Joumnal of the American Chemical Society Article mated on the h dips.with th anging between two states G and E with rate =[xu s to the E/2 0 E/2 0 -R-kGE 0 0 0 0 0 d山 -RG- 0 -R5 0 -R-kEc 0 2R5 0 -RE CEST pe In gro state,i important t ASSOCIATED CONTENT R 61 The cted exch ar pr neters and che and the A39GF the ble free o ■AUTHOR INFORMATION nding Author h@pound. ed.ut onto.ca;kay@pound.med.utoronto.ca ACKNOWLEDGMENTS Kay for Heatth Research (CIHR)for mry.Th work wa the initial c to Ni ■REFERENCES rates of the nide tons dxdolerg/10.1021/)30014191 Am.Cherm.Soc.2012.134.8148-816χ ξ ∑ ξ σ = − = ⎛ ⎝ ⎜⎜ ⎞ ⎠ ⎟⎟ I I ( ) ( ) i N i i i 2 1 exptl calcd exptl 2 (4) In eq 4, the summation extends over all the desired experimental points, σexptl is the error in the experimental intensity I exptl, I calcd is the calculated intensity, and ξ = {x1, ..., xn} refers to the different fitting parameters. The value of σexptl was estimated on the basis of noise in the regions of spectra that did not contain any intensity dips, with the minimum error set to the median error of all the residues. Intensities were calculated using the Bloch−McConnell equations77 for a single spin-1 /2 particle exchanging between two states G and E with rate constants kGE and kEG: ω ω ω ω ω ω ω ω = −− − − − − −− −− − − − − −− ⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ t E I I I I I I Rk k Rk k RI R k k k Rk k Rk RI k R k E I I I I I I d d /2 00 0 0 0 0 0 0 00 0 00 0 2 0 00 0 00 00 0 0 200 0 /2 x y z x y z x y z x y z G G G E E E 2 G GE G 1 EG G 2 G GE EG 1 G eq G 1 1 G GE EG GE 2 E EG E 1 GE E 2 E EG 1 E eq E GE 1 1 E EG G G G E E E (5) In eq 5, E is the identity operator, Ij K is component j ∈ {x, y, z} of the angular momentum for state K ∈ {G, E}, Rq K is a spin−lattice (q = 1) or spin−spin (q = 2) relaxation rate, ωG and ωE are the offsets (in rad/s) of the weak 15N irradiation field from states G and E (ωG is obtained from the ground-state peak position and is not a fitting parameter). Ieq G and Ieq E are the equilibrium populations of states G and E, respectively; the value of Iz G is calculated by solving eq 5 (subject to the appropriate set of initial conditions) as a function of the field offset B1. To mimic the phase cycling of ϕ1 (Figure 2), two sets of initial conditions, namely, Ix,y G/E = 0, Iz G = pG, Iz E = pE and Ix,y G/E = 0, Iz G = −pG, Iz E = −pE, were used in all of the calculations, and the difference in Iz G obtained in the two cases was retained. B1 field inhomogeneity was taken into account by performing 10 calculations with different B1 fields evenly spaced between ±2σ around the mean, where σ is the standard deviation of the measured B1 field distribution. The 10 calculations were averaged using coefficients that assumed a Gaussian profile. The data could not constrain R1 E because the molecules spend very little time in state E, so we assumed R1 G = R1 E ; using 0.1 s−1 ≤ R1 E ≤ 4 s−1 had no effect on the results. The fitting parameters are kex, pE, ω̃ E, R1 G, R2 G, R2 E , and a residue-specific initial intensity I0. It should be noted that kex and pE are residue-specific in the case of single-residue fits but global fitting parameters common to all of the residues in the case of multiresidue fits; R1 G, R2 G, and R2 E are residue-specific and dependent on the magnetic field strength B0; and is ω̃ E residue￾specific but independent of B0. In principle, it is possible to measure R1 G and R2 G in independent experiments and fix these parameters in fits of the CEST data to values obtained using other pulse schemes. We prefer, however, not to do this. First, in addition to recording a series of experiments with different positions of the B1 field applied for a time TEX, we also record an additional data set with TEX = 0. These data sets determine R1 G accurately because ln(I) = ln(I0) − R1 GTEX, where I is the intensity of the ground-state correlation when the B1 field is applied at a position far removed from the ground￾and excited-state peaks (so that they are not affected) and I0 is the intensity when TEX = 0. Second, when R1 G and R2 G are estimated using separate experiments, there is always a worry that what is measured is slightly different than in the CEST data set and that the differences could potentially translate into errors in the exchange parameters. As described above, the data were fit using the initial conditions Iz G = ±pG and Iz E = ±pE. We also fit the data taking into account relaxation during magnetization transfer from 1 H to 15N in the scheme shown in Figure 2 (between points a and b). This could only be done in an approximate manner because we did not have an estimate for the transverse relaxation rates of the amide protons, including contributions from chemical exchange. We therefore assumed identical relaxation decays during each of the two INEPT elements preceding the CEST period. In a separate analysis of the data, we assumed the initial condition Iz E = 0. In all cases, the extracted parameters were affected only very little by the assumptions used. For residues with substantial contributions from transverse relaxation in the ground state, it is important that these be taken into account. In such cases, we recommend that amide 1 H transverse relaxation rates be estimated from F2 line widths (e.g., in recorded CEST spectra) while the 15N line widths are allowed to emerge naturally from fits of the data. ■ ASSOCIATED CONTENT *S Supporting Information Tables listing extracted exchange parameters and chemical shifts; sets of fitted CEST profiles for all residues used in the global fits for both the Abp1p−Ark1p and the A39G FF domain exchanging systems. This material is available free of charge via the Internet at http://pubs.acs.org. ■ AUTHOR INFORMATION Corresponding Author pramodh@pound.med.utoronto.ca; kay@pound.med.utoronto.ca Author Contributions § P.V. and G.B. contributed equally. Notes The authors declare no competing financial interest. ■ ACKNOWLEDGMENTS We thank Dr. Ranjith Muhandiram for advice on the implementation of the pulse sequence and Prof. Julie Forman-Kay for providing laboratory facilities for sample preparation. G.B. acknowledges the Canadian Institutes of Health Research (CIHR) for a postdoctoral fellowship. L.E.K. holds a Canada Research Chair in Biochemistry. The work was supported by grants from the Natural Sciences and Engineering Research Council of Canada and the CIHR. ■ REFERENCES (1) Austin, R. H.; Beeson, K. W.; Eisenstein, L.; Frauenfelder, H.; Gunsalus, I. C. Biochemistry 1975, 14, 5355−5373. Journal of the American Chemical Society Article 8159 dx.doi.org/10.1021/ja3001419 | J. Am. Chem. Soc. 2012, 134, 8148−8161