Jourmnal of the American Chemical Society Article ites as igh a with inte n-cx ange bas RESULTS AND DISCUSSION where the po are highly kewed rson of CPMG and CESTf t Chemica he atic.hov CPMG ent an analo with the CPMG methodology tha trates s e ike the G erred【 、G and E,Pe e on k and pe visible in th corre ion (rec s also and t limit r m states). the CPMG pulse train that 200s 2000 the of th e app in gen by which ver d (ie.at the axis in the rotating ration t (DEST of( high t ft出 G e precis e pa 0 f the a39G Fe doma or wh the sare very 1-1nd165 ying su nge R d伍cult of the P in this limit 814 de /10 1021/300141914 Am.Chem.Sec.2012.13%4.8148-816rates as high as 6000 s−1 . At the opposite end of the exchange spectrum, systems with interconversion rates less than ∼100 s−1 can be studied using magnetization-exchange-based experi￾ments so long as the interconverting states can be observed in spectra.14,32 Cases where the populations are highly skewed (so only peaks from the ground-state conformer are obtained) and the exchange is slow have remained enigmatic, however, because they are not in general amenable to study using either CPMG or typical exchange-type experiments of the sort involving exchange of unperturbed longitudinal magnetization. It is the study of exchanging systems in this regime that we address here. Like the CPMG method, which was developed over 50 years ago16,17 and has subsequently found applications in biomo￾lecular NMR spectroscopy,21,33 the “saturation transfer” class of experiments was originated in the early 1960s by Forsen and Hoffman.34 In these experiments, a weak field is applied at the position of an exchanging peak of interest, and the “perturbation” that results (not necessarily saturation) is transferred to the interconverting state via chemical ex￾change.35−39 Gupta and Redfield40 applied this approach to study electron exchange between ferri- and ferrocytochrome c in a sample with approximately equal concentrations of reduced and oxidized protein and to assign methyl resonances in the ferro state by saturation transfer from the corresponding well￾resolved, hyperfine-shifted peaks of the ferri conformer. Feeney and Roberts used this methodology to assign the chemical shifts of small molecules such as cofactors and inhibitors bound to enzymes. In one such study involving dihydrofolate reductase, 1 H saturation from 2 to 7 ppm in small steps allowed the identification of the small-molecule bound￾state peak positions by perturbations to peaks derived from the well-resolved free state.41 Later on, Balaban and colleagues37 and subsequently van Zijl and Yadav42 developed one￾dimensional chemical exchange saturation transfer (CEST) spectroscopy, by which very low amplitude invisible signals from metabolites and proteins can be amplified manyfold and “read out” from the water resonance so long as the nuclei of interest exchange with water. Clore, Torchia, and co-workers introduced an elegant two-dimensional (2D) experiment, dark￾state exchange saturation transfer (DEST), to determine both the kinetics of interconversion between free amyloid-β (Aβ) peptide and very high molecular weight Aβ protofibrils and the 15N line widths of the invisible (“dark”)-state resonances.35 Building on the DEST experiment, we show here that CEST￾type experiments can be used to quantify slow chemical exchange precisely in the regime that challenges the CPMG approach, providing the kinetics and thermodynamics of the exchange process as well as the chemical shifts of the excited￾state nuclei often from direct inspection of the resulting spectra. The methodology was cross-validated with a protein−ligand two-state exchanging system that has been studied previously,28 with an exchange rate and minor state population of ∼150 s−1 and 2.5% (5 °C), respectively. Subsequently, the utility of the experiment was demonstrated with an application to the folding of the A39G FF domain,11,43 for which the CPMG dispersion profiles are very small and hence difficult to analyze. Accurate exchange parameters (51.6 ± 1 s−1 and 1.65 ± 0.02%) as well as excited-state chemical shifts were obtained via the CEST methodology. In contrast to other methods for studying invisible states (CPMG or R1,ρ relaxation dispersion, D-evolution), robust exchange parameters were obtained from fits of data recorded on a per-residue basis measured at a single magnetic field strength, allowing a rigorous evaluation of the two-state assumption that is often used in fits of dispersion data. ■ RESULTS AND DISCUSSION Comparison of CPMG and CEST for Studies of Chemical Exchange. Prior to a discussion of experimental details and applications to exchanging systems, we provide a brief discussion of the basic features of the CEST experiment and present an analogy with the CPMG methodology that illustrates some of the similarities between the two approaches. For simplicity, in what follows we consider an isolated 15N spin in a protein exchanging between two conformations, G (ground) and E (excited), G X Y ooo E k k EG GE with distinct chemical shifts ω̃ G and ω̃ E (Δω̃ = ω̃ E − ω̃ G) in each of the two states (Figure 1A). The fractional populations of states G and E, pG ≫ pE, are given by pG = kEG/kex and pE = kGE/kex = 1 − pG, where kex = kGE + kEG. In the cases of interest here, only major-state peaks are visible in the spectra, although in Figure 1A the excited-state correlation (red) is also shown for clarity. To simplify the discussion, we will assume that chemical exchange occurs in the slow-exchange limit, where kex ≪ Δω (i.e., we do not consider multiple transfers of magnetization between the states). Figure 1B illustrates the basic CPMG pulse train that is used to study exchanging systems in the approximate regime 200 s−1 ≤ kex ≤ 2000 s−1 and pE ≥ 0.5%. Here the effective transverse relaxation rates (R2,eff) of the visible peaks are quantified as a function of the frequency νCPMG = 1/(4τCPMG) at which refocusing 180° pulses are applied during a relaxation delay Trelax. The evolution of magnetization is illustrated in Figure 1C, where without any loss in generality it has been assumed that the carrier is placed on resonance for the major￾state correlation being considered (i.e., at ω̃ G). After the 90° pulse at the start of the echo train, magnetization from this state remains aligned along the y axis in the rotating frame while the magnetization from the minor state precesses in the xy plane, losing phase with the ground state. On average, the excited￾state spins accumulate a phase of ⟨ϕ⟩ = Δω/kEG between exchange events, so exchange leads to a reduction in the major￾state signal and hence a nonzero exchange-induced relaxation rate Rex. Each 180° pulse of the CPMG train inverts the sense in which the spins precess around the z axis, reducing the phase accumulation ⟨ϕ⟩ and decreasing Rex. Exchange parameters and minor-state chemical shifts can be obtained from fits of the R2,eff(νCPMG) profile so long as the exchange contribution to R2,eff (i.e., Rex) is quenched as νCPMG increases (Figure 1D). In the slow-exchange limit, Rex = kGE when νCPMG = 0, so the maximum observable change in the R2,eff(νCPMG) profile is kGE. By means of example, consider an exchanging system in the window of interest here with kex = 50 s−1 and pE = 1.5%, for which kGE = 0.75 s−1 . If a contribution of 10 s−1 to R2,eff from intrinsic relaxation is assumed, the maximum loss in the detected signal intensity during a “typical” Trelax delay of 50 ms from chemical exchange, which occurs when νCPMG → 0, is 1 − e−(10.75)(0.05)/e−(10)(0.05) ≈ 3.7%. Quantifying such a small change accurately in the presence of noise and systematic errors is very difficult, compromising the accuracy of the exchange parameters obtained from CPMG relaxation dispersion data in this limit. Journal of the American Chemical Society Article 8149 dx.doi.org/10.1021/ja3001419 | J. Am. Chem. Soc. 2012, 134, 8148−8161