Microsecond Time Scale Dynamics in Proteins A R T I C L E S Figure 2. Two-dimensional 1H-13C spectra recorded at 600 MHz using the 1H-CPMG-CHD2 experiment (scheme A, without the CPMG block). The complete methyl region of calbindin D9k is shown in the left panel (blue signals have an opposite sign and originate from CHD methylene groups), while for NtrCr an inset of the Leu region is shown (right panel). the ﬁtting parameters were determined from the covariance matrix obtained by inverting the Hessian matrix.91 Results and Discussion We have previously determined the isotopomer incorporation and residual protonation of methyl-containing amino acids for protein samples grown on U-[1H, 13C]-D-glucose in ∼100% D2O.58 The desired CHD2 isotopomer shows favorable incor- poration levels with the lowest value around 30% for Met-ε and between 41% and 56% for all other methyl-containing amino acids. Because the incorporation of the CH3 isotopomer is very low (<8%) for all amino acids, and signals from the CH2D are easily suppressed in our experiment, it is possible to obtain a clean, high-resolution CHD2 spectrum (see Figure 2). Validation of the Methodology for a System That Does Not Display Microsecond-Millisecond Time Scale Dynamics. The underlying assumption in CPMG relaxation dispersion experiments is that, in the absence of exchange, the obtained dispersion proﬁles are ﬂat (i.e., the signal intensity does not depend on the CPMG pulse repetition rate). In the case of calbindin D9k, previous studies have shown that there is little or no chemical exchange present,61-64 and, therefore, ﬂat curves are expected for all residues. In Figure 3, representative curves are shown for Ala, Ile-γ2, Met, and Val methyl groups (recorded with scheme A, Figure 1) for which we indeed observe ﬂat “proﬁles”. Following Tugarinov et al.,43 the pairwise root-mean-square deviation is used as a measure of how ﬂat the curves are and is deﬁned as rmsd ) N 1 N ∑i [R2i,eff(νCPMG,i) - k]2 (91) Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. Numerical Recipes in C, The Art of Scientiﬁc Computing, 2nd ed.; Cambridge University Press: Cambridge, 1992. Figure 3. Representative methyl transverse 1H relaxation dispersion proﬁles for Ala, Ile-γ2, Met, and Val methyl groups recorded at 600 MHz for calbindin D9k. where R2i, eff(νCPMG, i) is the effective transverse relaxation rate, k is the best ﬁt horizontal line to the experimental curve, and N is the number of experimental data points. For the above- mentioned residue types in calbindin D9k, we obtain an average rmsd of 0.20 ( 0.04 s-1, with a maximum of 0.27 s-1. It is, however, anticipated that methyl groups will display artifacts depending on the protonation level of their neighboring carbon atom. We have shown earlier that the deuteration level of neighboring carbons in the side chains ranges between 90% J. AM. CHEM. SOC. 9 VOL. 132, NO. 47, 2010 17009