Relaxation Dispersion Experiments Research Articles

Conformational exchange of aromatic side chains by 1H CPMG relaxation dispersion

Aromatic side chains are attractive probes of protein dynamics on the millisecond time scale, because they are often key residues in enzyme active sites and protein binding sites. Further they allow to study specific processes, like histidine tautomerization and ring flips. Till now such processes have been studied by aromatic 13C CPMG relaxation dispersion experiments. Here we investigate the possibility of aromatic 1H CPMG relaxation dispersion experiments as a complementary method. Artifact-free dispersions are possible on uniformly 1H and 13C labeled samples for histidine δ2 and ε1, as well as for tryptophan δ1. The method has been validated by measuring fast folding–unfolding kinetics of the small protein CspB under native conditions. The determined rate constants and populations agree well with previous results from 13C CPMG relaxation dispersion experiments. The CPMG-derived chemical shift differences between the folded and unfolded states are in good agreement with those obtained directly from the spectra. In contrast, the 1H relaxation dispersion profiles in phenylalanine, tyrosine and the six-ring moiety of tryptophan, display anomalous behavior caused by 3J 1H–1H couplings and, if present, strong 13C–13C couplings. Therefore they require site-selective 1H/2H and, in case of strong couplings, 13C/12C labeling. In summary, aromatic 1H CPMG relaxation dispersion experiments work on certain positions (His δ2, His ε1 and Trp δ1) in uniformly labeled samples, while other positions require site-selective isotope labeling.Graphical abstract

Equilibrium and Kinetic Unfolding of GB1: Stabilization of the Native State by Pressure.

NMR spectroscopy allows an all-atom view on pressure-induced protein folding, separate detection of different folding states, determination of their population, and the measurement of the folding kinetics at equilibrium. Here, we studied the folding of protein GB1 at pH 2 in a temperature and pressure dependent way. We find that the midpoints of temperature-induced unfolding increase with higher pressure. NMR relaxation dispersion experiments disclosed that the unfolding kinetics slow down at elevated pressure while the folding kinetics stay virtually the same. Therefore, pressure is stabilizing the native state of GB1. These findings extend the knowledge of the influence of pressure on protein folding kinetics, where so far typically a destabilization by increased activation volumes of folding was observed. Our findings thus point toward an exceptional section in the pressure-temperature phase diagram of protein unfolding. The stabilization of the native state could potentially be caused by a shift of p Ka values of glutamates and aspartates in favor of the negatively charged state as judged from pH sensitive chemical shifts.

Analysis of Artifacts Caused by Pulse Imperfections in CPMG Pulse Trains in NMR Relaxation Dispersion Experiments

Nuclear magnetic resonance relaxation dispersion (rd) experiments provide kinetics and thermodynamics information of molecules undergoing conformational exchange. Rd experiments often use a Carr-Purcell-Meiboom-Gill (CPMG) pulse train equally separated by a spin-state selective inversion element (U-element). Even with measurement parameters carefully set, however, parts of 1H–15N correlations sometimes exhibit large artifacts that may hamper the subsequent analyses. We analyzed such artifacts with a combination of NMR measurements and simulation. We found that particularly the lowest CPMG frequency (νcpmg) can also introduce large artifacts into amide 1H–15N and aromatic 1H–13C correlations whose 15N/13C resonances are very close to the carrier frequencies. The simulation showed that the off-resonance effects and miscalibration of the CPMG π pulses generate artifact maxima at resonance offsets of even and odd multiples of νcpmg, respectively. We demonstrate that a method once introduced into the rd experiments for molecules having residual dipolar coupling significantly reduces artifacts. In the method the 15N/13C π pulse phase in the U-element is chosen between x and y. We show that the correctly adjusted sequence is tolerant to miscalibration of the CPMG π pulse power as large as ±10% for most amide 15N and aromatic 13C resonances of proteins.

Transitions in DNA polymerase β μs-ms dynamics related to substrate binding and catalysis.

DNA polymerase β (pol β) plays a central role in the DNA base excision repair pathway and also serves as an important model polymerase. Dynamic characterization of pol β from methyl-TROSY 13C-1H multiple quantum CPMG relaxation dispersion experiments of Ile and Met sidechains and previous backbone relaxation dispersion measurements, reveals transitions in μs-ms dynamics in response to highly variable substrates. Recognition of a 1-nt-gapped DNA substrate is accompanied by significant backbone and sidechain motion in the lyase domain and the DNA binding subdomain of the polymerase domain, that may help to facilitate binding of the apoenzyme to the segments of the DNA upstream and downstream from the gap. Backbone μs-ms motion largely disappears after formation of the pol β–DNA complex, giving rise to an increase in uncoupled μs-ms sidechain motion throughout the enzyme. Formation of an abortive ternary complex using a non-hydrolyzable dNTP results in sidechain motions that fit to a single exchange process localized to the catalytic subdomain, suggesting that this motion may play a role in catalysis.

Ligand-Induced Variations in Structural and Dynamical Properties Within an Enzyme Superfamily.

Enzyme catalysis is a complex process involving several steps along the reaction coordinates, including substrate recognition and binding, chemical transformation, and product release. Evidence continues to emerge linking the functional and evolutionary role of conformational exchange processes in optimal catalytic activity. Ligand binding changes the conformational landscape of enzymes, inducing long-range conformational rearrangements. Using functionally distinct members of the pancreatic ribonuclease superfamily as a model system, we characterized the structural and conformational changes associated with the binding of two mononucleotide ligands. By combining NMR chemical shift titration experiments with the chemical shift projection analysis (CHESPA) and relaxation dispersion experiments, we show that biologically distinct members of the RNase superfamily display discrete chemical shift perturbations upon ligand binding that are not conserved even in structurally related members. Amino acid networks exhibiting coordinated chemical shift displacements upon binding of the two ligands are unique to each of the RNases analyzed. Our results reveal the contribution of conformational rearrangements to the observed chemical shift perturbations. These observations provide important insights into the contribution of the different ligand binding specificities and effects of conformational exchange on the observed perturbations associated with ligand binding for functionally diverse members of the pancreatic RNase superfamily.

Removal of slow-pulsing artifacts in in-phase 15N relaxation dispersion experiments using broadband 1H decoupling

Understanding of the molecular mechanisms of protein function requires detailed insight into the conformational landscape accessible to the protein. Conformational changes can be crucial for biological processes, such as ligand binding, protein folding, and catalysis. NMR spectroscopy is exquisitely sensitive to such dynamic changes in protein conformations. In particular, Carr–Purcell–Meiboom–Gill (CPMG) relaxation dispersion experiments are a powerful tool to investigate protein dynamics on a millisecond time scale. CPMG experiments that probe the chemical shift modulation of 15N in-phase magnetization are particularly attractive, due to their high sensitivity. These experiments require high power 1H decoupling during the CPMG period to keep the 15N magnetization in-phase. Recently, an improved version of the in-phase 15N-CPMG experiment was introduced, offering greater ease of use by employing a single 1H decoupling power for all CPMG pulsing rates. In these experiments however, incomplete decoupling of off-resonance amide 1H spins introduces an artefactual dispersion of relaxation rates, the so-called slow-pulsing artifact. Here, we analyze the slow-pulsing artifact in detail and demonstrate that it can be suppressed through the use of composite pulse decoupling (CPD). We report the performances of various CPD schemes and show that CPD decoupling based on the 90x–240y–90x element results in high-quality dispersion curves free of artifacts, even for amides with high 1H offset.

Residue selective 15N CEST and CPMG experiments for studies of millisecond timescale protein dynamics

Proteins are intrinsically dynamic molecules and undergo exchanges among multiple conformations to perform biological functions. The CPMG relaxation dispersion and CEST experiments are two important solution NMR techniques for characterizing the conformational exchange processes on the millisecond timescale. Traditional pseudo 3D 15N CEST and CPMG experiments have certain limitations in their applications. For example, both experiments have low sensitivity for broadened resonances, and the process of optimizing sample conditions and experimental parameters are often time consuming. To overcome these limitations, we herein present a new set of residue selective 15N CEST and CPMG pulse sequences by employing the Hartmann-Hahn cross-polarization transfer of magnetization in both 1D and 2D schemes. Combined with frequency labeling in the indirect dimension using only a small number of increments, the pulse sequences in the 2D scheme can be applied on resonances in overlapped regions of the 1H-15N HSQC spectrum. The pulse sequences were further applied on several proteins, demonstrating their advantages over the traditional CEST and CPMG experiments under specific circumstances.

Studying sparsely populated conformational states in RNA combining chemical synthesis and solution NMR spectroscopy.

Using chemical synthesis and solution NMR spectroscopy, RNA structural ensembles including a major ground state and minor populated excited states can be studied at atomic resolution. In this work, atom-specific 13C labeled RNA building blocks - a 5-13C-uridine and a 2,8-13C2-adenosine building block - are used to introduce isolated 13C-1H-spin topologies into a target RNA to probe such structural ensembles via NMR spectroscopy. First, the 5-13C-uridine 2'-O-TBDMS-phosphoramidite building block was introduced into a 21 nucleotide (nt) tP5c stem construct of the tP5abc subdomain of the Tetrahymena group I ribozyme. Then, the 2,8-13C2-adenosine 2'-O-TBDMS-phosphoramidite building block was incorporated into a 9 kDa and a 15 kD construct derived from the epsilon (ε) RNA element of the duck Hepatitis B virus. The 2,8-13C2-adenosine resonances of the 9 kDa 28 nt sequence could be mapped to the full-length 53 nt construct. The isolated NMR active nuclei pairs were used to probe for low populated excited states (<10%) via 13C-Carr-Purcell-Meiboom-Gill (CPMG)-relaxation dispersion NMR spectroscopy. The 13C-CPMG relaxation dispersion experiment recapitulated a secondary structure switching event in the P5c hairpin of the group I intron construct previously revealed by 15N relaxation dispersion experiments. In the ε-HBV RNA an unfolding event occurring on the millisecond time scale was found in the upper stem in-line with earlier observations. This unpaired conformational state is presumed to be important for the binding of the epsilon reverse transcriptase (RT) enzyme. Thus, a full description of an RNA's folding landscape helps to obtain a deeper understanding of its function, as these high energy conformational states often represent functionally important intermediates involved in (un)folding or ribozyme catalysis.

Overview of Relaxation Dispersion NMR Spectroscopy to Study Protein Dynamics and Protein-Ligand Interactions.

Proteins and nucleic acids are central to all biological processes. NMR spectroscopy has proven to be excellent for studying the dynamics of these macromolecules over various timescales. Relaxation rates and heteronuclear nuclear Overhauser-effect values can resolve motion on pico- to nanosecond timescales, residual dipolar couplings provide information on submicro- to millisecond timescales, and even slower dynamics over seconds to hours can be resolved by hydrogen-exchange experiments. Relaxation dispersion experiments are especially valuable because they resolve motion on micro- to millisecond timescales, encompassing biomolecular motions associated with ligand binding, enzymatic catalysis, and domain-domain opening. These experiments provide structural, kinetic, and thermodynamic information on "invisible" excited conformational states. Relaxation dispersion can be applied not only to single biomolecules but also to protein-ligand complexes to study the kinetics and thermodynamics of association and dissociation. We review recent developments in relaxation dispersion methodology, outline the R1ρ relaxation dispersion experiment, and discuss application to biomolecular interactions. © 2018 by John Wiley & Sons, Inc.

CONFORMATIONAL FLUCTUATIONS RELATED TO CATALYSIS IN HUMAN RIBONUCLEASE SUPERFAMILY

The high catalytic efficiency of enzymes is a result of structural and dynamical effects. The role of enzyme structure in catalysis has been understood for some time. The enzymes of the ribonuclease A (RNase) family possess identical or similar active site residues and conserved fold architecture. However, their catalytic efficiency differs by 105–106 fold. Moreover, the rate of dynamics among the RNases ranges from microsecond to second time‐scale, a factor 106 difference. Recent investigations provide insights into the role of conformational fluctuations (dynamics at multiple time‐scales) in enzyme catalysis. The fluctuations allow enzymes to sample inter‐converting conformations (called as conformational sub‐states). These conformational sub‐states are proposed to contain features that can promote the function of an enzyme. Therefore, correlating the role of time dependent dynamics in sampling functionally relevant conformational sub‐states would enable a better understanding of the catalytic mechanism of the various RNases. NMR relaxation dispersion experiments show distinct patterns of dynamical variations among the RNases clustered into sub‐families having different biological functions within the same fold. A combination of theoretical modeling, computer simulations and higher order statistics has enabled the identification of conformational sub‐states that regulate the mechanism substrate binding, catalysis and product removal in representative members of each sub‐family found in the human genome. The representative members of each sub‐family have diverse conformational sub‐states associated with each step of the catalytic cycle suggesting a possible correlation between dynamics and function.This abstract is from the Experimental Biology 2018 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

CCR5 RNA Pseudoknots: Residue and Site-Specific Labeling correlate Internal Motions with microRNA Binding.

Conformational dynamics of RNA molecules play a critical role in governing their biological functions. Measurements of RNA dynamic behavior sheds important light on sites that interact with their binding partners or cellular stimulators. However, such measurements using solution-state NMR are difficult for large RNA molecules (>70 nt; nt=nucleotides) owing to severe spectral overlap, homonuclear 13 C scalar couplings, and line broadening. Herein, a strategic combination of solid-phase synthesis, site-specific isotopic labeled phosphoramidites, and enzymatic ligation is introduced. This approach allowed the position-specific insertion of isotopic probes into a 96 nt CCR5 RNA fragment. Accurate measurements of functional dynamics using the Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion (RD) experiments enabled extraction of the exchange rates and populations of this RNA. NMR chemical shift perturbation analysis of the RNA/microRNA-1224 complex indicated that A90-C1' of the pseudoknot exhibits similar changes in chemical shift observed in the excited state. This work demonstrates the general applicability of a NMR-labeling strategy to probe functional RNA structural dynamics.

Measuring the signs of the methyl 1H chemical shift differences between major and 'invisible' minor protein conformational states using methyl 1H 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) ([Formula: see text]), population(s) of the minor state(s) and the absolute value of the chemical shift difference [Formula: see text] (ppm) between different exchanging states can be extracted from the CPMG data. However the sign of [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] 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 ~18kDa cavity mutant of T4 Lysozyme ([Formula: see text]) and (2) the [Formula: see text]kDa Peripheral Sub-unit Binding Domain (PSBD) from the acetyl transferase of Bacillus stearothermophilus ([Formula: see text]).

Glutamine Hydrolysis by Imidazole Glycerol Phosphate Synthase Displays Temperature Dependent Allosteric Activation.

The enzyme imidazole glycerol phosphate synthase (IGPS) is a model for studies of long-range allosteric regulation in enzymes. Binding of the allosteric effector ligand N'-[5'-phosphoribulosyl)formimino]-5-aminoimidazole-4-carboxamide-ribonucleotide (PRFAR) stimulates millisecond (ms) timescale motions in IGPS that enhance its catalytic function. We studied the effect of temperature on these critical conformational motions and the catalytic mechanism of IGPS from the hyperthermophile Thermatoga maritima in an effort to understand temperature-dependent allostery. Enzyme kinetic and NMR dynamics measurements show that apo and PRFAR-activated IGPS respond differently to changes in temperature. Multiple-quantum Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion experiments performed at 303, 323, and 343 K (30, 50, and 70°C) reveal that millisecond flexibility is enhanced to a higher degree in apo IGPS than in the PRFAR-bound enzyme as the sample temperature is raised. We find that the flexibility of the apo enzyme is nearly identical to that of its PRFAR activated state at 343 K, whereas conformational motions are considerably different between these two forms of the enzyme at room temperature. Arrhenius analyses of these flexible sites show a varied range of activation energies that loosely correlate to allosteric communities identified by computational methods and reflect local changes in dynamics that may facilitate conformational sampling of the active conformation. In addition, kinetic assays indicate that allosteric activation by PRFAR decreases to 65-fold at 343 K, compared to 4,200-fold at 303 K, which mirrors the decreased effect of PRFAR on ms motions relative to the unactivated enzyme. These studies indicate that at the growth temperature of T. maritima, PFRAR is a weaker allosteric activator than it is at room temperature and illustrate that the allosteric mechanism of IGPS is temperature dependent.

Structure and Dynamics of the CheY Response Regulators from Rhodobacter sphaeroides

The chemotaxis signalling network of E. coli. depends on autophosphorylation of a histidine protein kinase (HPK) in response to a signal from a sensor domain, with subsequent transfer of the phosphoryl group to an aspartate on response regulator (RR) proteins that bind to the flagellar motor and alter its rotation. CheY is a 14kDa single domain RR that is conserved across motile species. It is formed by 5 α-helices and 5 β-strands surrounding a conserved phosphoryl accepting aspartate residue, and once phosphorylated diffuses to the flagellar motor, binding to its FliM component to cause switching of rotational direction. The photosynthetic bacterium Rhodobacter sphaeroides has multiple chemosensory pathways formed by homologues of the E. coli chemosensory proteins. It has six CheY homologues with different effects on chemotaxis. Only CheY6 is able to stop the flagellar motor but either CheY3 or CheY4 are also required for chemotaxis. NMR and computational methods have been used to answer questions about the structure, dynamics and function of two of the CheY's, CheY3 and CheY6. NOEs, chemical shifts and residual dipolar couplings are used to define the structures of CheY3 and CheY6 in their inactive and active states, where phosphorylation is mimicked using BeF3-. We have investigated fast timescale backbone dynamics using the {1H}-15N heteronuclear NOE and have used CPMG relaxation dispersion experiments to detect low populations of alternative conformations. CheY6 differs from the other R. sphaeroides CheYs and E. coli CheY by the insertion of a ten-residue loop before the C-terminal helix. We have deleted this loop region from CheY6 in order to determine, using in vivo and in vitro assays, if it plays a role in the unique function of CheY6 in R. sphaeroides.

Probing Conformational Exchange in Weakly Interacting, Slowly Exchanging Protein Systems via Off-Resonance R1ρ Experiments: Application to Studies of Protein Phase Separation.

R1ρ relaxation dispersion experiments are increasingly used in studies of protein dynamics on the micro- to millisecond time scale. Traditional R1ρ relaxation dispersion approaches are typically predicated on changes in chemical shifts between corresponding probe spins, ΔωGE, in the interconverting states. Here, we present a new application of off-resonance 15N R1ρ relaxation dispersion that enables the quantification of slow exchange processes even in the limit where ΔωGE = 0 so long as the spins in the exchanging states have different intrinsic transverse relaxation rates (ΔR2 = R2,E - R2,G ≠ 0). In this limit, the dispersion profiles become inverted relative to those measured in the case where ΔωGE ≠ 0, ΔR2 = 0. The theoretical background to understand this effect is presented, along with a simplified exchange matrix that is valid in the limits that are germane here. An application to the study of the dynamics of the germ granule protein Ddx4 in a highly concentrated phase-separated state is described. Notably, exchange-based dispersion profiles can be obtained despite the fact that ΔωGE ≈ 0 and ΔR2 is small, ∼20-30 s-1. Our results are consistent with the formation of a significantly populated excited conformational state that displays increased contacts between adjacent protein molecules relative to the major conformer in solution, leading to a decrease in overall motion of the protein backbone. A complete set of exchange parameters is obtained from analysis of a single set of 15N off-resonance R1ρ measurements recorded at a single static magnetic field and with a single spin-lock radio frequency field strength. This new approach holds promise for studies of weakly interacting systems, especially those involving intrinsically disordered proteins that form phase-separated organelles, where little change to chemical shifts between interconverting states would be expected, but where finite ΔR2 values are observed.

Ab Initio Prediction of NMR Spin Relaxation Parameters from Molecular Dynamics Simulations.

1H-15N NMR spin relaxation and relaxation dispersion experiments can reveal the time scale and extent of protein motions across the ps-ms range, where the ps-ns dynamics revealed by fundamental quantities R1, R2, and heteronuclear NOE can be well-sampled by molecular dynamics simulations (MD). Although the principles of relaxation prediction from simulations are well-established, numerous NMR-MD comparisons have hitherto focused upon the aspect of order parameters S2 due to common artifacts in the prediction of transient dynamics. We therefore summarize here all necessary components and highlight existing and proposed solutions, such as the inclusion of quantum mechanical zero-point vibrational corrections and separate MD convergence of global and local motions in coarse-grained and all-atom force fields, respectively. For the accuracy of the MD prediction to be tested, two model proteins GB3 and Ubiquitin are used to validate five atomistic force fields against published NMR data supplemented by the coarse-grained force field MARTINI+EN. In Amber and CHARMM-type force fields, quantitative agreement was achieved for structured elements with minimum adjustment of global parameters. Deviations from experiment occur in flexible loops and termini, indicating differences in both the extent and time scale of backbone motions. The lack of systematic patterns and water model dependence suggests that modeling of the local environment limits prediction accuracy. Nevertheless, qualitative accuracy in a 2 μs CHARMM36m Stam2 VHS domain simulation demonstrates the potential of MD-based interpretation in combination with NMR-measured dynamics, increasing the utility of spin relaxation in integrative structural biology.

Simultaneous determination of fast and slow dynamics in molecules using extreme CPMG relaxation dispersion experiments.

Molecular dynamics play a significant rolein how molecules perform their function. A critical method that provides information on dynamics, at the atomic level, is NMR-based relaxation dispersion (RD) experiments. RD experiments have been utilized for understanding multiple biological processes occurring at micro-to-millisecond time, such as enzyme catalysis, molecular recognition, ligand binding and protein folding. Here, we applied the recently developed high-power RD concept to the Carr-Purcell-Meiboom-Gill sequence (extreme CPMG; E-CPMG) for the simultaneous detection of fast and slow dynamics. Using a fast folding protein, gpW, we have shown that previously inaccessible kinetics can be accessed with the improved precision and efficiency of the measurementby using this experiment.

Conformational Dynamics of Asparagine at Coiled-Coil Interfaces.

Coiled coils (CCs) are among the best-understood protein folds. Nonetheless, there are gaps in our knowledge of CCs. Notably, CCs are likely to be structurally more dynamic than often considered. Here, we explore this in an abundant class of CCs, parallel dimers, focusing on polar asparagine (Asn) residues in the hydrophobic interface. It is well documented that such inclusions discriminate between different CC oligomers, which has been rationalized in terms of whether the Asn can make side-chain hydrogen bonds. Analysis of parallel CC dimers in the Protein Data Bank reveals a variety of Asn side-chain conformations, but not all of these make the expected inter-side-chain hydrogen bond. We probe the structure and dynamics of a de novo-designed coiled-coil homodimer, CC-Di, by multidimensional nuclear magnetic resonance spectroscopy, including model-free dynamical analysis and relaxation–dispersion experiments. We find dynamic exchange on the millisecond time scale between Asn conformers with the side chains pointing into and out of the core. We perform molecular dynamics simulations that are consistent with this, revealing that the side chains are highly dynamic, exchanging between hydrogen-bonded-paired conformations in picoseconds to nanoseconds. Combined, our data present a more dynamic view for Asn at CC interfaces. Although inter-side-chain hydrogen bonding states are the most abundant, Asn is not always buried or engaged in such interactions. Because interfacial Asn residues are key design features for modulating CC stability and recognition, these further insights into how they are accommodated within CC structures will aid their predictive modeling, engineering, and design.

CPMG Experiments for Protein Minor Conformer Structure Determination.

CPMG relaxation dispersion NMR experiments have emerged as a powerful method to characterize protein minor states that are in exchange with a visible dominant conformation, and have lifetimes between ~0.5 and 5 milliseconds (ms) and populations greater than 0.5%. The structure of the minor state can, in favorable cases, be determined from the parameters provided by the CPMG relaxation dispersion experiments. Here, we go through the intricacies of setting up these powerful CPMG experiments.

An optimal control approach to design entire relaxation dispersion experiments

A general approach is introduced to optimize experiments for the analysis of spin systems in the presence of chemical exchange. Rather than optimizing individual pulse sequence elements, such as refocusing pulses, entire relaxation dispersion sequences are optimized in the form of a single shaped pulse. This is achieved by defining a performance index that is only based on the remaining signal after the relaxation dispersion sequence for a range of exchange, relaxation, offset, and rf inhomogeneity parameters. The approach is demonstrated by optimizing energy-limited broadband relaxation dispersion sequences that closely approach the overall effect of ideal CPMG sequences. As illustrated both theoretically and experimentally, significant improvements are found compared to standard amplitude or energy-limited CPMG sequences.