PMC:2728246 / 34215-45086 JSONTXT

{"project":"2_test","denotations":[{"id":"19652920-16276548-56190979","span":{"begin":1424,"end":1428},"obj":"16276548"},{"id":"19652920-16518697-56190980","span":{"begin":1430,"end":1434},"obj":"16518697"},{"id":"19652920-18556554-56190982","span":{"begin":1463,"end":1467},"obj":"18556554"},{"id":"19652920-10805131-56190983","span":{"begin":1483,"end":1487},"obj":"10805131"},{"id":"19652920-11414844-56190984","span":{"begin":1489,"end":1493},"obj":"11414844"},{"id":"19652920-16939274-56190986","span":{"begin":3949,"end":3953},"obj":"16939274"},{"id":"19652920-12862493-56190987","span":{"begin":4139,"end":4143},"obj":"12862493"},{"id":"19652920-15213434-56190988","span":{"begin":4777,"end":4781},"obj":"15213434"},{"id":"19652920-16939274-56190989","span":{"begin":5392,"end":5396},"obj":"16939274"},{"id":"19652920-12862493-56190990","span":{"begin":7347,"end":7351},"obj":"12862493"}],"text":"MFA detects important supra-τc motion in the side chains\nPrevious studies have reported on the dynamics of methyl groups in ubiquitin using different techniques. It is of interest to compare these results with the RDC-based order parameters reported here. It is important, however to highlight the differences between the various approaches with regards to the time scales as well as the conformational space sampled by the methyl group motion.\nOrder parameters were measured (Lee et al. 1999) from 2H relaxation on selectively 2H-labeled ubiquitin under conditions very similar to ours in concentration, composition and temperature. As for the RDC-based order parameters, the relaxation-based order parameters, (CC) [subscript LS for Lipari-Szabo, in reference to (Lipari and Szabo 1982)], reflect motional fluctuations of the methyl axial CC bond relative to an external reference frame, but with the important difference that the time scale sampled by these motions is strictly faster than the correlation time (τc) of ubiquitin corresponding to about 4 ns. Since RDC-based order parameters are additionally susceptible to the motions over time scales 5–6 orders of magnitude slower than τc, it is generally expected that the condition:10 will be respected for every methyl group, in a similar fashion than what has been described for backbone amide groups when comparing relaxation and RDC-dynamics data (Lakomek et al. 2005, 2006, 2008a, 2008b; Lange et al. 2008; Meiler et al. 2000, 2001). It is however, noteworthy to mention that, whereas the overall scaling of amide order parameters, (NH), strictly depends on the corresponding condition ( within the experimental error), no additional scaling is used here for the methyl groups, since the alignment tensor is predetermined from the amide order parameters (which already include this condition).\nThe relaxation-based order parameters are represented in a correlation plot against the corresponding model-free RDC-based order parameters from our analysis and on a per-residue context in Fig. 4a and b. In both figures, for all but a single residue, the condition described by (10) is respected within the error ranges. It can also be appreciated from those figures that the is much smaller than for a large majority of residues. Not surprisingly, this indicates that there are very important additional motions present in the ns–μs time scale, which are invisible to relaxation. The mean and standard deviation for corresponding sets of methyl groups are  ± σ = 0.66 ± 0.25 and  ± σ = 0.43 ± 0.25. An estimate of the extent of the supra-τc order parameters gives indicating that there is almost as much mobility present in the supra-τc as in the sub-τc ranges for methyl groups This supra-τc mobility of the methyl groups has much larger amplitude than what was observed for amide groups in the same time window. From a similar comparison, the respective amount of backbone motion in the supra-τc region was observed to be on the order of  = 0.93 (Lakomek et al. 2008a). Despite these large differences, the order parameters on both scales show a correlation coefficient of r = 0.72, suggesting that a fair portion of the additional mobility in the supra-τc region can be interpreted mostly as a “broadening” of the amplitude of motion.\nFig. 4 Methyl order parameters measured by other methods are plotted against order parameters obtained from RDCs in ubiquitin (a, c, g, e) and against residue position (b, d, f, h) in color ( are in black). a,b are obtained from 2H relaxation experiments (Lee et al. 1999) and sample motions faster than the correlation time. c,d are obtained from the CxH dipolar splitting reduction for ubiquitin in a microcrystalline form using separated local field experiments by solid-state NMR under magic-angle spinning condition. of CxHx are plotted with the of CxCmet. These values are obtained by squaring the values reported by (Lorieau and McDermott 2006). The time scale sampled also includes the ns–ms range. e,f obtained from rotameric fitting of χ1 based on averaged 3JNCγ- and 3JC′Cγ-couplings and on CH RDCs according to (Chou et al. 2003). These order parameters are based on a finite rotameric jump model and sample dynamics over similar time scales. g,h The same order parameters are multiplied by S2(NH)LS for the same residue (i, green) and for the following residue (i + 1, red) to include rapid small-scale fluctuations. The Pearson correlation r (with p value) and rmsd fit are also given\nA simple analytical method was proposed to back-predict methyl group Lipari-Szabo-type sub-τc order parameters from static protein structures based on the distribution of local contacts around methyl carbons and the number of χ angles to the backbone (Ming and Brüschweiler 2004). Interestingly, since a similar correlation coefficient is obtained from the back-predicted order parameters, (individual data not shown, correlation coefficient r = 0.66), it is reasonable to suppose that this simple local contact model would also apply in the supra-τc time window.\nA second set of order parameters, , comes from solid-state NMR measurements of the dynamic averaging of the CxH dipolar couplings, adjacent to a CxCmet bond, using separated local field (SLF) methodologies on ubiquitin in microcrystalline form undergoing magic-angle spinning near ambient temperatures (Lorieau and McDermott 2006). It is reasonable to expect that the adjacent CxH and CxCmet bonds would have similar mobility, assuming that concerted motions are not dominant. Despite the important difference in the sample configuration, the averaging of the dipolar couplings in solids or of the residual dipolar couplings in solution is susceptible to motions including the supra-τc (faster than μs for SLF, faster than ms for RDCs). The SLF generalized order parameters reported as |S| = |\u003cP2(cosθ)\u003e| represents the coefficient of reduction of the corresponding static CH dipolar coupling. For comparison with our order parameters, these coefficient were squared, giving |S|2 = .\nFigure 4c and d show the correlation between methyl groups and the corresponding methine and methylene groups (in the solid state) for which both dynamic parameters were measured using the two different methods. Whereas agreement for individual residues cannot be expected, we find remarkable concurrence of the overall scale of order parameters for the ensemble of methyl groups. Indeed, we notice a much less pronounced tendency for these order parameters to be either larger or smaller. For comparison, whereas the average order parameters measured using relaxation methods is generally higher the average order parameters from SS-NMR are much closer to that of the RDC-based order parameters  = 0.48 vs.  = 0.43. Furthermore, we see agreement within error ranges for over 61% of the order parameters using SLF. The correlation coefficient r in this analysis is 0.38 which indicates that there is quite a bit of variation in the differences between the solid-state derived order parameters and the ones derived from our MFA. The rmsd is with 0.24, however, relatively low.\nAnother relevant set of order parameters, , available in the literature are those obtained indirectly for methyl groups at position Cγ using 3-bond J-couplings and a set of RDCs from two alignment media by (Chou et al. 2003). From the rotameric angular distributions obtained from grid search protocols, the corresponding order parameters ranges for each residue were back-calculated. represents the intersecting range between J-coupling- and RDC-based ensembles of rotameric solutions. Since these order parameters sample the same time scales as those presented here, they are expected to fit in the optimal way to the model-free order parameters derived here. Of course, there are differences in the sensitivity of the involved observables to certain motions. For example, the J-coupling averaging is, to a first approximation, only susceptible to axial fluctuation about the Cα–Cβ bond, such as rotameric jumps of the χ1 torsion angle. They are insensitive to the orientational fluctuation of the Cα–Cβ axis itself and because of the nature of the Karplus curves, especially around the gauche positions, they are rather insensitive to fast fluctuations around each rotameric equilibrium position. In contrast, RDCs are sensitive to all types of fluctuations as long as the 5-dimensional space is properly represented, owing to sufficiently linearly independent alignment media. Despite these important differences, the overall correlation between these order parameters and our model-free is rather good with a correlation coefficient of r = 0.58 and an rmsd of 0.28.\nMost striking, however, is the observation of in all available cases as seen in Fig. 4e, f. The obvious interpretation is that the rotameric jump model only explains part of the mobility experienced by the Cβ–Cγ bond. Just like the ratio defines the temporally distinct supra-τc order parameters, the ratio could define a geometrically distinct libration order parameter around the equilibrium positions. For instance, I30(Cγ1) is predicted to mostly sample a single rotamer with the gauche− rotamer dominating the χ1 distribution, based on . This same methyl group is however, quite mobile based on (0.48 ± 0.20). Interestingly, the backbone at that position over the same time scale is relatively flexible based on (NH) = 0.78, which would suggest that some of the mobility would be due to “wobbling” of the Cα–Cβ bond with the backbone. Nevertheless, for other residues where the Cγ undergo significant rotameric interconversions, is exquisitely sensitive to supra-τc motions. Notably, the were significantly lower than the (CC) for several residues in the first pair of ubiquitin’s anti-parallel β-strand, indicating that rotameric averaging on a time scale slower than the rotational correlation time is taking place.\nDespite already good agreement, we could improve the correlation between the two independently determined order parameters even further in the following way: We multiplied the rotamer-based order parameter (CCi) with a local backbone order parameter, (NHi) or (NHi+1), representing small-scale rapid fluctuation (compare Fig. 4g, h). Slightly better agreement is obtained using the following NHi+1 order parameters (Fig. 4g, h, residue i + 1, red, rmsd = 0.18 and r = 0.63) compared to those from the previous NHi (Fig. 4g, h, residue i, green, rmsd = 0.22 and r = 0.47). This result indicates that both rotameric sampling and fast small-scale libration around equilibrium positions generally have an important contribution to the overall mobility of the CCmet bond. With this correction of the (CCi) order parameters, they fit with the largest correlation coefficient r and the smallest rmsd to the order parameters derived from our MFA."}