parameters are in the −4/4 range, the worse values being observed for RAMCHK. The run wNCS_nmrII displays the worse number of inter-atomic bumps (BMPCHK), arising from residues mainly located in the N terminal region 1–30, which is the sign of a badly defined dimer interface. All quality parameters are constant in the four runs, which means that the application of looser restraints does not degrade the physical relevance of the generated conformations in the sets wNCS_nmrI and wNCS_nmrII.
To summarize, the lack of convergence and accuracy in the Crh dimer appears if fuzzier restraints are applied. The use of a qualitative short-range modeling of the intermolecular organization reminiscent of the crystal situation, improves drastically the dimer convergence. In the hierarchy of the restraints defining the crystal organization, the NCS restraint is thus prominent to impose the convergence toward the crystal structure, and this is an argument in favor of the early appearance of the dimer of dimers interaction in transition path from solution to crystal.
Relative monomer orientation in the dimer
The relative orientation of the monomers into the dimer was monitored () through the Euler angles Ψ, Θ and Φ, defining the rotations around the principal inertia axes X, Y and Z (). The largest standard deviation is always observed for Ψ which corresponds to a largest variability around the X axis. This is in agreement with the variability in relative monomer orientation in the ssNMR structure of Crh17
2rlz and between the crystallographic structures 1mo1 and 1mu4 (). In a similar way, the set of 16 dimers of dimers conformations (ens_XR) obtained from a crystallographic ensemble refinement20
displays also Ψ as the most variable angle ().
Table 4 Analysis of the relative position of the monomers inside the dimer: (a) in the Crh PDB structures (2rlz,17 1mo1, 1mu416) and in the sets of 16 dimers of dimers conformers (ens_XR) obtained from the crystallographic ensemble refinement;20 and (b) during (more ...)
The lowest-energy conformer of each cluster () is close to the structure 1mu4, except the lowest energy conformer of wNCS_nmrII () which displays a difference in the relative orientation of the monomers. This difference comes from the largest bias displayed by Ψ among the orientation angles (). This feature of wNCS_nmrII may correspond to an orientation transiently populated during the Crh transition from solution to crystal.
Figure 5 A) Crh dimer structure 1mu4 and lowest-energy conformers from B) w_xray_exact, C) wNCS_xray_nmr, D) wNCS_nmrI and E) wNCS_nmrII. The Crh chains are colored in blue and red. This figure was realized with pymol 0.98.51
During molecular dynamics (MD) simulations, larger conformational drifts are observed (data not shown) in the simulation sol_dimer than in the simulations sol_tetra, cryst_tetra, and the monomer RMSD are always smaller than the dimer RMSD. These two features agree well with the variability of monomer relative orientation, observed among the ARIA conformers, as well as with the drift from the X-ray crystallographic structure observed in wNCS_nmrII. The Euler angles stay close to the values observed in crystallographic structures (), but again Ψ displays the largest standard deviations, in agreement with the observations made for ARIA conformers. The distance between monomer centers of mass () is smaller than the value observed in the crystallographic structures, and decreases along the whole sol_dimer simulation from 21 Å down to 19.5 Å, whereas it stays constant around 20.5 Å for simulations sol_tetra and cryst_tetra.
The relative orientation of the monomers displays the largest variability for the rotations around the longitudinal axis X of the dimer. This feature is observed for independently calculated conformations, as the sets of ARIA conformers, the ssNMR structure 2rlz, or the conformers obtained from a crystallographic ensemble refinement,20
as well as for conformations sampled in MD simulations. This variation Ψ of may thus correspond to relative monomer orientations sampled during the transition from solution to crystal.
The oligomer architecture was analyzed by monitoring: the distances between secondary structure elements of the Crh dimer (), the hydrogen bonds in the secondary structure elements (df 6) and the water bridges ().
Distances (Å) between secondary structure elements in the ARIA conformers and during the MD simulations
Figure 7 Water bridges observed in the MD simulations: A) sol_dimer, B) sol_tetra, C) cryst_tetra. The cuto3 distance for the detection of hydrogen bonds between water atoms and acceptor/donor groups was 2.5 Å. The Crh chains are colored in blue and red, (more ...)
The increase of the β4-β2, α3-β4 and α3-α1 distances in wNCS_nmrI
() with respect with the other ARIA conformers sets, is consistent with the disorder observed in the Crh precipitate for these secondary structure elements.41
Beside, in the same sets, the α2-β1a distance increases and the α2-β3 distance decreases, which corresponds to α2 going apart from β1a and closer to monomer core, in agreement with the variability in the monomers orientation. During MD simulations, the distances between secondary structures () generally increase from the dimer to the dimer of dimers architecture.
Contrary to the other distances between secondary structure elements, the distance β1a-β1a shows a tendency to decrease in ARIA conformers generated in geometric force field with looser restraints (nmr: data not shown) or in the MD simulation sol_dimer (). In the same way, the distance β1-β4 is slightly larger in w_exact_xray, whereas in MD simulations, the inter-monomer distance β1-β4 is larger for dimer of dimers. A modeling of the long-range crystal order thus forces the β strands involved in inter-monomer interaction to go apart.
The hydrogen bond lifetime was monitored in the secondary structures as the percentage of simulation time or of ARIA conformers for which the distance is smaller than 2.2 Å (). Within each contact map, the hydrogen bonds in the helices are the least formed in α2 (residues 47–50), which was also shown46
to be labile in MD simulations of HPr. Among the ARIA conformers sets, shorter lifetimes are observed in wNCS_nmrI
() and wNCS_nmrII
() than in wNCS_nmr
(), specially in the helices α1 (residues 17–28), α2 (residues 47–50), and between the strands β2 (residues 31–37) and β4 (residues 60–67). In MD simulations, the helices α2 and α3 are less stable in sol_dimer
than α1 (), but improve their stability in sol_tetra
() and cryst_tetra
(). Overall, a greater secondary structure stability is observed for conformations closer to the crystallographic structure. But, the inter-monomer hydrogen bonds between the strands β1a (residues 12–14) display the opposite pattern, as their lifetimes are shorter in w_exact_xray
(data not shown) than in other sets of conformers, revealing thus a feature of the crystalline state. Similarly, in MD simulations, the inter-monomer hydrogen bonds between the strands β1a are more stable in sol_dimer
than in cryst_tetra
, in agreement with the variations of the β1a-β1a distance, described above.
Figure 6 Contact maps showing the hydrogen bond formation along the MD trajectories or among the ARIA conformers. (a) cryst_tetra (chains A, B), (b) sol_tetra (chains A, B), (c) sol_dimer, (d) wNCS_nmrI, (e) wNCS_nmrII, (f) wNCS_nmr_xray. The percentage of hydrogen (more ...)
The water bridges were detected in MD simulations as water molecules for which at least two atoms display a distance smaller than 2.5 Å to a protein acceptor or donor groups. Seven bridges are present in more than 25% of the molecular dynamics (MD) simulation sol_dimer
, but this number is multiplied by 3 in the dimer of dimers simulations, where the size of the solute is multiplied by 2. The water bridges thus appear in presence of a more rigid structure and may induce this rigidity. In sol_dimer
(), two water bridges are observed at the dimer interface, between O Met- 51 (chain A)/H Arg-17 (chain B) and between the strands β4 and β1: H Glu-7 (chain A)/O
1 Gln-82 (chain B). During the dimer of dimers MD simulations (sol_tetra
), more water bridges are located () between the dimers and at the monomer interfaces, and inter-monomer bridges appear between: H Ala-54/O
1 Gln-24, O Lys-11/H Gln-15, Leu-21/Hζ3 Lys-40, H Lys-41/O Gln-24, O Met-51/H Ala-16. The appearance of water bridges is observed for MD simulations, for which the strands β1a tend to separate from each other according to the previous analyses, and may be thought to compensate for the induced structure destabilization.
The inter-molecular crystallographic water bridge between Thr-57 and Thr-12, which corresponds to a bridge conserved in the crystallographic structure,47
is not observed in any of the MD simulations. In cryst_tetra
, the crystallographic water positions are not observed, and this may be the consequence of not modeling the exact environment and packing of the crystal. On the other hand, the disappearance of the Thr-57/Thr-12 bridge in MD simulations is correlated with a larger variability of the relative monomer orientation than in the crystallographic ensemble refinement, and supports the importance of this bridge for stabilizing the dimeric structure, in agreement with the observation of Lesage et al.47
Indeed, the position of the Thr-57/Thr-12 bridge is appropriate to block the rotation around the axis X, which is responsible for the largest part of the variability in monomers orientation inside the dimer.
To summarize, the Crh conformations closest to the crystal structure, are characterized by more stable intra-monomer secondary structures along with a paradoxical separation of the β1a strands. This separation is accompanied by the apparition of a larger number of water bridges stabilizing the oligomer architecture. In that respect, the absence in MD simulations of water bridges present in the crystal is probably a reason for the residual variability in the monomers relative orientation.