Error estimation and global fitting in transverse-relaxation dispersion experiments to determine chemical-exchange parameters

Off-resonance effects can introduce significant systematic errors in R₂ measurements in constant-time Carr-Purcell-Meiboom-Gill (CPMG) transverse relaxation dispersion experiments. For an off-resonance chemical shift of 500 Hz, ¹⁵N relaxation dispersion profiles obtained from experiment and computer simulation indicated a systematic error of ca. 3%. This error is three- to five-fold larger than the random error in R₂ caused by noise. Good estimates of total R₂ uncertainty are critical in order to obtain accurate estimates in optimized chemical exchange parameters and their uncertainties derived from χ² minimization of a target function. Here, we present a simple empirical approach that provides a good estimate of the total error (systematic + random) in ¹⁵N R₂ values measured for the HIV protease. The advantage of this empirical error estimate is that it is applicable even when some of the factors that contribute to the off-resonance error are not known. These errors are incorporated into a χ² minimization protocol, in which the Carver–Richards equation is used fit the observed R₂ dispersion profiles, that yields optimized chemical exchange parameters and their confidence limits. Optimized parameters are also derived, using the same protein sample and data-fitting protocol, from ¹H R₂ measurements in which systematic errors are negligible. Although ¹H and ¹⁵N relaxation profiles of individual residues were well fit, the optimized exchange parameters had large uncertainties (confidence limits). In contrast, when a single pair of exchange parameters (the exchange lifetime, τ_ex, and the fractional population, p_a), were constrained to globally fit all R₂ profiles for residues in the dimer interface of the protein, confidence limits were less than 8% for all optimized exchange parameters. In addition, F-tests showed that quality of the fits obtained using τ_ex, p_a as global parameters were not improved when these parameters were free to fit the R₂ profiles of individual residues. Finally, nearly the same optimized global τ_ex, p_a values were obtained, when the ¹H and ¹⁵N data sets for residues in the dimer interface, were fit independently; the difference in optimized global parameters, ca. 10%, was of marginal significance according to the F-test.     

Cross-correlated spin relaxation effects in methyl <Superscript>1</Superscript>H CPMG-based relaxation dispersion experiments: Complications and a simple solution

Artifacts associated with the measurement of methyl ¹H single quantum CPMG-based relaxation dispersion profiles are described. These artifacts arise due to the combination of cross-correlated spin relaxation effects involving intra-methyl ¹H–¹H dipolar interactions and imperfections in ¹H refocusing pulses that are applied during CPMG intervals that quantify the effects of chemical exchange on measured transverse relaxation rates. As a result substantial errors in extracted exchange parameters can be obtained. A simple work-around is presented where the ¹H chemical shift difference between the exchanging states is extracted from a combination of ¹³C single quantum and ¹³C–¹H multiple quantum dispersion profiles. The approach is demonstrated with an application to a folding/unfolding reaction involving a G48M mutant Fyn SH3 domain.     

Backbone 1H and 15N resonance assignments of the N-terminal SH3 domain of drk in folded and unfolded states using enhanced-sensitivity pulsed field gradient NMR techniques

Summary The backbone ¹H and ¹⁵N resonances of the N-terminal SH3 domain of the Drosophila signaling adapter protein, drk, have been assigned. This domain is in slow exchange on the NMR timescale between folded and predominantly unfolded states. Data were collected on both states simultaneously, on samples of the SH3 in near physiological buffer exhibiting an approximately 1:1 ratio of the two states. NMR methods which exploit the chemical shift dispersion of the ¹⁵N resonances of unfolded states and pulsed field gradient water suppression approaches for avoiding saturation and dephasing of amide protons which rapidly exchange with solvent were utilized for the assignment.Abbreviations 2D, 3D two-, three-dimensional - drkN SH3 N-terminal SH3 domain of Drosophila drk - HSQC heteronuclear single-quantum spectroscopy - NOE nuclear Overhauser enhancement - SH3 Src homology domain 3 - TOCSY total correlation spectroscopy     

Identification of a collapsed intermediate with non-native long-range interactions on the folding pathway of a pair of Fyn SH3 domain mutants by NMR relaxation dispersion spectroscopy

Recent 15N and 13C spin-relaxation dispersion studies of fast-folding mutants of the Fyn SH3 domain have established that folding proceeds through a low-populated on-pathway intermediate (I) where the central beta-sheet is at least partially formed, but without interactions between the NH2- and COOH-terminal beta-strands that exist in the folded state (F). Initial studies focused on mutants where Gly48 is replaced; in an effort to establish whether this intermediate is a general feature of Fyn SH3 folding a series of 15N relaxation experiments monitoring the folding of Fyn SH3 mutants N53P/V55L and A39V/N53P/V55L are reported here. For these mutants as well, folding proceeds through an on-pathway intermediate with similar features to those observed for G48M and G48V Fyn SH3 domains. However, the 15N chemical shifts extracted for the intermediate indicate pronounced non-native contacts between the NH2 and COOH-terminal regions not observed previously. The kinetic parameters extracted for the folding of A39V/N53P/V55L Fyn SH3 from the three-state folding model F<-->I<-->U are in good agreement with folding and unfolding rates extrapolated to zero denaturant obtained from stopped-flow experiments analyzed in terms of a simplified two-state folding reaction. The folding of the triple mutant was studied over a wide range of temperatures, establishing that there is no difference in heat capacities between F and I states. This confirms a compact folding intermediate structure, which is supported by the 15N chemical shifts of the I state extracted from the dispersion data. The temperature-dependent relaxation data simplifies data analysis because at low temperatures (< 25 degrees C) the unfolded state (U) is negligibly populated relative to I and F. A comparison between parameters extracted at low temperatures where the F<-->I exchange model is appropriate with those from the more complex, three-state model at higher temperatures has been used to validate the protocol for analysis of three-site exchange relaxation data.     

Practical considerations for investigation of protein conformational dynamics by <Superscript>15</Superscript>N <Emphasis Type="Italic">R</Emphasis><Subscript>1ρ</Subscript> relaxation dispersion

It is becoming increasingly apparent that proteins are not static entities and that their function often critically depends on accurate sampling of multiple conformational states in aqueous solution. Accordingly, the development of methods to study conformational states in proteins beyond their ground-state structure (“excited states”) has crucial biophysical importance. Here we investigate experimental schemes for optimally probing chemical exchange processes in proteins on the micro- to millisecond timescale by ¹⁵N R _1ρ relaxation dispersion. The schemes use selective Hartmann–Hahn cross-polarization (CP) transfer for excitation, and derive peak integrals from 1D NMR spectra (Korzhnev et al. in J Am Chem Soc 127:713–721, 2005; Hansen et al. in J Am Chem Soc 131:3818–3819, 2009). Simulation and experiment collectively show that in such CP-based schemes care has to be taken to achieve accurate suppression of undesired off-resonance coherences, when using weak spin-lock fields. This then (i) ensures that relaxation dispersion profiles in the absence of chemical exchange are flat, and (ii) facilitates extraction of relaxation dispersion profiles in crowded regions of the spectrum. Further improvement in the quality of the experimental data is achieved by recording the free-induction decays in an interleaved manner and including a heating-compensation element. The reported considerations will particularly benefit the use of CP-based R _1ρ relaxation dispersion to analyze conformational exchange processes in larger proteins, where resonance line overlap becomes the main limiting factor.     

Off-resonance rotating-frame amide proton spin relaxation experiments measuring microsecond chemical exchange in proteins

NMR spin relaxation in the rotating frame (R_1ρ) is a unique method for atomic-resolution characterization of conformational (chemical) exchange processes occurring on the microsecond time scale. Here, we use amide ¹H off-resonance R_1ρ relaxation experiments to determine exchange parameters for processes that are significantly faster than those that can be probed using ¹⁵N or ¹³C relaxation. The new pulse sequence is validated using the E140Q mutant of the C-terminal domain of calmodulin, which exhibits significant conformational exchange contributions to the transverse relaxation rates. The ¹H off-resonance R_1ρ data sample the entire relaxation dispersion profiles for the large majority of residues in this protein, which exchanges between conformations with a time constant of approximately 20 μs. This is in contrast to the case for ¹⁵N, where additional laboratory-frame relaxation data are required to determine the exchange parameters reliably. Experiments were performed on uniformly ¹⁵N-enriched samples that were either highly enriched in ²H or fully protonated. In the latter case, dipolar cross-relaxation with aliphatic protons were effectively decoupled to first order using a selective inversion pulse. Deuterated and protonated samples gave the same results, within experimental errors. The use of deuterated samples increases the sensitivity towards exchange contributions to the ¹H transverse relaxation rates, since dipolar relaxation is greatly reduced. The exchange correlation times determined from the present ¹H off-resonance R_1ρ experiments are in excellent agreement with those determined previously using a combination of ¹⁵N laboratory-frame and off-resonance R_1ρ relaxation data, with average values of and 21 ± 3 μs, respectively.     

Measuring <Superscript>13</Superscript>C<Superscript>β</Superscript> chemical shifts of invisible excited states in proteins by relaxation dispersion NMR spectroscopy

A labeling scheme is introduced that facilitates the measurement of accurate ¹³C^β chemical shifts of invisible, excited states of proteins by relaxation dispersion NMR spectroscopy. The approach makes use of protein over-expression in a strain of E. coli in which the TCA cycle enzyme succinate dehydrogenase is knocked out, leading to the production of samples with high levels of ¹³C enrichment (30–40%) at C^β side-chain carbon positions for 15 of the amino acids with little ¹³C label at positions one bond removed (≈5%). A pair of samples are produced using [1-¹³C]-glucose/NaH¹²CO₃ or [2-¹³C]-glucose as carbon sources with isolated and enriched (>30%) ¹³C^β positions for 11 and 4 residues, respectively. The efficacy of the labeling procedure is established by NMR spectroscopy. The utility of such samples for measurement of ¹³C^β chemical shifts of invisible, excited states in exchange with visible, ground conformations is confirmed by relaxation dispersion studies of a protein–ligand binding exchange reaction in which the extracted chemical shift differences from dispersion profiles compare favorably with those obtained directly from measurements on ligand free and fully bound protein samples.     

Measuring the signs of the methyl <Superscript>1</Superscript>H chemical shift differences between major and ‘invisible’ minor protein conformational states using methyl <Superscript>1</Superscript>H multi-quantum spectroscopy

Carr–Purcell–Meiboom–Gill (CPMG) type relaxation dispersion experiments are now routinely used to characterise protein conformational dynamics that occurs on the μs to millisecond (ms) timescale between a visible major state and ‘invisible’ minor states. The exchange rate(s) (\( k_{{{\text{ex}}}} \)), population(s) of the minor state(s) and the absolute value of the chemical shift difference \(|{\Delta \varpi }|\) (ppm) between different exchanging states can be extracted from the CPMG data. However the sign of \({\Delta \varpi }\) that is required to reconstruct the spectrum of the ‘invisible’ minor state(s) cannot be obtained from CPMG data alone. Building upon the recently developed triple quantum (TQ) methyl \( ^{1} {\text{H}} \) CPMG experiment (Yuwen in Angew Chem 55:11490–11494, 2016) we have developed pulse sequences that use carbon detection to generate and evolve single quantum (SQ), double quantum (DQ) and TQ coherences from methyl protons in the indirect dimension to measure the chemical exchange-induced shifts of the SQ, DQ and TQ coherences from which the sign of \({\Delta \varpi }\) is readily obtained for two state exchange. Further a combined analysis of the CPMG data and the difference in exchange induced shifts between the SQ and DQ resonances and between the SQ and TQ resonances improves the estimates of exchange parameters like the population of the minor state. We demonstrate the use of these experiments on two proteins undergoing exchange: (1) the ~ 18 kDa cavity mutant of T4 Lysozyme (\( k_{{{\text{ex}}}} \sim\,3500{\text{ s}}^{{ - 1}} \)) and (2) the \(\sim\,4.7\) kDa Peripheral Sub-unit Binding Domain (PSBD) from the acetyl transferase of Bacillus stearothermophilus (\(k_{ex} \sim\,13,000\hbox { s}^{-1}\)).     

Addressing the overlap problem in the quantitative analysis of two dimensional NMR spectra: Application to <Superscript>15</Superscript>N relaxation measurements

A quantitative analysis of 2D ¹H-¹⁵N spectra is often complicated by resonance overlap. Here a simple method is presented for resolving overlapped correlations by recording 2D projection planes from HNCO data sets. Applications are presented involving the measurement of ¹⁵N T₁ relaxation rates in a high molecular weight protein, malate synthase G, and in a system that exchanges between folded and unfolded states, the drkN SH3 domain. By supplementing relaxation data recorded in the conventional way as a series of 2D ¹H-¹⁵N data sets with a series of a pair of projection planes the number of dynamics probes is increased significantly for both systems studied.     

Histidine side-chain dynamics and protonation monitored by 13C CPMG NMR relaxation dispersion

The use of ¹³C NMR relaxation dispersion experiments to monitor micro-millisecond fluctuations in the protonation states of histidine residues in proteins is investigated. To illustrate the approach, measurements on three specifically ¹³C labeled histidine residues in plastocyanin (PCu) from Anabaena variabilis (A.v.) are presented. Significant Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion is observed for ¹³C^ε1 nuclei in the histidine imidazole rings of A.v. PCu. The chemical shift changes obtained from the CPMG dispersion data are in good agreement with those obtained from the chemical shift titration experiments, and the CPMG derived exchange rates agree with those obtained previously from ¹⁵N backbone relaxation measurements. Compared to measurements of backbone nuclei, ¹³C^ε1 dispersion provides a more direct method to monitor interchanging protonation states or other kinds of conformational changes of histidine side chains or their environment. Advantages and shortcomings of using the ¹³C^ε1 dispersion experiments in combination with chemical shift titration experiments to obtain information on exchange dynamics of the histidine side chains are discussed.     

A simple method for measuring signs of <Superscript>1</Superscript>H<Superscript>N</Superscript> chemical shift differences between ground and excited protein states

NMR relaxation dispersion spectroscopy is a powerful method for studying protein conformational dynamics whereby visible, ground and invisible, excited conformers interconvert on the millisecond time-scale. In addition to providing kinetics and thermodynamics parameters of the exchange process, the CPMG dispersion experiment also allows extraction of the absolute values of the chemical shift differences between interconverting states, | \Updelta [(w)\tilde] | \left| {\Updelta \tilde{\omega }} \right| , opening the way for structure determination of excited state conformers. Central to the goal of structural analysis is the availability of the chemical shifts of the excited state that can only be obtained once the signs of \Updelta [(w)\tilde] \Updelta \tilde{\omega } are known. Herein we describe a very simple method for determining the signs of ¹H^N \Updelta [(w)\tilde] \Updelta \tilde{\omega } values based on a comparison of peak positions in the directly detected dimensions of a pair of ¹H^N–¹⁵N correlation maps recorded at different static magnetic fields. The utility of the approach is demonstrated for three proteins that undergo millisecond time-scale conformational rearrangements. Although the method provides fewer signs than previously published techniques it does have a number of strengths: (1) Data sets needed for analysis are typically available from other experiments, such as those required for measuring signs of ¹⁵N \Updelta [(w)\tilde] \Updelta \tilde{\omega } values, thus requiring no additional experimental time, (2) acquisition times in the critical detection dimension can be as long as necessary and (3) the signs obtained can be used to cross-validate those from other approaches.     

Probing slowly exchanging protein systems via 13Cα-CEST: monitoring folding of the Im7 protein

A ¹³C^α chemical exchange saturation transfer based experiment is presented for the study of protein systems undergoing slow interconversion between an ‘observable’ ground state and one or more ‘invisible’ excited states. Here a labeling strategy whereby [2-¹³C]-glucose is the sole carbon source is exploited, producing proteins with ¹³C at the C^α position, while the majority of residues remain unlabeled at CO or C^β. The new experiment is demonstrated with an application to the folding reaction of the Im7 protein that involves an on-pathway excited state. The obtained excited state ¹³C^α chemical shifts are cross validated by comparison to values extracted from analysis of CPMG relaxation dispersion profiles, establishing the utility of the methodology.     

The influence of muscle type and dystrophin deficiency on murine expression profiles

The phenotypic differences among Duchenne muscular dystrophy patients, mdx mice, and mdx^5cv mice suggest that despite the common etiology of dystrophin deficiency, secondary mechanisms have a substantial influence on phenotypic severity. The differential response of various skeletal muscles to dystrophin deficiency supports this hypothesis. To explore these differences, gene expression profiles were generated from duplicate RNA targets extracted from six different skeletal muscles (diaphragm, soleus, gastrocnemius, quadriceps, tibialis anterior, and extensor digitorum longus) from wild-type, mdx, and mdx^5cv mice, resulting in 36 data sets for 18 muscle samples. The data sets were compared in three different ways: (1) among wild-type samples only, (2) among all 36 data sets, and (3) between strains for each muscle type. The molecular profiles of soleus and diaphragm separate significantly from the other four muscle types and from each other. Fiber-type proportions can explain some of these differences. These variations in wild-type gene expression profiles may also reflect biomechanical differences known to exist among skeletal muscles. Further exploration of the genes that most distinguish these muscles may help explain the origins of the biomechanical differences and the reasons why some muscles are more resistant than others to dystrophin deficiency. Electronic Supplementary Material Electronic Supplementary material is available for this article at and accessible for authorised users. Judith N. Haslett, Peter B. Kang These authors contributed equally to this work.     

Conformational entropy changes upon lactose binding to the carbohydrate recognition domain of galectin-3

The conformational entropy of proteins can make significant contributions to the free energy of ligand binding. NMR spin relaxation enables site-specific investigation of conformational entropy, via order parameters that parameterize local reorientational fluctuations of rank-2 tensors. Here we have probed the conformational entropy of lactose binding to the carbohydrate recognition domain of galectin-3 (Gal3), a protein that plays an important role in cell growth, cell differentiation, cell cycle regulation, and apoptosis, making it a potential target for therapeutic intervention in inflammation and cancer. We used ¹⁵N spin relaxation experiments and molecular dynamics simulations to monitor the backbone amides and secondary amines of the tryptophan and arginine side chains in the ligand-free and lactose-bound states of Gal3. Overall, we observe good agreement between the experimental and computed order parameters of the ligand-free and lactose-bound states. Thus, the ¹⁵N spin relaxation data indicate that the molecular dynamics simulations provide reliable information on the conformational entropy of the binding process. The molecular dynamics simulations reveal a correlation between the simulated order parameters and residue-specific backbone entropy, re-emphasizing that order parameters provide useful estimates of local conformational entropy. The present results show that the protein backbone exhibits an increase in conformational entropy upon binding lactose, without any accompanying structural changes.     

<Superscript>15</Superscript>N transverse relaxation measurements for the characterization of µs–ms dynamics are deteriorated by the deuterium isotope effect on <Superscript>15</Superscript>N resulting from solvent exchange

¹⁵N R₂ relaxation measurements are key for the elucidation of the dynamics of both folded and intrinsically disordered proteins (IDPs). Here we show, on the example of the intrinsically disordered protein α-synuclein and the folded domain PDZ2, that at physiological pH and near physiological temperatures amide—water exchange can severely skew Hahn-echo based ¹⁵N R₂ relaxation measurements as well as low frequency data points in CPMG relaxation dispersion experiments. The nature thereof is the solvent exchange with deuterium in the sample buffer, which modulates the ¹⁵N chemical shift tensor via the deuterium isotope effect, adding to the apparent relaxation decay which leads to systematic errors in the relaxation data. This results in an artificial increase of the measured apparent ¹⁵N R₂ rate constants—which should not be mistaken with protein inherent chemical exchange contributions, R_ex, to ¹⁵N R₂. For measurements of ¹⁵N R₂ rate constants of IDPs and folded proteins at physiological temperatures and pH, we recommend therefore the use of a very low D₂O molar fraction in the sample buffer, as low as 1%, or the use of an external D₂O reference along with a modified ¹⁵N R₂ Hahn-echo based experiment. This combination allows for the measurement of R_ex contributions to ¹⁵N R₂ originating from conformational exchange in a time window from µs to ms.     

Effects of decomposition and storage conditions on the δ13C and δ15N isotope values of killer whale (Orcinus orca) skin and blubber tissues

Several different factors in the collection and preservation of whale skin and blubber samples were examined to determine their effect on the results obtained by stable nitrogen and carbon isotope (δ¹⁵N and δ¹³C) analysis. Samples of wet killer whale skin retained their original stable isotope values for up to 14 d at 4°C or lower. However, decomposition significantly changed the δ¹⁵N value within 3 d at 20°C. Storage at ?20°C was as effective as ?80°C for the preservation of skin and blubber samples for stable isotope analysis for at least a year. By contrast, once a skin sample had been freeze‐dried and lipid extracted, the stable isotope values did not change significantly when it was stored dry at room temperature for at least 12 mo. Preservation of whale skin samples for a month in DMSO‐salt solution, frozen or at room temperature, did not significantly change the δ¹⁵N and δ¹³C values of lipid extracted tissues, although the slight changes seen could influence results of a study if only small changes are expected.     

A methyl <Superscript>1</Superscript>H double quantum CPMG experiment to study protein conformational exchange

Protein conformational changes play crucial roles in enabling function. The Carr–Purcell–Meiboom–Gill (CPMG) experiment forms the basis for studying such dynamics when they involve the interconversion between highly populated and sparsely formed states, the latter having lifetimes ranging from ~?0.5 to ~?5 ms. Among the suite of experiments that have been developed are those that exploit methyl group probes by recording methyl ¹H single quantum (Tugarinov and Kay in J Am Chem Soc 129:9514–9521, 2007) and triple quantum (Yuwen et al. in Angew Chem Int Ed Engl 55:11490–11494, 2016) relaxation dispersion profiles. Here we build upon these by developing a third experiment in which methyl ¹H double quantum coherences evolve during a CPMG relaxation element. By fitting single, double, and triple quantum datasets, akin to recording the single quantum dataset at static magnetic fields of B_o, 2B_o and 3B_o, we show that accurate exchange values can be obtained even in cases where exchange rates exceed 10,000 s^?1. The utility of the double quantum experiment is demonstrated with a pair of cavity mutants of T4 lysozyme (T4L) with ground and excited states interchanged and with exchange rates differing by fourfold (~?900 s^?1 and ~?3600 s^?1), as well as with a fast-folding domain where the unfolded state lifetime is ~?80 µs.     

Controls of nitrogen isotope patterns in soil profiles

To determine the dominant processes controlling nitrogen (N) dynamics in soils and increase insights into soil N cycling from nitrogen isotope (δ¹⁵N) data, patterns of ¹⁵N enrichment in soil profiles were compiled from studies on tropical, temperate, and boreal systems. The maximum ¹⁵N enrichment between litter and deeper soil layers varied strongly with mycorrhizal fungal association, averaging 9.6 ± 0.4‰ in ectomycorrhizal systems and 4.6 ± 0.5‰ in arbuscular mycorrhizal systems. The ¹⁵N enrichment varied little with mean annual temperature, precipitation, or nitrification rates. One main factor controlling ¹⁵N in soil profiles, fractionation against ¹⁵N during N transfer by mycorrhizal fungi to host plants, leads to ¹⁵N-depleted plant litter at the soil surface and ¹⁵N-enriched nitrogen of fungal origin at depth. The preferential preservation of ¹⁵N-enriched compounds during decomposition and stabilization is a second important factor. A third mechanism, N loss during nitrification and denitrification, may account for large ¹⁵N enrichments with depth in less N-limited forests and may account for soil profiles where maximum δ¹⁵N is at intermediate depths. Mixing among soil horizons should also decrease differences among soil horizons. We suggest that dynamic models of isotope distributions within soil profiles that can incorporate multiple processes could provide additional information about the history of nitrogen movements and transformations at a site.     

Sequential assignments in uniformly 13C- and 15N-labelled RNAs: The HC(N,P) and HC(N,P)-CCH-TOCSY experiments

Summary An approach for the simultaneous acquisition of HCN and HCP as well as HCN-CCH-TOCSY and HCP-CCH-TOCSY triple resonance data sets for ¹³C-/¹⁵N-labelled RNAs is presented. The new HCN-CCH-TOCSY scheme unambiguously links all sugar resonances to the base nitrogen. In addition, simultaneous acquisition of HCN-CCH-TOCSY and HCP-CCH-TOCSY data sets provides sequential and base-type information in a single experiment, thereby saving data acquisition time as well as providing complementary data sets that are useful in clarifying ambiguous assignments. Virtually complete sequence-specific phosphate-ribose ¹H, ³¹P, and base ¹⁵N1,9 assignments as well as partial ¹³C assignments could be obtained in a single experiment for a 0.5-mM sample of a 19-mer ribonucleotide.