Journal of the American Chemical Society Article offeran attractive avenue for the study of slowly exchanging )rondettearein solution e m he the tep the weak fi ple,if the ion of ffet to de se to zerc R5-205 the minor state,leading ing to a de onouhethat occursnCPMGt 1.at least for agnetization(E to G)is magne vecto d the s (Figu dies of Slowly Exchanging. G) 1H orre mange par ion of the ne basic pulse s is esse n o B d.Th R. -state peak is clea seen This pertain CEST MG exp in direc ofh with P1 H.(a→15N.6)s5N.(⊙ of Tex in the b →15N,(d)-rH( derived by Millet et a owing appre Briefly.the amide p I(Trx)=lo exp(-RTrx) where the wate H re 1+(岳 site pulse he N carriers are returnec PP ag sand m.2 Nchemical shifts as M.(TEx)=Mo +RR+aRR (21) T tha saturatin where cept that work)with N TROSY/anti-TROS f款aa2a es at 100ms f(T)= ed.i h 8151 d dolerg/10.1021/)30014191 Am.Chem.Soc.2012.134.8148-816order of magnitude or more lower than the transverse relaxation rates R2. For this reason, CEST-based experiments offer an attractive avenue for the study of slowly exchanging systems. The CEST experiment is illustrated schematically in Figure 1E; in what follows, we initially assume that R1 = R2 = 0 (but see below). A weak B1 field (ν1 = 5−50 Hz for the studies described here) is applied at a specific offset from the major￾state peak for a time TEX, followed by a 90° pulse and recording of the 15N spectrum. Successive experiments “step” the weak field through the entire spectrum, and the intensity of the visible major-state peak is quantified as a function of offset to detect the position of the corresponding minor-state correlation. When the B1 offset is far from either the major- or minor-state correlation, it has no effect on the spins of interest, and the intensity of the major-state peak is unaffected relative to the case where B1 = 0. However, when the field is placed at ω̃ E (green vector in Figure 1F), it induces Rabi oscillations in the nuclei transiently populating the minor state, leading to precession around the y axis in the xz plane in analogy to the precession about the z axis that occurs in a CPMG experiment (Figure 1C). The bulk magnetization vector corresponding to the excited state rotates on average by an angle ⟨θ⟩ = 2πν1/kEG around the y axis between exchange events (Figure 1G), leading to a net reduction in the polarization of the ground state that is detected, leading to the profile illustrated in Figure 1H. Here the intensity I of the major-state correlation (normalized to I0, the intensity when TEX = 0) is plotted as a function of the position of the B1 field. The reduction in the observed magnetization of state G when the B1 field overlaps with the minor-state peak is clearly seen. This phenomenon is directly analogous to chemical-exchange-induced line broadening, with ν1 in CEST corresponding to Δω/2π (Δω = ωE − ωG) in the CPMG experiment. Therefore, in direct analogy with CPMG relaxation dispersion, the intensity of the major-state correlation as a function of TEX in the pG ≫ pE limit can be calculated from the following approximate expression for Rex derived by Millet et al.:47 I( ) exp( ) T I RT EX 0 ex EX = − (1) where = + ( ) πν R ppk 1 k ex G E ex 2 2 ex 1 The above discussion assumed that that R1 = R2 = 0. In general, the situation is more complicated because relaxation occurs during precession of the magnetization about B1 and potentially also saturation. If exchange is neglected, the time dependence of the z component of the magnetization upon application of an on-resonance B1 field is given by ω ω ω = + + + ⎛ ⎝ ⎜ ⎞ ⎠ M T M ⎟ R R R R f T R R () () z EX 0 1 2 1 2 1 2 EX 1 2 1 2 1 2 (2.1) where ρ ρω ρ ρω = + × − | |≥Δ + × − | |<Δ ⎧ ⎨ ⎪ ⎪⎪ ⎩ ⎪ ⎪ ⎪ f T T RT T R T R T RT T R T R ( ) [cos( ) sinc( )] exp( ), [cosh( ) sinhc( )] exp( ), EX EX avg EX EX avg EX 1 EX avg EX EX avg EX 1 (2.2) and Ravg = (R1 + R2)/2, ΔR = (R2 − R1)/2, ρ = |ω1 2 − (ΔR) 2 | 1/2, and ω1 = γB1. From eqs 2.1 and 2.2, it can be seen that magnetization decays to the steady-state value M0R1R2/(ω1 2 + R1R2) with a time constant Ravg. The corresponding solution of the Bloch equations that includes chemical exchange and a weak B1 field corresponding to the CEST experiment is complicated and offers little understanding in its most general form.48,49 However, some insight can be obtained from the expressions that neglect exchange (eqs 2.1 and 2.2). For example, if the lifetime of the excited state, 1/kEG, is such that 1/kEG ≤ TEX and Ravg/kEG > 1, then the excited-state magnetization approaches its steady-state value [i.e., f(TEX) ≈ 0 in eq 2.1 since exp(−Ravg/kEG) is small], which is close to zero (saturation) even for small values of ω1 and typical relaxation rates (e.g., ω1 = 2π × 10 rad/s, R1 ≈ 1 s−1 , R2 = 5−20 s−1 ). In this case, chemical exchange transfers the saturation from state E to G, with the magnetization in the E state subsequently “replenished” by exchange from G to E, leading to a decrease in the magnetization of the ground state. For many exchanging systems it is not the case that Ravg/kEG > 1, at least for some of the spins, in which case the transferred magnetization (E to G) is only partially saturated [i.e., f(TEX) ≠ 0]. CEST Experiment for Studies of Slowly Exchanging, Highly Skewed Protein Systems. Figure 2 shows the gradient-coherence-selected, enhanced-sensitivity-based pulse scheme for quantifying the exchange parameters and excited￾state chemical shifts in slowly exchanging 15N-labeled protein systems. The basic pulse scheme is essentially a modification of the standard experiment used to measure 15N R1 values in amide groups of proteins;50 only the salient features as they pertain to the CEST experiment will be described here. The magnetization transfer pathway is summarized succinctly as → ⎯→⎯ → ⎯→ ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ − ab c d e H() N() N() N( ) H () z z T z x t x y 1 15 15 15 /SE RINEPT 1 / EX 1 (3) Briefly, the amide proton z magnetization at point a is trans￾ferred via a refocused INEPT element51 to 15N longitudinal magnetization at point b. The 1 H and 15N carriers, originally on the water 1 H resonance and in the middle of the amide 15N spectrum, respectively, are positioned in the center of the amide 1 H region and at the desired position for weak 15N irradiation during the subsequent TEX period. 1 H composite pulse decoupling is applied during this interval, effectively reducing the 15N−1 H spin system to an isolated 15N spin. At the end of the TEX period (point c), the 1 H and 15N carriers are returned to their original positions, and the 15N transverse magnetization evolves during the subsequent t1 period followed by transfer to 1 H for detection during t2. The intensities of the cross-peaks in the resulting 2D 15N−1 H spectra are quantified to obtain the exchange parameters and excited-state 15N chemical shifts as described later. The basic pulse scheme is similar to that recently used in a study of Aβ peptide protofibril exchange dynamics,35 except that significantly larger 15N B1 “saturating” fields were used there (ν1 ≈ 170 Hz vs 5−50 Hz in the present work) with 15N TROSY/anti-TROSY components52,53 inter￾converted through the application of 1 H 180° pulses at 100 ms intervals. In cases where excited-state chemical shifts are to be measured, it is preferable to use very weak B1 fields, since the peak line widths increase with B1 (see below). 1 H decoupling is more critical in these cases because ν1 ≪ JHN, where JHN is the Journal of the American Chemical Society Article 8151 dx.doi.org/10.1021/ja3001419 | J. Am. Chem. Soc. 2012, 134, 8148−8161