Proton-Decoupled CPMG Experiment for 15NR2 Relaxation

Proton-decoupled CPMG: A better experiment for measuring relaxation in disordered proteins 15 N R2 a b s t r a c t 15 N R2 relaxation is one of the most informative experiments for characterization of intrinsically disordered proteins (IDPs). Small changes in nitrogen R2 rates are often used to determine how IDPs respond to various biologically relevant perturbations such as point mutations, posttranslational modifications and weak ligand interactions. However collecting high-quality 15N relaxation data can be difficult. Of necessity, the samples of IDPs are often prepared with low protein concentration and the measurement time can be limited because of rapid sample degradation. Furthermore, due to hardware limitations standard experiments such as 15N spin-lock and CPMG can sample the relaxation decay only to ca. 150 ms. This is much shorter than 15N T2 times in disordered proteins at or near physiological temperature. As a result, the sampling of relaxation decay profiles in these experiments is suboptimal, which further lowers the precision of the measurements. Here we report a new implementation of the proton-decoupled (PD) CPMG experiment which allows one to sample 15N R2 relaxation decay up to ca. 0.5–1 s. The new experiment has been validated through comparison with the well-established spin-lock measurement. Using dilute samples of denatured ubiquitin, we have demonstrated that PD-CPMG produces up to 3-fold improvement in the precision of the data. It is expected that for intrinsically disordered proteins the gains may be even more substantial. We have also shown that this sequence has a number of favorable properties: (i) the spectra are recorded with narrow linewidth in nitrogen dimension; (ii) 15N offset correction is small and easy to calculate; (iii) the experiment is immune to various spurious effects arising from solvent exchange; (iv) the results are stable with respect to pulse miscalibration and rf field inhomogeneity; (v) with minimal change, the pulse sequence can also be used to measure R2 relaxation of 15Ne spins in arginine side chains. We anticipate that the new experiment will be a valuable addition to the NMR toolbox for studies of IDPs. 1. Introduction 15 N relaxation measurement is one of the most useful NMR experiments – it is fast, reasonably simple to interpret, and immediately provides information on protein backbone flexibility. This information can be further used to characterize the role of motions (i.e. conformational entropy) in ligand binding [1,2], protein stability [3,4], allosteric regulation [5,6], etc. The spin context of 15N relaxation is fairly straightforward. It is normally assumed that nitrogen relaxation is driven by 1HN–15N dipolar interaction and, to a lesser degree, by 15N CSA mechanism. Nevertheless, even in this sufficiently simple spin system there is room for uncertainty – the appropriate length of N–H bond was a subject of debate and the degree of anisotropy and site-to-site variation of the 15N CSA tensors have also been widely discussed [7,8]. Furthermore, small and difficult-to-quantify Rex contribu- tions into 15N R2 appear to be more common than previously thought [9]. In addition to these fundamental sources of uncertainty, there are also a number of errors associated with specific measurement schemes that have been uncovered in recent years. For example, it has been found that frequent application of 1H pulses during the spin-lock period with the intention to suppress dipolar-CSA cross-correlation may actually re-introduce the undesirable J-coupling evolution [10]. In 1HN–15N saturation-transfer NOE experiment it was found that the standard saturation sequence tends to create a number of unwanted spin modes [11]. The artefacts associated with solvent exchange were also recently exposed [12]. Finally, there are also uncertainties associated with the choice of the model. The most common approach is to choose from several versions of the model-free model which make different assumptions about the underlying dynamics – in particular, with regard to local motions on 1 ns time scale [13–15]. While there are statistical criteria that guide this choice, it has been shown that the outcome is often influenced by the random noise-like errors and depends on availability of data measured at different magnetic fields [16–18]. An additional level of complexity is added by the protein’s overall tumbling, which should be properly modeled using a fully asymmetric diffusion tensor [19–22]. With all of these sources of uncertainty combined, it is not surprising that 15N-relaxation-derived motional parameters are not necessarily very accurate. Consider, for example, the well-studied model protein ubiquitin, where several groups independently measured and analyzed 15N relaxation in solution [20,23–25]. The backbone order parameters reported in these studies differ significantly from each other: the rms deviations between the independently determined sets of S2 are in the range from 0.02 to 0.07 and the correlation coefficients are in the range from 0.56 to 0.94. In practice, however, the perceived lack of accuracy is not very important so long as most experimental studies focus on the difference in order parameters, DS2, rather than the absolute values. It is reasonably safe to assume that systematic biases subtract out in calculating DS2 and the result correctly represents changes in local dynamics. The examples include changes in order parameters in response to ligand binding, point mutations, various post-translational modifications, etc. [26–29]. Given that such changes are typically small, on the order of 0.05 or less, the primary concern is the precision of the data – i.e. it is important to ensure that small DS2 values can be experimentally reproduced and quantitated in a reliable fashion. These considerations are especially relevant for intrinsically disordered proteins (IDPs), which have emerged as the area of major biomedical interest [30]. IDPs do not lend themselves to the standard methods of structural characterization. Instead, the dynamics-oriented experiments play a prominent role. In particular, 15N relaxation and paramagnetic relaxation enhancements (PREs) are arguably two most informative experiments in the field of intrinsically disordered proteins. At the same time, it is often considerably more difficult to achieve high precision in measuring 15 N relaxation rates in IDPs. Many disordered proteins are prone to aggregation which makes it necessary to work with low-concentration NMR samples, often in the range 10–100 lM, and/or collect the data over a short period of time to avoid sample degradation [31–33]. If the studies are conducted at or near physiological conditions (37 °C, pH 7.4), the quality of the already crowded spectra suffers from the line-broadening caused by solvent exchange, which further lowers the signal-to-noise ratio. Finally, there is one other issue that is concerned specifically with 15N R2 measurements as discussed below. For disordered proteins at 37 °C the 15N T2 relaxation times are relatively long, on the order of 0.5–1.0 s. On the other hand, the length of the spin-lock period srel in the standard R1q experiment does not exceed ca. 100–150 ms, as dictated by hardware limitations. It is clearly not possible to properly sample the magnetization decay curve over such a short interval of time. This situation is illustrated in Fig. 1a, which shows the R1q decay curve from residue L15 in a 100 lM sample of denatured ubiquitin at 37 °C. The expansion of this relaxation profile in Fig. 1b demonstrates the problem with such measurement – generally, when srel is much shorter than T2 the decay profile appears flat, which makes it difficult to accurately determine the relaxation rate constant. A rigorous treatment indicates that the best results are obtained when srel is extended beyond T2 [34]. The restrictions concerning the maximum length of srel are ultimately due to low gyromagnetic ratio of nitrogen, x1 = cNB1. In order to generate sufficiently strong 15N rf field which is necessary to suppress the effect of 1JNH coupling, a very strong current should be applied to the transmitter coil. This pushes the probe to the limits of its performance. In the case of spin-lock measurements, the room-temperature probe can sustain 1.7 kHz nitrogen rf field for a period of time ca. 150 ms. In the case of R2 CPMG measurements, the probe can withstand the pulse train with the repetition time of 1 ms for ca. 100 ms. For early-generation cryogenic probes the power limits are even more restrictive. Extending srel beyond these limits can lead to excessive heating of the sample and cause probe arcing [35] which severely degrades the performance of the pulse sequence. In the worst-case scenario, the probe can be permanently damaged. It appears that the latest-generation hardware and particularly new cryogenic probes should make it possible to run spin-lock experiment with long srel [36]. Preliminary data obtained by Ban and Lee suggest that nitrogen rf field with the strength of 3 kHz can be maintained for 500 ms using reasonable duty cycle of 20% (personal communication). In these trial experiments rf power remains stable (i.e. there is no observable amplifier drooping) and rf coil experiences little or no heating. The sample heating is also modest, even for high-salt samples, which can be attributed to the improvements in probe head design. These favorable properties can potentially lead to a robust R2 experiment well suited for application to samples of IDPs at or near physiological conditions. However, to the best of our knowledge, such strategy has never been tested experimentally. One should also bear in mind that the latest-generation hardware which is necessary for such measurements is available only to a handful of research groups. The problem can also be managed without recourse to advanced hardware. For example, Palmer and co-workers demonstrated that 1JNH coupling can be suppressed by using relatively weak 15N spin lock plus a small number of strategically placed 1 H pulses [37]. This experiment, however, is semi-selective – to collect a complete R1q dataset one needs to repeat the measurements several times using different 15N carrier settings. The alternative solution, which we pursue in this report, is to use 1H decoupling to suppress 1JNH. Because of the high gyromagnetic ratio of the proton, it is easy to generate a sufficiently strong rf field without overloading the probe. In the presence of proton decoupling, 15N 180° pulses can be applied only infrequently (for the purpose of refocusing chemical shift evolution). Using this approach, srel can be extended by at least a factor of 5 without risking adverse consequences to a probe. A suitable pulse sequence, proton-decoupled CPMG (PD-CPMG), has been introduced a long time ago and used to measure 15N relaxation in proteins [38–41]. Essentially all of these reports note the presence of bias in R2 rates measured with PD-CPMG, on the order of 5% [38,39,41]. Because of this unresolved issue PD-CPMG has seen little use over the last two decades. Here we present a new and upgraded version of PD-CPMG which can reliably reproduce the results of the well-established R1q spin-lock experiment. The new pulse sequence allows one to extend the observation window srel to 500 ms and beyond, Fig. 1c. The proper sampling of the relaxation decay curve, down to the level of 0.2 on the relative intensity scale, facilitates the accurate determination of R2. For the samples at hand, the precision of the relaxation measurements is improved by up to a factor of 3 compared to the standard R1q experiment. In addition to the extended observation window, the new version of PD-CPMG experiment offers a number of other valuable properties, as discussed below. 2. Results 2.1. PD-CPMG pulse sequence for 15 N R2 measurements The new pulse sequence shown in Fig. 2 is essentially a decoupled, sensitivity-enhanced HSQC, similar to what has been previously used for 15N R1q measurements [10]. Inserted in this sequence is the proton-decoupled CPMG element of the net Fig. 1. Examples of relaxation curves from 15N R1q spin-lock experiment (panels A and B) and R2 PD-CPMG experiment (panel C). The data are from residue L15 in 100 lM sample of unfolded ubiquitin at 37 °C. Panel (B) is the expansion of panel (A). Fig. 2. PD-CPMG pulse sequence for measuring 15N R2 relaxation rates. The design is based on the experiment by Korzhnev et al. [10]; the portions of the sequence which are new and distinct are enclosed in red boxes. The pulse and delay settings listed below are for the measurements on denatured ubiquitin (see Section 5 for sample conditions). Hard 1H pulses are applied with the carrier set on water resonance and rf field strength of 40 kHz. Two consecutive water purge pulses [51] have the durations of 6.0 and 3.7 ms and use the rf field of 12.4 kHz (shaded rectangles in the plot). DIPSI-2 decoupling [46] is applied with the carrier shifted to the middle of the amide region (8.3 ppm). The decoupling rf field corresponds to 90° pulse of duration 61 ls (rf field strength 4.1 kHz). Considering that one DIPSI-2 cycle corresponds to 10,360° rotation, the duration of the cycle is determined to be DDIPSI2 = 7.0218 ms. The 15N CPMG sequence is applied in a form of ½sCP  180 x  sCP  sCP  180 x  sCP  sCP  180 y  sCP  sCP  180 y  sCP n pulse train, where n is an integer number. When n = 0 this element becomes nil, i.e. it does not contain any pulses or delays. The interval between the consecutive 180° 15N CPMG pulses should be adjusted according to the synchronization condition 2sCP + pN(180) = mDDIPSI2, where pN(180) is the duration of 180° 15N pulse and m is an integer number. In our main series of measurements we used the setting m = 2 corresponding to 2sCP = 13.9676 ms. All 15N pulses, including 180° CPMG pulses, have been applied with the maximum rf field strength, in our case 6.6 kHz (pN(180) = 76 ls). WALTZ-16 decoupling during the acquisition period employs 1.1 kHz rf field. The delay settings are sa = 2.25 ms, sb = 1/(4JNH) = 2.75 ms, and d = 0.75 ms. The recycling delay employed is d1 = 2 s. Gradient strengths in G/cm (length in ms) are g1 = 5.0 (1.0), g2 = 4.0 (0.5), g3 = 10.0 (1.0), g4 = 8.0 (0.5), g5 = 25.0 (1.0), g6 = 15.0 (1.25), g7 = 4.0 (0.5), g8 = 14.8 (0.125), g9 = 20.0 (3.5), g10 = 20.0 (2.0). The phase cycle employed is /1 = (x, x), /2 = y, /3 = 2(x), 2(y), 2(x), 2(y), /4 = x, /rec = (x, x, x, x), with DIPSI-2 rf field applied along x. Quadrature detection in F1 is achieved by using the enhanced sensitivity approach [52,53] whereby separate spectra are recorded with (/4, g6) and (/4 + p, g6) settings for each t1 increment. Phase /2 is inverted in concert with the receiver phase for each t1 increment such as to shift axial peaks to the edge of the spectrum [54]. While the sequence is primarily aimed at the backbone amide sites, it can also be adapted to measure arginine side-chain 15Ne R2 relaxation rates. For this purpose 15N carrier needs to be set to 85 ppm, rectangular 15N 180° pulse marked by () should be replaced with r-SNOB pulse [55] with ca. 15 ppm bandwidth, and 15N 180° pulses in the CPMG train need to be changed into REBURP shapes [56] with ca. 15 ppm bandwidth covering 15Ne resonances, but not 15Ng. duration srel. The CPMG pulse train uses [0 0 1 3] phase cycle which was recently shown to have favorable compensation properties [42–45]. The pulse repetition rate in the PD-CPMG sequence is relatively low, with the pulse spacing 2sCP ca. 14 ms. The proton decoupling during the CPMG train is achieved by application of the DIPSI-2 sequence [46] with the rf field strength 4 kHz. The relatively low level of combined 1H and 15N rf power allows us to extend srel period to 500 ms and beyond. In the pulse sequence Fig. 2 proton decoupling is extended to also cover t1 evolution period. It is well known that proton decoupling during t1 generally leads to sharper spectral peaks [47,48]. This is particularly important for IDPs where the spectra are highly crowded. Under physiological conditions, IDPs experience fast solvent exchange which efficiently destroys two-spin modes such as 2NxHz [49]. For conventional HSQC experiment, this causes substantial line broadening in 15N dimension resulting in poor-quality spectra. In contrast, decoupled HSQC experiment records the evolution of pure in-phase coherence, Nx, and therefore avoids this problem. The sequence shown in Fig. 2 is conceptually similar to the previously published scheme [50], although the objectives of the two experiments and the technical details are different (discussed later in the article). As discussed in detail below, the 15N 180° CPMG pulses should be calibrated with care for the purpose of PD-CPMG measurements. However, standard calibration scheme is sufficient – we recommend using the HSQC-based calibration experiment.1 The calibration of proton 90° pulse for DIPSI-2 decoupling does not need to be particularly accurate since PD-CPMG sequence is highly tolerant to pulse calibration errors. It is advisable to use the HSQC-based calibration experiment, but water-based calibration is also acceptable. It is important, however, that the duration of sCP is calculated rigorously according to the synchronization condition. For example, the experiment described in Fig. 2 was set up with 2sCP = 13.9676 ms, even though for the sake of brevity we refer to it as 2sCP = 14 ms (see figure caption for details). Note that fast solvent exchange partially cancels the advantage of the sensitivity enhancement in the pulse sequence Fig. 2. A maximum potential gain from thepuse ffiffiffi of the sensitivity enhancement scheme is given by a factor 2. However, the sequence requires an extra transfer step of ca. 5 ms duration. Assuming that amide solvent exchange rate is 100 s1, it is easy to estimate that the loss of signal due to solvent exchange completely offsets the sensitivity gain. Nevertheless, for most samples of practical interest the exchange rate is lower than 100 s1 and therefore the use of the sensitivity enhancement scheme is likely justified (also due to its excellent water suppression properties). Finally, under the conditions of fast solvent exchange there is a potential risk associated with partial saturation of the water signal [57,58]. Generally speaking, the degree of saturation is variable and, in particular, depends on srel. Since the saturation is effectively transmitted to the amide sites, the magnitude of 1HN magnetization available prior to each scan also turns out to be dependent on srel. This causes an unwanted modulation of the measured relaxation curves, which can seriously compromise the accuracy of the experiment [59,60]. To avoid these artefacts we have chosen to ‘‘crush’’ water magnetization following the acquisition period and prior to the recycling delay, thus creating highly reproducible initial conditions. This design leads to a very accurate experiment. In principle, the sensitivity is to a certain degree sacrificed relative to a sequence that preserves water magnetization. However, in practice the sensitivity is similar to the standard 15N relaxation experiments where the water signal is strongly saturated with no regard for solvent exchange. 2.2. The results from PD-CPMG are consistent with experiment 15 N spin-lock In order to confirm that PD-CPMG scheme achieves consistency with other commonly used R2 measurement strategies such as 15N spin-lock experiment, we have collected both types of data on the samples of chicken a-spectrin SH3 domain (1.5 mM) and unfolded ubiquitin (2.0 mM). Only those peaks that do not have any significant spectral overlaps have been selected for processing and analyses (58 residues for a-spc SH3 domain and 48 residues for unfolded ubiquitin). The quality of the relaxation curves is excellent in both experiments, with very low fitting residual. Importantly, the results of the two independent measurements show an excellent correlation with each other, as evidenced by the cor1 Specifically, 1D version of 1HN–15N HSQC, where a variable-length nitrogen pulse is inserted following the initial INEPT period (Daiwen Yang and Lewis Kay, unpublished). relation coefficients 0.999 and 0.993, see Fig. 3. The systematic deviation between the two datasets is very small. Specifically, the difference between the mean values of R2 from the new PDCPMG experiment and the standard spin-lock experiment is +0.9% in the case of a-spc SH3 and 1.3% in the case of ubiquitin. Even though such differences are negligibly small, we have a fairly good idea of what causes them. In the case of ubiquitin, the conductivity of the acidic sample is relatively high and therefore it experiences a substantial amount of heating [61]. PD-CPMG sequence heats the sample a little more than spin-lock sequence, 0.45 vs. 0.30 °C, leading to slightly lower R2 rates. For a-spc SH3 the amount of heating generated by both experiments is small, less than 0.1 °C. However, one has to bear in mind that a-spc SH3 is a folded protein with broadly dispersed 1HN spectrum. DIPSI-2 decoupling does not work quite as well in this case, leading to a small magnetization loss and consequently slightly overestimated R2 rates. Both aspects – the performance of proton composite decoupling and sample heating – are discussed in greater detail in what follows. We have also recorded a control PD-CPMG experiment where the strength of the DIPSI-2 decoupling was lowered from ca. 4 kHz to ca. 3 kHz. The results remain virtually unchanged, as illustrated in Fig. 4 (correlation coefficients 0.999 and 0.998). The observed amount of systematic deviation is vanishingly small (and can be rationalized along the same lines as above). Importantly, this result means that PD-CPMG experiment with relatively low level of decoupling power, ca. 3 kHz, can be used to sample the relaxation profiles up to srel  1 s and beyond. It can also be used to collect the data from samples with high conductivity (high ionic strength) where sample heating due to deposition of the rf power needs to be reduced. 2.3. PD-CPMG scheme improves the precision of 15N R2 measurements The PD-CPMG sequence is intended to improve the sampling of N relaxation curves in the situation when R2 relaxation is relatively slow, on the order of 1–3 s1. Specifically, the experiment is relevant for IDPs at or near the physiological temperature. Of necessity, NMR studies of IDPs are often conducted at low concentration, 100 lM or less. Furthermore, the time frame of the measurements is usually limited, since the samples have a tendency to rapidly deteriorate. For those samples where pH is close to physiological, the signal-to-noise ratio is further lowered by amide solvent exchange which in the case of IDPs affects all residues in the protein. Under these circumstances, the precision of 15N R2 data can become a critical issue. In order to model this type of a situation, we have prepared two samples of unfolded ubiquitin with protein concentration 100 and 50 lM and collected the relaxation data at 37 °C. Toward this end, we employed the standard 15N R1q experiment [10] as well as the new PD-CPMG scheme. All experiments were recorded in duplicate to assess the reproducibility of the results. The outcome is illustrated in Figs. 5 and 6. The relaxation curves recorded in the repeat spin-lock and PDCPMG experiments are illustrated in Fig. 5. The results for residue L15 are shown as is, i.e. in a form of R1q decay and apparent Rapp 2 decay, with no correction for 15N frequency offset. The quality of the fits is similar for the two experiments, as can be appreciated from the magnitude of the fitting residual v. However, the reproducibility of the relaxation rates as determined in the spin-lock measurements (2.41 and 2.81 s1) is clearly worse than for PDCPMG (2.67 and 2.56 s1). This happens because the spin-lock experiment is limited to short srel delays and therefore cannot properly sample the relaxation decay profile [34]. The summary of the data from the repeat experiments is shown in Fig. 6. Clearly, PD-CPMG achieves a much better reproducibility 15 Fig. 3. Comparison of 15N R2 rates from the PD-CPMG experiment and the standard spin-lock measurement [10]. Each experiment took ca. 2 h to record. The PD-CPMG experiment used 4 kHz DIPSI-2 decoupling. All datasets have been corrected for 15N frequency offset effects (see below for details). PD-CPMG experiment on the sample of a-spc SH3 was carried out with 2sCP = 13.7373 ms and the set of six srel delays ranging from 0 to 275 ms. Fig. 4. Comparison of 15N R2 rates from the PD-CPMG measurements using ca. 4 kHz and 3 kHz DIPSI-2 decoupling. In the experiments with 3 kHz decoupling, the data from a-spc SH3 were obtained using m = 1, 2sCP = 9.6509 ms, and the set of six srel delays ranging from 0 to 193 ms, whereas the data from ubiquitin were collected using m = 1, 2sCP = 9.8235 ms and the set of six srel delays ranging from 0 to 589 ms. than the standard spin-lock measurement [10]. The average absolute-value error in R1q data is three times as large as in PD-CPMG data: 9.1% vs. 3.7% for 100 lM sample and 22.6% vs. 7.5% for Rapp 2 50 lM sample. This difference in precision can be critical for studies that use 15N relaxation to quantify changes in IDPs conformational dynamics in response to various perturbations, e.g. point mutations, posttranslational modifications, variations in pH, crowding effects, etc. Such changes are typically subtle and can be successfully identified only when high-precision 15N relaxation data are available. Note that R1q data shown in Fig. 6c are essentially useless in this regard since the measurement errors are of the same magnitude as per-residue R2 variations. In contrast, Rapp 2 data shown in Fig. 6d retain the ability to distinguish between mobile residues, constrained residues, and those residues that experience exchange broadening. 2.4. Modified PD-CPMG scheme for arginine side-chain 15 Ne After small modifications, the PD-CPMG scheme Fig. 2 can also be used to measure R2 relaxation rates of 15Ne spins in Arg side chains. Arginine side chains are long and flexible; in globular pro- teins they are typically immersed in solvent and move in a relatively unconstrained fashion. Consequently, 15Ne R2 rates tend to be low compared to the backbone 15N rates and thus particularly well suited for PD-CPMG measurements. It is also worth noting that Ne are more prone to solvent exchange than the backbone amide sites. Therefore, the favorable properties of the PD-CPMG experiment with regard to solvent exchange are especially useful in the context of 15Ne measurements. The pulse sequence requires some alterations, as described in the caption of Fig. 2. The main source of difficulties is the weak 15 e 15 g N – N two-bond coupling with the magnitude ca. 1 Hz [62]. This coupling remains active during the standard CPMG pulse train which employs hard nitrogen pulses. Since srel times employed in our measurements are long, the 2JNeNg coupling achieves partial conversion of Nex into 2Ney Ng z during this time period. This causes partial loss of signal and distorts the observed relaxation decay profiles. Since 15Ne and 15Ng have significantly different chemical shifts (separated in the spectrum by ca. 10 ppm), this problem can be easily overcome by application of selective 180° pulses during the CPMG period. For this purpose we have employed REBURP Fig. 5. Relaxation decay profiles for residue L15 in 0.1 mM sample of unfolded ubiquitin as obtained from the repeat measurements using 15N spin-lock experiment (panels A ¼ 2:58 s1 (uncorrected for 15N offset and B) and PD-CPMG (panels C and D). For reference, the measurements using 2.0 mM sample of unfolded ubiquitin yield R1q = Rapp 2 effects). Parameter v indicated in the plot is the rmsd between the experimental and fitted intensities. pulses which have been used in the context of CPMG measurements before [63,64]. One of the potential problems with such strategy is that REBURP pulses are relatively long, 4.0 ms, so that nitrogen magnetization spends part of the time away from the transverse plane. As a result, the measured relaxation decay may potentially represent a mixture of R2 and R1 rates. However, numerical simulations suggest that this effect introduces only a very small error, on the order of 1%. To understand this result, one should take into consideration several factors. (i) REBURP pulses are applied relatively infrequently, 2sCP P 10 ms. (ii) REBURP pulses are applied on-resonance or close to resonance (since 15 e N chemical shifts are confined to a relatively narrow range). Under these conditions the magnetization mostly remains in the transverse plane during the REBURP pulse. (iii) REBURP pulses are applied with [0 0 1 3] phase cycle. Considering Nx magnetization, we observe that it is locked by the first two pulses, such that no R1 character is introduced into spin relaxation. Similarly Ny magnetization is locked by the last two pulses. (iv) In rapidly moving Arg side chains, R2 and R1 rates tend to be similar. Ultimately we rely on the comparison with R1q experiment to confirm that PD-CPMG measurement is error-free. Importantly, R1q experiment is insensitive to the effect of 2JNeNg. Numerical simulations show that given a relatively large chemical shift offset between 15Ne and 15Ng, ca. 10 ppm, moderate spin-lock strength, 1.5–2 kHz, very weak coupling, 1 Hz, and relatively short srel delays, 100 ms, it is safe to neglect Hartmann–Hahn transfer during the spin-lock period. In Fig. 7 we compare the R2 rates obtained from the standard R1q experiment with those measured by 15Ne PD-CPMG. The two datasets are consistent within 0.5%, which is approximately the same as the level of agreement previously observed for the backbone amide sites, see Fig. 3a. This result provides validation for the modified version of the PD-CPMG sequence aimed at 15Ne spins. Potential gains in precision in this case should be even more significant than for backbone measurements. 3. Experimental details 3.1. 15 N offset dependence One significant shortcoming of the traditional CPMG experiment is that it requires a numerical procedure to correct for 15N offset effect [65]. In contrast, the PD-CPMG experiment using [0 0 1 3] phase cycle allows for a simple analytical correction [44]: Rapp  R2 þ ðR1  R2 Þl2 2 ð1Þ l ¼ mNoff =mNð180Þ 1 Here Rapp is the apparent decay rate as derived directly from the PD2 CPMG measurement, mNoff is the nitrogen frequency offset for a given Nð180Þ is the field strength of the hard 15N amide resonance, and m1 180° CPMG pulses in the units of Hz. For the experimental settings used in this study the magnitude of l2 does not exceed 0.03. Consequently, it is safe to ignore higher-order corrections which are proportional to l4. The formula Eq. (1) reflects the fact that during srel period (or more specifically during 2sCP intervals) 15N magnetization moves on a path which takes it away from the transverse plane. By the end of each [0 0 1 3] cycle, however, the magnetization is returned to the transverse plane as a result of the good self-compensation properties of this cycle. The original correction formula published by Bain et al. contains an extra term which describes spin relaxation during 15N 180° pulses [44]. In our case this additional term can be safely neglected because 15N 180° pulses are very short compared to 2sCP P 10 ms. The resulting simple expression Eq. (1) can be easily inverted to determine the true relaxation rate constant R2. The validity of Eq. (1) has been tested by means of numeric simulations. Briefly, spin evolution in the two-spin (1HN, 15N) system was modeled using full product operator basis of dimension 15. Fig. 6. The reproducibility of R1q and Rapp relaxation rates as measured in the repeat spin-lock and PD-CPMG experiments using low-concentration samples of unfolded 2 ubiquitin at 37 °C. Each experiment was recorded in a total of ca. 2 h. Fig. 7. Comparison of arginine 15Ne R2 rates from the PD-CPMG experiment and the standard spin-lock measurement. The results are from two arginine residues in a-spc SH3 domain, R21 and R49. Protein concentration in the sample is 1.5 mM. The PD-CPMG sequence has been adapted to measure 15Ne relaxation as discussed in the text. In running this experiment one has to be mindful of 15Ne and 15Ng chemical shifts specific to a given protein. The spin-lock sequence [10] was used as is, with nitrogen rf carrier set to 85 ppm. Both datasets have been corrected for 15N frequency offset effects. All coherent evolution mechanisms were included (chemical shift, rf pulses, scalar coupling) as well as the standard relaxation mechanisms (dipolar and CSA). In terms of rf pulses, the simulations reproduce the experimental setup described in the caption of Fig. 2. We have also included the effects of 15N rf field inhomogeneity which was modeled via Gaussian distribution with the width 2r ¼ 0:1  mN1 . Further details can be found in Materials & Methods. rate In Fig. 8a we illustrate the dependence of the apparent Rapp 2 rates on 15N frequency offset mNoff . Shown are the simulated Rapp 2 (red circles) as well as the predictions using Eq. (1) (black curve). The true value of R2 is indicated by the horizontal dashed line. This result suggests that the rates measured via PD-CPMG experiment and corrected by means of Eq. (1) provide a very accurate measure of R2 relaxation. Note also that the offset dependence illustrated in Fig. 8a is rather weak. This is not surprising since PD-CPMG employs a train of hard 15N 180° pulses which effectively refocus nitrogen magnetization across the entire spectrum. In fact, if the offset dependence is ignored the resulting error in determination of R2 does not exceed 1%. In most cases the error of this magnitude can be tolerated and therefore it is safe to assume that R2 ¼ Rapp 2 . This obviates the need in 15N R1 measurement which is otherwise needed to calculate the offset correction according to Eq. (1). Finally, it is worth noting that the result shown in Fig. 8a is independent of the rf field 162 Fig. 8. Simulated dependencies (A) Rapp vs. mNoff for the PD-CPMG experiment and (B) R1q vs. mNoff for the spin-lock experiment. The results from numeric simulations are shown 2 with red circles (red lines), the calculations using analytical formulas are shown with solid black lines, the target value of R2 is shown with the horizontal dashed line. The CPMG and spin-lock pulse sequence elements are modeled with the same settings as used in the experimental study (see Fig. 2 and Section 5). In particular, proton DIPSI-2 decoupling is assumed to be applied on-resonance with the rf field strength 4 kHz. inhomogeneity on both 15N and 1H channels (assuming any reasonable rf field distribution). For comparison, in Fig. 8b we show the equivalent dependence for the spin-lock experiment, R1q vs. mNoff [10]. Notably, there is a shift between the simulated R1q rates (red circles) and the standard correction formula, R1q = R2 sin2h + R1 cos2h (black curve). The shift, which has a magnitude of 0.03–0.04 s1, can also be found in the Korzhnev’s original report (see Figs. 2 and 3 therein). It arises from the interplay between the spin-lock, 1JNH coupling, and 1H 180° pulses used to suppress dipolar-CSA cross-correlations [10]. Even though such pulses are applied infrequently, they can still give rise to a discernible error. In relative terms, this error can be safely neglected for slowly tumbling globular proteins, but not necessarily so for highly mobile IDPs. As it turns out, in the case of high-conductivity ubiquitin sample the systematic error associated with spin-lock experiment, Fig. 8b, is compensated by the effect from sample heating (see below). Such error cancelation, however, is fortuitous. For samples with low conductivity the error would persist at the level of ca. 2%. Furthermore, the magnitude of the error is sensitive to the details of 15N rf field inhomogeneity and may potentially increase beyond this level. 3.2. 1H decoupling and choice of sCP As already pointed out, proton decoupling should be synchronized with 15N CPMG pulse train according to 2sCP þ pNð180Þ ¼ mDDIPSI2 ð2Þ For this purpose, one should calibrate the proton 90° pulse at the chosen decoupling power (3–4 kHz), calculate the duration of the decoupling cycle DDIPSI2, and then set sCP accordingly (see caption of Fig. 2). What happens if the synchronization condition is not met? DIPSI-2 sequence is designed to achieve near-complete suppression of 1 JNH over the time period DDIPSI2. However, if at some point during DDIPSI2 one applies a 15N 180° pulse this would interfere with the decoupling scheme, leading to less-than-perfect suppression of 1 JNH. As a consequence, nitrogen spin would experience a certain amount of scalar-coupled evolution and suffer from additional magnetization loss (e.g. due to dephasing of 2NyHz under the effect of the proton rf field). From the perspective of PD-CPMG measurements, this would result in overestimated nitrogen R2 rates. Indeed, we have been able to reproduce this effect via simulations and experimentally. When PD-CPMG experiment is set up with no regard for synchronization conditions, the determined R2 rates prove to be systematically higher. For example, in trial experi- ments involving unfolded ubiquitin we observed the bias of ca. 0.07 s1. While such relatively small deviations can usually be neglected for slowly tumbling globular proteins, they are not necessarily insignificant in the case of IDPs. The undesirable effects can be avoided by enforcing the synchronization condition Eq. (2). In principle, the value of m used in the synchronization condition should be even. However in practice odd values of m are equally acceptable (verified both experimentally and by simulations). This is so because one-half of the standard DIPSI-2 cycle still offers excellent decoupling properties. For example, in the case of ubiquitin measurements described in the caption of Fig. 2 the synchronization condition reads 2sCP = (m 7.0218–0.0760) ms, where m = 1, 2, 3, . . . . The choice m = 2 corresponds to the strength of the effective rf = 1/4sCP = 36 Hz. This is much lower than the strength field mCPMG 1 of the rf field used for proton decoupling, 4.1 kHz. Thus, the experiment should be safe with regard to a potential risk of Hartmann– Hahn transfer. Indeed, our simulations predict that the outcome of the experiment is independent of the choice of m, confirming that Hartmann–Hahn transfer is not an issue. However, the experimental tests revealed a different type of complication. As it turns out, the measurements using large values of m (i.e. long sCP delays) yield slightly higher than expected R2 rates. For instance, in the case of ubiquitin, increasing m from 2 to 6 leads to 0.1 s1 increase in the average R2 value. The trend is reverse of what could be expected from Hartmann–Hahn crosspolarization. It also cannot be explained by a variable degree of sample heating (the effect is also observed in a-spectrin SH3, where there is very little heating). We have considered a number of possible scenarios: (i) dispersion-like effect associated with pervasive small Rex contributions; (ii) the effect from small scalar couplings between 15N and 1Ha, 1Hb; (iii) the effect from small scalar couplings between 15N and natural-abundance 13C; (iv) the effect of dipole–dipolar cross-correlations in a three-spin system 15N, 1 N H , and 1Ha (1Hb); (v) the effect of diffusion (convection flow) in inhomogeneous static magnetic field. Using additional experimental tests and/or numeric simulations we were able to rule out each of these explanations. Instead, we hypothesize that the performance of DIPSI-2 decoupling is not quite as efficient as suggested by numeric simulations. Small instrumental defects such as finite pulse rise time, phase transients, or amplifier drooping have a subtle, yet discernible effect on the real-life performance of the decoupling sequence. To demonstrate the feasibility of this hypothesis we conducted additional experimental measurements. Specifically, the PD-CPMG experiment was repeated with 1H rf carrier shifted from 8.3 ppm to 6.5 ppm. The numeric simulations (including carefully designed Fig. 9. The effect of rf pulse miscalibration on (A) Rapp rates from PD-CPMG experiment and (B) R1q rates from spin-lock experiment. The miscalibration factor represents the 2 ratio of the actual m1 to the target m1. The simulations have been conducted assuming mNoff ¼ 0 and 2r ¼ 0:1  mN1 . For proton channel, the effects of frequency offset and rf field inhomogeneity were found to be negligibly small. three-spin simulations) predict that such carrier jump should have no effect on the measured R2 rates. Yet the experimentally measured R2 values in the sample of unfolded ubiquitin increased on average by 0.03 s1. In the case of a-spc SH3 with its widely dispersed 1HN spectrum the increase was more substantial, 0.06 s1. This lends support to our hypothesis that the real-life performance of proton decoupling is less perfect than can be inferred from the simulations. This result makes us suggest that DIPSI-2 decoupling is less efficient than expected in suppressing 1JNH coupling. In this situation we rely on 15N 180° pulses to assist with decoupling. In order to fully suppress 1JNH evolution, nitrogen pulses should be applied sufficiently frequently. It is also important that nitrogen pulses are applied with maximum power, in our case 6.6 kHz.2 To summarize, the PD-CPMG experiment presented in this paper should be executed with proton decoupling rf power of 3–4 kHz and 2sCP  10–15 ms (subject to synchronization condition, m = 1–2). Use of the lower decoupling power or longer sCP delays results in a small but measurable bias, leading to overestimated R2 rates. Finally, we would like to comment on the choice of proton decoupling scheme. DIPSI-2 was selected primarily for its excellent J-coupling suppression properties. The decoupling bandwidth is a secondary consideration (particularly for disordered proteins with their narrow range of 1HN chemical shifts). The PD-CPMG measurements using DIPSI-3 decoupling produce the results that are virtually identical to those obtained with DIPSI-2. Choosing between the two, we prefer the latter scheme since it offers a benefit of a shorter cycle. Accurate results have also been obtained using WALTZ-16. However, in this case the experiment becomes more sensitive to synchronization condition – away from the correct setting expressed by Eq. (2) the measured R2 rates turn out to be significantly overestimated (confirmed both experimentally and by simulations). Along these lines we can explain the appearance of bias in the earlier implementations of PD-CPMG [38]. Finally, GARP-1 decoupling sequence shows relatively poor performance. This is not surprising since GARP offers excellent bandwidth, but mediocre J-coupling suppression properties [66]. 3.3. Rf pulse miscalibration The numeric simulations modeling the effect of rf pulse miscaland R1q rates are illustrated in Fig. 9. ibration on the measured Rapp 2 The PD-CPMG experiment turns out to be remarkably stable with respect to miscalibration of proton pulses in the DIPSI-2 decou2 If CPMG pulses are applied with reduced level of power (4 kHz) some of the recorded decay curves become slightly distorted. This effect occurs only at certain specific values of 15N frequency offset. pling scheme (red circles3 in Fig. 9a). This reflects excellent selfcompensation properties of the DIPSI-2 sequence as manifested in our simulations. On the other hand, the miscalibration of 15N 180° pulses leads to nitrogen magnetization spending part of the time away from the transverse plane. This results in the increased R1 character of the spin relaxation and lower Rapp rates (blue circles). 2 Note that in practice 15N pulse calibration should be accurate to at least within ±5%. Hence the actual miscalibration factor is likely conrates obfined to the narrow range 0.95–1.05. In this range the Rapp 2 tained from the PD-CPMG measurements remain essentially unchanged. We have also considered the scenario where both 15N and 1H pulses are miscalibrated. The results are no different from the situation where 15N pulses alone are misset. As a point of comparison, the effect of rf field miscalibration on R1q experiment is also illustrated, Fig. 9b. There is certain amount of error associated with this experiment as manifested in the shift between the simulated and the target relaxation rates (see Fig. 8 and related discussion). Varying the strength of on-resonance 15N spin lock in the interval from 1.2 to 2.2 kHz modulates the magnitude of error as shown in the plot; the sinusoidal modulation pattern is similar to the one previously observed [10]. There is also an additional element of bias associated with spin-lock experiment which is not reflected in Fig. 9b. The failure to correctly determine mN1 leads to an error in applying the 15N offset correction. The amount of error can be substantial, on the order of 0.1 s1. This is much worse than in the case of PD-CPMG experiment, which is fairly insensitive to the 15N offset effects (see Fig. 8).4 Finally, we have conducted additional experimental measurements to test the validity of the simulations illustrated in Fig. 9a. For this purpose we have deliberately misset the proton pulse in the DIPSI-2 decoupling sequence – instead of the properly calibrated value, pH(90) = 61 ls, we have used 56 or 66 ls. Using this altered experimental setup, we repeated the PD-CPMG measurements on the sample of unfolded ubiquitin. The results proved to be in perfect agreement with the previously obtained data, thus confirming that PD-CPMG experiment is immune to miscalibration of the DIPSI-2 proton pulses. Along the same lines we have tested the incorrect settings for nitrogen CPMG pulses: instead of pN(180) = 76 ls we have used 66 or 86 ls. As expected, this led to appreciable decreases in the measured R2 rates (on average by 0.09 and 0.06 s1, respectively). One should keep in mind, however, that these tests involve a significant element of exaggeration. In 3 For interpretation of color in Fig. 9, the reader is referred to the web version of this article. 4 As for the proton pulses, their sole purpose in the spin-lock experiment is to suppress the dipolar-CSA cross-correlation. In this role they remain efficient even when their actual flip angle is varied between 130° and 230° (red circles in Fig. 9b). practice, hard 15N pulses are calibrated with much better accuracy, on the order of ±1 ls. Under these conditions the PD-CPMG experiment is essentially insensitive to the effects of pulse miscalibration. 3.4. The importance of using external 2H lock It is clearly desirable to study IDPs at or near physiological conditions. However, so far such studies have been rare [67]. The main difficulties arise from fast solvent exchange, kex  10–100 s1, which undercuts the sensitivity of HSQC experiment and worsens the situation with spectral overlaps. There are also other, more technical, problems associated with solvent exchange that can compromise the accuracy of 15N relaxation measurements. Most biological NMR samples are prepared with 5–10% D2O for the purpose of frequency locking. However, under fast solvent exchange conditions the presence of D2O in the sample could have a number of undesirable consequences for 15N R2 measurements [12]. (i) Standard relaxation experiments use 1HN(15N) sites as a point of origin. During the course of the sequence, and in particular during srel, the original 1HN(15N) groups are partially converted into unobservable 2HN(15N). This transition process modulates the recorded decay profile and thus interferes with R2 determination. (ii) If solvent exchange is fast on the time scale of srel, the measured R2 rate represents a weighted average of 15N(1HN) and 15 N(2HN) relaxation rates. (iii) In the latter case, 15N(2HN) relaxation contains a sizable contribution from the scalar mechanism due to fast deuterium relaxation and solvent exchange. In PDCPMG experiment this contribution is only partially suppressed by infrequent application of 180° 15N pulses. (iv) In addition, the apparent R2 may include an Rex-type term which stems from the isotopic frequency shift between 15N(1HN) and 15N(2HN). To avoid all of these complications, we use the external frequency lock, i.e. 100 lL D2O placed in a coaxial insert fitted into the standard NMR tube. Such inserts can be purchased inexpensively from a number of vendors (we used WGS-5BL from Wilmad). They have been widely used in the past in the studies dealing with fast solvent exchange [68,69]. It has been shown that the samples using coaxial inserts are less likely to suffer from convection flow effects [70]. On the downside, such inserts are currently unavailable for Shigemi tubes. 3.5. Manipulating water magnetization As discussed above, PD-CPMG sequence is intended for use with intrinsically disordered proteins at physiological temperature. If sample pH is also close to physiological, then solvent exchange becomes a major factor. Specifically the accuracy of the measurements can be compromised by the transfer of the saturation from water to amides mediated by fast exchange. Other transfer mechanisms, such as (i) intermolecular NOE and (ii) solvent exchange involving hydroxyl and amine groups followed by intramolecular NOE, can potentially add to the problem. Additional damage can be caused by radiation damping. There are several ways of dealing with this complication. For instance, one can try to preserve water magnetization during the course of the pulse sequence. In principle, this is feasible since DIPSI-2 sequence can be used to lock water magnetization [71]. However, in practice this method is not well suited for our experiment. During the long srel delays,  0.5–1 s, spin-locked water magnetization undergoes significant relaxation decay and therefore fails to be conserved. The alternative approach is to use very long recycling delays allowing for complete recovery of water magnetization. For obvious reasons this is also impractical. Instead, we have chosen to apply water purge element [51] following the acquisition period and prior to the recycling delay. This method guarantees that the amount of water magnetization present at the beginning of each scan always remains the same. Consider the situation where solvent exchange is fast on the time scale of spin–lattice relaxation, kex  10 s1 or higher. In this case the recovery of amide magnetization is controlled by the water R1 rate, which is 0.2 s1 at 37 °C [72]. Under these circumstances, the optimal recycling delay is approximately 5.0 s. Long recovery time means that the sensitivity of the experiment suffers – it is ca. 2-fold lower compared to the schemes that preserve water magnetization. However, this is the sacrifice that is necessary to ensure the accuracy of R2 measurements. Note that there is also a positive aspect to longer recycling delays as they help to reduce sample heating (discussed below). The same problems are encountered in the standard relaxation experiments when applied to IDPs at or near physiological conditions. For example, in the standard R1q experiment the status of water magnetization changes depending on the number of 1H 180° pulses applied during srel. This gives rise to a distinctive modulation pattern in the recorded relaxation curves (data not shown). To avoid such spurious effects, we have also inserted the watercrusher element in the standard R1q pulse sequence [10]. All R1q measurements reported in this work were conducted using this amended version of the original sequence (see Materials & Methods). 3.6. Contribution from solvent exchange to Rapp 2 Above we have discussed two potential complications associated with solvent exchange: (i) proton-deuterium exchange in a D2O-containing sample and (ii) saturation transfer from H2O to amide protons. In this section we discuss a third mechanism whereupon solvent exchange can interfere with 15N R2 measurements. In the absence of proton decoupling, the in-phase Nx magnetization interconverts with the anti-phase 2NyHz. The latter is destroyed by solvent exchange, which physically separates the two correlated spins [49]. When solvent exchange is sufficiently fast on the time scale of 1JHN the resulting loss of magnetization can be described as scalar relaxation of the second kind. In the PD-CPMG and spin-lock experiments, 1JHN evolution during srel is suppressed. Therefore, one may expect that scalar relaxation should be absent. This is not quite so. For spin-lock experiment, the standard expression for scalar relaxation rate 2 2 Rsc 2 ¼ ðpJHN Þ sex =ð1 þ ð2pm1 sex Þ Þ [73] immediately suggests that the effect can be significant.5 A similar outcome can be expected for the PD-CPMG experiment, although no analytical formula is available to address the situation involving DIPSI-2 decoupling. The simulated R1q and Rapp constants for a range of solvent ex2 change rates kex are shown in Fig. 10. The graph demonstrates that slow exchange, kex < 10 s1, has virtually no effect on the extracted relaxation rates. As the exchange rate increases to 10–100 s1, a significant amount of error is generated. The R1q experiment using 1 kHz spin lock is particularly vulnerable (green curve). The R1q experiment using 2 kHz spin lock and PD-CPMG experiment using 4 kHz DIPSI-2 decoupling produce a similar amount of error, which is not necessarily negligible (orange and red curves, respectively). One should be mindful of this effect when conducting measurements under somewhat extreme conditions where kex exceeds several tens of s1. In this situation it may be advisable to collect the data using higher decoupling power, which helps to eliminate the contribution from solvent exchange into Rapp 2 . For example, we have successfully recorded PD-CPMG experiment with 6 kHz DIPSI-2 decoupling and srel extending to 640 ms (data not shown). Under certain circumstances one may also want to collect the data at 5 In this expression sex ¼ k1 ex and m1 is the strength of the spin-lock. Fig. 10. Dependence of R1q and Rapp rates from 15N spin-lock and PD-CPMG experiments on solvent exchange rate kex. The dependence arises from the loss of 1HN–15N spin 2 correlations due to amide solvent exchange. The simulations have been conducted using the same model as in Fig. 8, with mNoff ¼ 0. Solid lines correspond to the conditions of practical interest; black dashed horizontal line represents the true value of R2. kex is given in the units of s1. two decoupling field strengths, 3 and 4 kHz, to identify the rates affected by solvent exchange. The range kex  10–100 s1 is relevant for IDPs under physiological conditions [74]. This is also the range where 15N relaxation can be measured using the standard HSQC-based schemes. The remaining portion of Fig. 10, corresponding to ultra-fast solvent exchange, is mainly of academic interest (although suitable experimental schemes have also been developed [75,76]). The scalar reaches several s1 when exchange contribution into R1q and Rapp 2 1 (the simulated data fall outside rate increases to ca. 10,000 s the area of the plot). With further increase in kex the scalar relaxation declines. This phenomenon is known as self-decoupling; in principle, self-decoupling leads to complete suppression of 1JNH evolution and allows for extraction of accurate R2 rates (all profiles in the plot converge to the dashed horizontal line). For spin-lock experiment, the numeric results shown in Fig. 10 are in quantitative agreement with the calculations using Redfield-theory formula for scalar relaxation [73]. 3.7. Sample heating Sample heating is a potential concern in all heteronuclear spin– spin relaxation experiments as they deposit a copious amount of rf power into the sample. This is also true for the PD-CPMG scheme where proton decoupling is applied for a lengthy period of time, up to 0.5–1.0 s. The problem is exacerbated for samples with high conductivity. When using a sample of ubiquitin with pH 2.0 and recording PD-CPMG experiment with 6 kHz DIPSI-2 decoupling, we have observed heating-related artefacts such as characteristically distorted peak shapes [77]. This is attributable to the high content of H+ ions in acidic solution; the problem disappears in the pH 3.0 sample (see below). To mitigate the effect of heating, we have programmed the pulse sequence Fig. 2 in an interleaved fashion. In our scheme t1 incrementation is controlled by an outer loop, whereas the array of srel is parsed by an inner loop, alternating between short and long delays (e.g. 0, 560, 112, 448, 224, and 336 ms in the case of ubiquitin measurements). In this manner the degree of heating remains near-constant throughout the experiment. If necessary, the interleaved scheme can be further improved as described by Orekhov and co-workers [78]. The heat-equalizing element [77] can also be included into the sequence. With the experimental setup used in our study it is straightforward to monitor the change in temperature during the PD-CPMG experiment. Toward this goal we have prepared a buffer solution of 8 M urea in D2O, pH 3.0, which imitates ubiquitin sample. This solution was placed into NMR tube while the coaxial insert was filled with methanol. The original pulse sequence was then modified such as to allow for observation of the methanol 1H spectrum (see Materials & Methods for details). This sequence was used to record a dataset which was equivalent to the original PD-CPMG in every way, except that each FID contained a strong methanol signal. The FIDs pertaining to the same srel value have been added together, and the resulting methanol spectrum was used to determine the effective temperature associated with this particular srel [79]. The results of this procedure are presented in Fig. 11. Fig. 11 demonstrates that the sample heating in PD-CPMG experiment is close to uniform, as desired. In the absence of any rf pulsing, the temperature of the sample is determined to be 37.0 °C. The application of PD-CPMG sequence with 4 kHz DIPSI2 decoupling and 2 s recycling delay raises the temperature to between 37.4 and 37.5 °C (green circles in the plot). When proton decoupling power is lowered to 3 kHz, the temperature is stabilized just under 37.4 °C (red circles). This is comparable to the spin-lock experiment employing srel from 5 to 140 ms, where the similar interleaved setup heats the sample to slightly more than 37.3 °C (blue circles). How significant is this level of heating? The data on 15N R2 relaxation in denatured ubiquitin are available at several different temperatures ([80,81], this work). From these data one can readily estimate that the temperature dependence of nitrogen R2 is ca. 0.1 s1/°C. For the experiment at hand the increase in temperature amounts to ca. 0.4–0.5 °C, which translates into approximately 2% bias in the measured relaxation rates. While this amount of error may be tolerable, it can as well be eliminated by adjusting the setting of variable-temperature unit (in our case, to 36.5–36.6 °C). Note the results illustrated in Fig. 11 pertain to the sample with moderately high conductivity. In contrast, for the sample in low conductivity buffer (a-spc SH3) the heating generated by spin-lock experiment is only 0.1 °C. For the same sample the PD-CPMG experiment employing 4 kHz DIPSI-2 decoupling and srel delays as long as 843 ms produces only 0.2 °C heating. 4. General discussion and concluding remarks The concepts used in our PD-CPMG experiment are similar to those previously used in the context of relaxation dispersion measurements [50,82]. In particular, Hansen et al. developed a constant-time CW-CPMG experiment where the loss of the signal is 15 N pulses. measured as a function of n180 tot , the total number of 180° The use of the proton decoupling allows one to focus on the inphase coherence Nx which has more favorable relaxation properties than the combination of Nx and 2NyHz previously used in the context of relaxation-compensated CPMG experiment [83]. The Fig. 11. True temperature associated with different srel values as sampled by the PD-CPMG and spin-lock experiments (denatured ubiquitin, 8 M urea, pH 3.0). The same amount of heating is generated when one uses the sample with neutral pH and 50 mM NaCl. new scheme can also be employed with a smaller number of pulses n180 tot , which improves the sampling of relaxation dispersion profiles . As it should become clear from this brief at low frequency mCPMG 1 discussion, the objectives of CW-CPMG experiment are quite different from what is described in this paper, and the technical details are different as well. In fact, it would be difficult to adapt CW-CPMG for the purpose of 15N R2 measurements since this sequence uses a continuous-wave proton decoupling with a relatively high level of power, 15 kHz. The new proton-decoupled CPMG experiment has been developed with the goal to improve the precision of 15N R2 measurements in intrinsically disordered proteins at or near physiological conditions. However, the test measurements described in this paper only partially satisfy these conditions. While ubiquitin data have been collected at 37 °C, the sample was chemically denatured by application of 8 M urea, the pH was 3.0, and no particular attention has been paid to the ionic strength of the solution. How will our experiment fare if the measurements are conducted under more physiologically relevant conditions? At 37 °C, pH 7.4 amide solvent exchange presents a potentially grave problem. Under these conditions, the exchange rates in disordered proteins mostly fall in the range 20–200 s1 [74], causing significant line broadening and potentially compromising the accuracy of relaxation measurements. Although PD-CPMG measurements under these conditions should be possible, they will be extremely demanding. In this situation it may be advisable to lower pH to 7.0, as this value remains relevant for cytosol [84]. Given that histidine side chains in IDPs titrate near pH 6.0 [85], it should be possible to lower the pH without significantly altering the charges on the protein. The ion content of the cytosol is typically assumed to be equivalent to 150 mM NaCl. We executed the PD-CPMG experiment on a sample containing this amount of salt and found that the temperature of the sample increased by 1.3 °C. This amount of heating is tolerable and does not affect the appearance of the spectra (verified experimentally). The increase in temperature can be compensated by adjusting the setting of the VT unit. We conclude that PD-CPMG measurements can be conducted using the samples with physiologically relevant salt concentrations. Finally, let us consider solvent viscosity and the effect of co-solvents. The inside of the cells is known to be crowded, which causes substantial increases in 15N R2 rates [86]. Similarly, in our ubiquitin measurements the presence of 8 M urea led to elevated R2 values, both through increased solvent viscosity and coordination of urea to the unfolded protein [87]. In contrast, NMR samples of IDPs are usually prepared without crowding agents or osmolytes. The 15 N R2 rates in such samples are typically found to be 2–3 s1 at the temperatures 15–20 °C [88–90], which corresponds to R2 of ca. 1 s1 at our target temperature 37 °C. For relaxation decay that is so slow, the advantages of the proposed PD-CPMG scheme should be even more significant. In other words, one may expect gains in precision that would surpass the factor of 3 found in this study. The issue of precision can be critical for 15N relaxation measurements in IDPs. Because of the propensity to aggregate and precipitate, the samples of IDPs often need to be prepared with low protein concentration, in the range of 10–100 lM. Furthermore, the measurement time is often limited to 1–10 h because the samples tend to quickly deteriorate. Solvent exchange further compounds to the problem, causing line-broadening in the already crowded spectra and further lowering signal-to-noise ratio. Under such circumstances it can be difficult to obtain high-quality data. At the same time it is very important that the data are precise. Indeed, 15N relaxation measurements in IDPs typically pursue the effects that are subtle in nature. For instance, this may be a tenuous a-helical propensity which distinguishes physiologically relevant IDP from a random-coil-like peptide chain or a putative local cluster which is formed in response to a certain point mutation. In each case we rely on small changes in 15N R2 rates to pinpoint the effect of interest. Thus we are faced with the situation where it is essential, but at the same time very difficult, to collect high-precision 15 N R2 data. The new PD-CPMG experiment is expected to be quite helpful in this regard. The accuracy of the new experiment has been established through comparison with well-established R1q scheme. Such comparison was carried out for both unfolded and folded protein samples. We have determined that PD-CPMG experiment has a number of favorable properties. First, it records pure in-phase evolution during t1 period and therefore offers an advantage in sensitivity and resolution. The signal-to-noise ratio in the PD-CPMG spectra of a-spc SH3 and ubiquitin are ca. 15% higher than in the comparable R1q spectra. This advantage becomes dramatic for proteins or peptides experiencing significant solvent exchange. Second, PDCPMG data can be easily corrected for 15N offset effect. In fact, this correction is small and can even be neglected, thus obviating the need for companion R1 experiment. Third, the experiment is designed in such a way that solvent exchange does not interfere with the measurements. We avoid adding D2O to the sample and maintain the constant degree of water saturation. The contribution from scalar relaxation of the second kind arising from solvent exchange remains minimal. Fourth, the experiment is highly stable with regard to pulse miscalibration and rf field inhomogeneity. The amount of sample heating is on par with the R1q measurements. Fifth, possible Rex contributions into 15N R2 rates, which may arise from transient oligomerization or other potentially interesting effects, are largely retained in the PD-CPMG experiment because of . This is arguably preferable to the standard measurethe low VCPMG 1 ment schemes where the application of strong spin-lock field or frequent 15N 180° pulses leads to partial suppression of Rex. Sixth, PD-CPMG experiment has been adapted to probe 15Ne spins in Arg side chains which are likely to be a valuable target for future studies of protein internal dynamics. We have also verified that PD-CPMG sequence can be employed with 13C-labeled samples using the setting 2sCP5–10 ms (to be reported elsewhere). All of these attractive properties make us believe that PD-CPMG 15N R2 experiment will become a valuable addition to the arsenal of NMR experiments targeted at intrinsically disordered proteins. 5. Materials and methods 5.1. Protein samples SH3 domain from chicken a-spectrin and human ubiquitin have been expressed in 15N enriched M9 media and purified as described previously [91,92]. Protein concentrations were determined using UV absorbance at 280 nm. The sample of 1.5 mM aspc SH3 has been prepared in H2O, 20 mM citrate, 0.02% NaN3, pH 3.5. The sample of 2.0 mM unfolded ubiquitin was prepared in H2O, 8 M urea, pH 3.0. Two additional ubiquitin samples were prepared with protein concentration 50 and 100 lM. Sample volume in each case was 500 lL, with 100 lL of D2O added into the coaxial insert of the NMR tube (Wilmad, WGS-5BL) to serve as external lock. 5.2. NMR spectroscopy All NMR experiments were performed on Varian Inova-600 spectrometer equipped with triple-resonance z-axis gradient probe. The measurements were carried out at 25 °C for a-spc SH3 and 37 °C for unfolded ubiquitin. The backbone amide spectra were recorded with 15N carrier at 119 ppm and 15N spectral width of 30 ppm (a-spc SH3) or 22 ppm (ubiquitin). The data were collected with 64 t1 increments and 1800 points in t2 domain. The spectra of Arg (1He,15Ne) in a-spc SH3 were recorded with 15N carrier as 85 ppm, 15N spectral width of 10 ppm, and 16 t1 increments. All data were collected with 4 scans per t1 increment. The spectra were processed using NMRPipe [93]. Squared phase-shifted sinebell window function was applied in both dimensions and the spectra were zero-filled to the size 4096  512 (1HN,15N) or 4096  256 (1He,15Ne). To ensure a clean comparison between PD-CPMG and spin-lock experiments, we have amended the standard R1q sequence [10] by adding a water-crusher element (red box on the right side of Fig. 2). In the spin-lock experiment we have used the following srel delays: 5(1), 30(1), 60(2), 90(3), 120(4), and 140(4) ms (shown in brackets is the number of 1H 180° pulses used to suppress dipolar-CSA cross-correlations). The 15N spin-lock has been applied with rf field strength 1.7 kHz. All other experimental settings were the same as in PD-CPMG experiment, including the recycling delay d1 = 2 s. 15N R1 data have also been recorded in order to determine 15 N offset correction for both R1q and PD-CPMG data (cf. Eq. (1)). The spectra were integrated using the autoFit/nlinLS routines from the NMRPipe package. These routines operate on the entire ‘‘stack’’ of spectral planes, making an assumption that the peak position and the linewidths do not change significantly from one plane to the other and hence can be fitted in a global sense. This approach is especially helpful for quantitation of the weak peaks. The data were fitted assuming Gaussian peak shapes, as appropriate for the squared sine-bell apodization. The spectral assignments of a-spc SH3 and denatured ubiquitin were obtained from the previous reports [94,95]. To monitor sample temperature during the PD-CPMG experiment we have developed a special scheme based on the pulse se- quence Fig. 2. Specifically, we changed the original sequence beginning with the acquisition period. Starting from this point the modified sequence reads: g11  sblank  pH(90)  t2  d1. Here g11 is the clean-up gradient with the strength 20 G/cm and duration 3.5 ms, sblank is 100 ms delay during which time the 15N WALTZ-16 decoupling is turned on, pH(90) is hard proton pulse with the same phase as the receiver, t2 is the acquisition period of 0.5 s, and d1 is the recycling delay of 1.5 s. The purpose of this sequence is to record 1D spectrum of methanol (which is contained in the NMR tube coaxial insert) under the conditions that emulate the actual PD-CPMG measurement. We recommend using this accessory experiment when working with high conductivity (high ionic strength) samples, provided that accurate absolute values of R2 are of interest. 5.3. Numerical simulations We have simulated spin evolution of the two-spin (1HN, 15N) and three-spin (1HN, 15N and 1Ha) systems during the srel period of the PD-CPMG and spin-lock experiments. Taken into consideration were all sources of coherent evolution: rf fields, frequency offsets, and scalar couplings. In addition, Redfield matrix has been generated by rigorously including dipolar and CSA contributions. In the 2-spin simulations we have also included the ‘‘external’’ 1Ha spin, which manifested itself through dipolar contribution into the auto-relaxation rates of (1HN, 15N) spin modes. In the 3-spin simulations, 1Ha was treated as a part of the spin system. We have assumed that 3JHNHa = 10 Hz, 2JNHa = 5 Hz which is the upper limit for the respective experimentally observed couplings [96,97]. 15N and 1HN CSA tensors were modeled according to the literature data [8,98]; 1Ha CSA tensor was assumed to be zero. The distance between 1HN and 1Ha was set to 1.84 Å. In order to emphasize the effect of dipole–dipolar cross-correlations, the angle between 15 N–1HN and 1HN–1Ha vectors was set to zero. All simulations used a simple form of Lipari-Szabo spectral density [99], where it was assumed that sC = 2 ns, S2 = 0.5, and sfast = 0. This parameterization is consistent with the previous analyses of 15N relaxation in denatured protein [100] and correctly reproduces typical R1 and R2 values observed in denatured ubiquitin at 37 °C (Fig. 3b). Rf pulses were simulated with finite length. To model the effect of rf field inhomogeneity, the simulations were repeated for 100 discrete values of rf field strength uniformly distributed in the interval [m1  2r, m1 + 2r]. The signal intensity was then calculated as a weighted average of the results from multiple simulations. Solvent exchange was modeled as described previously [49]. Specifically, we recognize that any multi-spin mode combining 15N and 1HN spin operators undergoes exchange-induced decay with the rate kex. The simulations featuring 15  15 and 63  63 propagator matrices were repeated for the same set of srel delays as used experimentally. The simulated signal intensities were then fitted with a single exponential, yielding the values of R1q or Rapp 2 . The results from 2- and 3-spin simulations proved to be virtually identical. 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