ournal of the American Chemical Society Article 250 600 A 200 y=2.5 2400 15 100 ,100 50l 50 00500 50 0。 ded state of th fit.th ded at1 117 117 ack curve y =4.65x corresponds to the best bile the bost-ft lin mical shift ould be and CEST data. ially the ntras resi G FE ng that this es recor at 1 decre 18.8T.s ate the stati etic field gths(18.82/11 2.56i ofiles are 117 11.7 the (Figure 7A.B)and fit the dis sion profiles glo ally to a twe mall△o ne t fast excha -state Rvalu R wh e is appr el hen is th third tate?Figure 6 DE (11.7T nad third is d the previ 2 nediate state isre nbly fast on the NMr ch n this ng c oppe ow fl nce a CPMG dispe nce is a reaso he s gesting that th (A.B)N C 11.7 (rd)40 in th ewil-typeo and the I undertaken to characterize further this additional sly.s (C)Linear o chemical t to o the cs-0 is aso sh .201213481-818 changes in chemical shift, would be in the fast-exchange limit, with n = 2. In contrast, residues with larger Rex E values would have smaller values of n, since they would not be in the fast￾exchange limit. Figure 6B shows that this was observed for the Rex E values obtained from the CEST profiles recorded at 11.7 and 18.8 T. Small values of Rex E scale as the square of the ratio of the static magnetic field strengths (18.82 /11.72 = 2.56 in the present case), while larger values scale with progressively smaller ratios. For this reason, the correlation between Rex E values measured at 18.8 and 11.7 T follows the linear relation, y = 2.56x (solid line in Figure 6B) for small values of Rex E (small Δω̃values corresponding to fast exchange with a third state), with a decreasing dependence as Rex E (and hence Δω̃) becomes larger. In this analysis, we estimated the excited-state Rex E values as R2 E − 0.5R2 G, where we assumed that the intrinsic R2 of the unfolded state is approximately half that of the folded state.65 What then is the origin of the third state? Figure 6C plots fitted Rex E values from the CEST profiles of the A39G FF domain (11.7 T) versus the difference in the 15N chemical shifts of the intermediate and unfolded states, Δω̃IU, determined in a previous study of the wild-type FF domain.11 If the third state is indeed the previously characterized intermediate and the exchange between the unfolded and intermediate states is reasonably fast on the NMR chemical shift time scale, then a strong correlation between Rex E and Δω̃IU 2 should be observed. In this regard, it is worth noting that both stopped-flow fluorescence and CPMG dispersion studies have shown that the intermediate exchanges rapidly with the unfolded ensemble (kex FI ≪ kex IU),11,43 so a quadratic depend￾ence is a reasonable first model. The solid curve in Figure 6C shows a modest correlation assuming a quadratic depen￾dence (certainly much better than that for a linear correlation, shown by the dashed line), suggesting that the third state may be structurally related to the intermediate that has been studied previously in the wild-type protein11 and the L24A FF domain mutant.60 However, additional studies must be undertaken to characterize further this additional exchanging conformer. It is of interest to compare the exchange parameters and chemical shift differences extracted from fits of CPMG relaxation dispersion and CEST data, especially since the A39G FF domain is a challenging case with small dispersion profiles. A previous study of the Abp1p SH3 domain−Ark1p peptide exchanging system as a function of temperature established that as exchange rates decrease, the accuracy of the extracted (kex, pE) values becomes poor, as was also noted in simulations.12 Of course, dispersion profiles are sensitive only to the pEkex product in the slow-exchange limit. We recorded CPMG dispersion profiles at 11.7, 14.0, and 18.8 T (Figure 7A,B) and fit the dispersion profiles globally to a two-site Figure 6. The invisible unfolded state of the A39G FF domain exchanges on a micro-to-millisecond time scale with another sparsely populated invisible state. (A) Ground (R2 G)- and excited (R2 E )-state 15N transverse relaxation rates for the 37 residues showing clear evidence of a second state in CEST profiles at 1 °C and 11.7 T. Although the relaxation rates do not contain contributions from the exchange process that was fit, they are influenced by additional exchange processes. (B) Comparison of the exchange contributions to R2 E (Rex E ) recorded at 18.8 and 11.7 T; small to intermediate values of Rex E scale as the square of the ratio of the field strengths, 2.56 (see the text). All of the data recorded at the two B0 fields were together fit to a global two-state process. (C) Correlation between the Rex E values at 11.7 T and the difference in the chemical shifts of the unfolded state and a previously characterized11 intermediate state for the wild-type FF domain, |Δω̃IU|. The black curve y = 4.65x2 corresponds to the best quadratic fit to the data, while the best-fit linear relation y = 18.8x is shown as a dashed line. Figure 7. (A, B) 15N CPMG relaxation dispersion profiles for a pair of residues of the A39G FF domain at 1 °C and 11.7 T (red), 14.0 T (green), and 18.8 T (blue), along with best fits of dispersion profiles (solid lines) obtained from simultaneous analysis of all of the data, as described previously.18 (C) Linear correlation plot of |Δω̃ CPMG| vs |Δω̃ CEST|, along with the solid line representing |Δω̃ CPMG| = |Δω̃ CEST|; a pairwise rmsd of 2.4 ppm was obtained. (D) Plot of ||Δω̃ CPMG| − |Δω̃ CEST|| vs residue number. The horizontal line corresponding to |Δω̃ CPMG| − |Δω̃ CEST| = 0 is also shown. Journal of the American Chemical Society Article 8156 dx.doi.org/10.1021/ja3001419 | J. Am. Chem. Soc. 2012, 134, 8148−8161