An exact solution for R2,eff in CPMG experiments in the case of two site chemical exchange

Structural Characterization of Food Allergens by Nuclear Magnetic Resonance Spectroscopy

As allergies, especially those triggered by food, are becoming more and more prevalent, it is of increasing importance to fully understand the structures and dynamic behaviors of allergenic proteins along with their interactions with potential natural ligands. Therefore, we have established a solid routine to achieve structural characterization of food allergens, especially for birch pollen-related cross-reactive proteins from the class 10 of pathogenesis-related proteins (PR-10), by nuclear magnetic resonance (NMR) spectroscopy. Following expression of the desired allergen in Escherichia coli in isotope-labeled minimal media, the three-dimensional solution structures of these proteins can be determined, and insight into ligand binding mechanics and structural dynamic properties are accessible through NMR spin relaxation experiments.

Insights into the Structure of Invisible Conformations of Large Methyl Group Labeled Molecular Machines from High Pressure NMR

Most proteins are highly flexible and can adopt conformations that deviate from the energetically most favorable ground state. Structural information on these lowly populated, alternative conformations is often lacking, despite the functional importance of these states. Here, we study the pathway by which the Dcp1:Dcp2 mRNA decapping complex exchanges between an autoinhibited closed and an open conformation. We make use of methyl Carr-Purcell-Meiboom-Gill (CPMG) NMR relaxation dispersion (RD) experiments that report on the population of the sparsely populated open conformation as well as on the exchange rate between the two conformations. To obtain volumetric information on the open conformation as well as on the transition state structure we made use of RD measurements at elevated pressures. We found that the open Dcp1:Dcp2 conformation has a lower molecular volume than the closed conformation and that the transition state is close in volume to the closed state. In the presence of ATP the volume change upon opening of the complex increases and the volume of the transition state lies in-between the volumes of the closed and open state. These findings show that ATP has an effect on the volume changes that are associated with the opening-closing pathway of the complex. Our results highlight the strength of pressure dependent NMR methods to obtain insights into structural features of protein conformations that are not directly observable. As our work makes use of methyl groups as NMR probes we conclude that the applied methodology is also applicable to high molecular weight complexes.

Assessing the applicability of 19F labeled tryptophan residues to quantify protein dynamics

Nuclear magnetic resonance (NMR) spectroscopy is uniquely suited to study the dynamics of biomolecules in solution. Most NMR studies exploit the spins of proton, carbon and nitrogen isotopes, as these atoms are highly abundant in proteins and nucleic acids. As an alternative and complementary approach, fluorine atoms can be introduced into biomolecules at specific sites of interest. These labels can then be used as sensitive probes for biomolecular structure, dynamics or interactions. Here, we address if the replacement of tryptophan with 5-fluorotryptophan residues has an effect on the overall dynamics of proteins and if the introduced fluorine probe is able to accurately report on global exchange processes. For the four different model proteins (KIX, Dcp1, Dcp2 and DcpS) that we examined, we established that ¹⁵N CPMG relaxation dispersion or EXSY profiles are not affected by the 5-fluorotryptophan, indicating that this replacement of a proton with a fluorine has no effect on the protein motions. However, we found that the motions that the 5-fluorotryptophan reports on can be significantly faster than the backbone motions. This implies that care needs to be taken when interpreting fluorine relaxation data in terms of global protein motions. In summary, our results underscore the great potential of fluorine NMR methods, but also highlight potential pitfalls that need to be considered.

Changes in Natural Silk Fibres by Hydration, Tensile Loading and Heating as Studied by 1H NMR: Anisotropy in NMR Relaxation Times

B. mori silkworm natural silk is a fibrous biopolymer with a block copolymer design containing both hydrophobic and hydrophilic regions. Using ¹H NMR relaxation, this work studied B. mori natural silk fibres oriented at 0° and 90° to the static magnetic field B₀ to clarify how measured NMR parameters reflect the structure and anisotropic properties of hydrated silk fibres. The FTIR method was applied to monitor the changes in the silk I and β-sheet conformations. Unloaded B. mori silk fibres at different hydration levels (HL), the silk threads before and after tensile loading in water, and fibres after a stepped increase in temperature have been explored. NMR data discovered two components in T₁ and T₂ relaxations for both orientations of silk fibres (0° and 90°). For the slower T₂ component, the results showed an obvious anisotropic effect with higher relaxation times for the silk fibres oriented at 90° to B₀. The T₁ component (water protons, HL = 0.11) was sequentially decreased over a range of fibres: 0° oriented, randomly oriented, silk B. mori cocoon, 90° oriented. The degree of anisotropy in T₂ relaxation was decreasing with increasing HL. The T₂ in silk threads oriented at 0° and 90° also showed anisotropy in increased HL (to 0.42 g H₂O/g dry matter), at tensile loading, and at an increasing temperature towards 320 K. The changes in NMR parameters and different relaxation mechanisms affecting water molecular interactions and silk properties have been discussed. The findings provide new insights relating to the water anisotropy in hydrated Bombyx mori silk fibres at tensile loading and under a changing HL and temperature.

The Structural Flexibility of PR-10 Food Allergens

PR-10 proteins constitute a major cause of food allergic reactions. Birch-pollen-related food allergies are triggered by the immunologic cross-reactivity of IgE antibodies with structurally homologous PR-10 proteins that are present in birch pollen and various food sources. While the three-dimensional structures of PR-10 food allergens have been characterized in detail, only a few experimental studies have addressed the structural flexibility of these proteins. In this study, we analyze the millisecond-timescale structural flexibility of thirteen PR-10 proteins from prevalent plant food sources by NMR relaxation-dispersion spectroscopy, in a comparative manner. We show that all the allergens in this study have inherently flexible protein backbones in solution, yet the extent of the structural flexibility appears to be strikingly protein-specific (but not food-source-specific). Above-average flexibility is present in the two short helices, α1 and α2, which form a V-shaped support for the long C-terminal helix α3, and shape the internal ligand-binding cavity, which is characteristic for PR-10 proteins. An in-depth analysis of the NMR relaxation-dispersion data for the PR-10 allergen from peanut reveals the presence of at least two subglobal conformational transitions on the millisecond timescale, which may be related to the release of bound low-molecular-weight ligands from the internal cavity.

Insights into the Cross Talk between Effector and Allosteric Lobes of KRAS from Methyl Conformational Dynamics

KRAS is the most frequently mutated RAS protein in cancer patients, and it is estimated that about 20% of the cancer patients in the United States carried mutant RAS proteins. To accelerate therapeutic development, structures and dynamics of RAS proteins had been extensively studied by various biophysical techniques for decades. Although 31P NMR studies revealed population equilibrium of the two major states in the active GMPPNP-bound form, more complex conformational dynamics in RAS proteins and oncogenic mutants subtly modulate the interactions with their downstream effectors. We established a set of customized NMR relaxation dispersion techniques to efficiently and systematically examine the ms-μs conformational dynamics of RAS proteins. This method allowed us to observe varying synchronized motions that connect the effector and allosteric lobes in KRAS. We demonstrated the role of conformational dynamics of KRAS in controlling its interaction with the Ras-binding domain of the downstream effector RAF1, the first kinase in the MAPK pathway. This allows one to explain, as well as to predict, the altered binding affinities of various KRAS mutants, which was neither previously reported nor apparent from the structural perspective.

Flanking Disorder of the Folded αα-Hub Domain from Radical Induced Cell Death1 Affects Transcription Factor Binding by Ensemble Redistribution

Protein intrinsic disorder is essential for organization of transcription regulatory interactomes. In these interactomes, the majority of transcription factors as well as their interaction partners have co-existing order and disorder. Yet, little attention has been paid to their interplay. Here, we investigate how order is affected by flanking disorder in the folded αα-hub domain RST from Radical-Induced Cell Death1 (RCD1), central in a large interactome of transcription factors. We show that the intrinsically disordered C-terminal tail of RCD1-RST shifts its conformational ensemble towards a pseudo-bound state through weak interactions with the ligand-binding pocket. An unfolded excited state is also accessible on the ms timescale independent of surrounding disordered regions, but its population is lowered by 50% in their presence. Flanking disorder additionally lowers transcription factor binding-affinity without affecting the dissociation rate constant, in accordance with similar bound-states assessed by NMR. The extensive dynamics of the RCD1-RST domain, modulated by flanking disorder, is suggestive of its adaptation to many different transcription factor ligands. The study illustrates how disordered flanking regions can tune fold and function through ensemble redistribution and is of relevance to modular proteins in general, many of which play key roles in regulation of genes.

Analysis of conformational exchange processes using methyl-TROSY-based Hahn echo measurements of quadruple-quantum relaxation

Transverse nuclear spin relaxation is a sensitive probe of chemical exchange on timescales on the order of microseconds to milliseconds. Here we present an experiment for the simultaneous measurement of the relaxation rates of two quadruple-quantum transitions in 13 CH3 -labelled methyl groups. These coherences are protected against relaxation by intra-methyl dipolar interactions and so have unexpectedly long lifetimes within perdeuterated biomacromolecules. However, these coherences also have an order of magnitude higher sensitivity to chemical exchange broadening than lower order coherences and therefore provide ideal probes of dynamic processes. We show that analysis of the static magnetic field dependence of zero-, double- and quadruple-quantum Hahn echo relaxation rates provides a robust indication of chemical exchange and can determine the signed relative magnitudes of proton and carbon chemical shift differences between ground and excited states. We also demonstrate that this analysis can be combined with established Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion measurements, providing improved precision in parameter estimates, particularly in the determination of 1 H chemical shift differences.

Inverse relation between structural flexibility and IgE reactivity of Cor a 1 hazelnut allergens

A major proportion of allergic reactions to hazelnuts (Corylus avellana) are caused by immunologic cross-reactivity of IgE antibodies to pathogenesis-related class 10 (PR-10) proteins. Intriguingly, the four known isoforms of the hazelnut PR-10 allergen Cor a 1, denoted as Cor a 1.0401-Cor a 1.0404, share sequence identities exceeding 97% but possess different immunologic properties. In this work we describe the NMR solution structures of these proteins and provide an in-depth study of their biophysical properties. Despite sharing highly similar three-dimensional structures, the four isoforms exhibit remarkable differences regarding structural flexibility, hydrogen bonding and thermal stability. Our experimental data reveal an inverse relation between structural flexibility and IgE-binding in ELISA experiments, with the most flexible isoform having the lowest IgE-binding potential, while the isoform with the most rigid backbone scaffold displays the highest immunologic reactivity. These results point towards a significant entropic contribution to the process of antibody binding.

Impact of chemical exchange on transverse relaxation at low and moderate magnetic field strengths for sugar solutions representative of fruit tissues analyzed by simulation and MRI experiments

Proton exchange effects on transverse relaxation rate were studied at low and moderate magnetic fields. Analysis was conducted on low-concentrate simple sugar (fructose and glucose) solutions modeling the vacuolar liquid in fruits. Simulated data obtained from Carver and Richards equations were used to analyze the effects of temperature and pH on parameters involved in the chemical exchange mechanisms. The results have highlighted that measurement conditions and tissue characteristics (echo time, magnetic field strength, temperature, pH, etc.) significantly impact the transverse relaxation rate via chemical exchange, even for low and mid magnetic fields and the narrow echo time ranges of TD-NMR and MRI measurements. This explains some of the divergent relaxation data from plant tissue NMR measurements reported in the literature and emphasizes the importance of taking experimental conditions and tissue characteristics into account when interpreting results. It also clearly demonstrates that the appropriate choice of experimental conditions can emphasize the effects of sugar concentration or pH variations on transverse relaxation in vacuolar liquids, making it possible to monitor these parameters accurately via transverse relaxation measurements. The impact of concentration, solute type, pH and temperature on transverse relaxation of sugar solutions were demonstrated experimentally at 1.5 T with an MRI scanner. These data were interpreted using the Carver-Richards model which was effective in estimating parameters involved in chemical exchange mechanism in the imaging experiment.

Algebraic expressions for Carr-Purcell-Meiboom-Gill relaxation dispersion for N-site chemical exchange

The Carr-Purcell-Meiboom-Gill (CPMG) NMR relaxation dispersion experiment measures the effective relaxation rate constant during a train of spin-echo pulse sequence elements as a function of the echo time. The CPMG experiment is a powerful method for characterizing chemical and conformational dynamic processes, termed chemical and conformational exchange, on μs-ms time scales, comparable to the experimentally accessible echo times. Approximate theoretical expressions for the effective relaxation rate constant for N-site chemical exchange have been reported (H. Koss, M. Rance, and A. G. Palmer, Biochemistry 57, 4753-4763 (2018)). Expressions for the effective relaxation rate constant have been improved by using the Cayley-Hamilton theorem to obtain simple and accurate approximations of the average Liouvillian for the CPMG experiment. The improved accuracy of the results allows efficient analyses of experimental data. In addition, the relationship is clarified between the approach of Koss and coworkers and that of Jen (1978).

Binding site exchange kinetics revealed through efficient spin-spin dephasing of hyperpolarized 129Xe

Spin exchange between different chemical environments is an important observable for characterizing chemical exchange kinetics in various contexts, including protein folding, chelation chemistry, and host-guest interactions. Such spins experience effective spin-spin relaxation rate, R _2,eff, that typically shows a dispersive behavior which requires detailed analysis. Here, we describe a class of highly simplified R _2,eff behavior by relying on hyperpolarized ¹²⁹Xe as a freely exchanging ligand reporter. It provides large chemical shift separations that yield reduced expressions of both the Swift-Connick and the Carver-Richards treatment of exchange-induced relaxation. Despite observing a diamagnetic system, R _2,eff is dominated by large Larmor frequency jumps and thus allows detection of otherwise inaccessible analyte concentrations with a single spin echo train (only 0.01% of the overall hyperpolarized spins need to be transiently bound to the molecule). The two Xe hosts cryptophane-A monoacid (CrA-ma) and cucurbit[6]uril (CB6) represent two exemplary families of container molecules (the latter one also serving as drug delivery vehicles) that act as highly efficient phase shifters for which we observed unprecedented exchange-induced relaxivity r ₂ (up to 866 s^-1 mM^-1). By including methods of spatial encoding, multiple data points can be collected simultaneously to isolate the exchange contribution and determine the effective exchange rate in partially occupied binding sites with a single delivery of hyperpolarized nuclei. The relaxivity is directly related to the guest turnover in these systems and temperature-dependent measurements yield an activation energy of E _A = 41 kJ mol^-1 for Xe@CrA-ma from simple relaxometry analysis. The concept is transferable to many applications where Xe is known to exhibit large chemical shifts.

NMR as a "Gold Standard" Method in Drug Design and Discovery

Studying disease models at the molecular level is vital for drug development in order to improve treatment and prevent a wide range of human pathologies. Microbial infections are still a major challenge because pathogens rapidly and continually evolve developing drug resistance. Cancer cells also change genetically, and current therapeutic techniques may be (or may become) ineffective in many cases. The pathology of many neurological diseases remains an enigma, and the exact etiology and underlying mechanisms are still largely unknown. Viral infections spread and develop much more quickly than does the corresponding research needed to prevent and combat these infections; the present and most relevant outbreak of SARS-CoV-2, which originated in Wuhan, China, illustrates the critical and immediate need to improve drug design and development techniques. Modern day drug discovery is a time-consuming, expensive process. Each new drug takes in excess of 10 years to develop and costs on average more than a billion US dollars. This demonstrates the need of a complete redesign or novel strategies. Nuclear Magnetic Resonance (NMR) has played a critical role in drug discovery ever since its introduction several decades ago. In just three decades, NMR has become a "gold standard" platform technology in medical and pharmacology studies. In this review, we present the major applications of NMR spectroscopy in medical drug discovery and development. The basic concepts, theories, and applications of the most commonly used NMR techniques are presented. We also summarize the advantages and limitations of the primary NMR methods in drug development.

Protein Dynamics revealed by NMR Relaxation Methods

Structural biology often focuses primarily on three-dimensional structures of biological macromolecules, deposited in the Protein Data Bank (PDB). This resource is a remarkable entity for the world-wide scientific and medical communities, as well as the general public, as it is a growing translation into three-dimensional space of the vast information in genomic databases, e.g. GENBANK. There is, however, significantly more to understanding biological function than the three-dimensional coordinate space for ground-state structures of biomolecules. The vast array of biomolecules experiences natural dynamics, interconversion between multiple conformational states, and molecular recognition and allosteric events that play out on timescales ranging from picoseconds to seconds. This wide range of timescales demands ingenious and sophisticated experimental tools to sample and interpret these motions, thus enabling clearer insight into functional annotation of the PDB. NMR spectroscopy is unique in its ability to sample this range of timescales at atomic resolution and in physiologically relevant conditions using spin relaxation methods. The field is constantly expanding to provide new creative experiments, to yield more detailed coverage of timescales, and to broaden the power of interpretation and analysis methods. This review highlights the current state of the methodology and examines the extension of analysis tools for more complex experiments and dynamic models. The future for understanding protein dynamics is bright, and these extended tools bring greater compatibility with developments in computational molecular dynamics, all of which will further our understanding of biological molecular functions. These facets place NMR as a key component in integrated structural biology.

Conformational plasticity of ligand-bound and ternary GPCR complexes studied by 19F NMR of the β1-adrenergic receptor

G-protein-coupled receptors (GPCRs) are allosteric signaling proteins that transmit an extracellular stimulus across the cell membrane. Using ¹⁹F NMR and site-specific labelling, we investigate the response of the cytoplasmic region of transmembrane helices 6 and 7 of the β₁-adrenergic receptor to agonist stimulation and coupling to a G_s-protein-mimetic nanobody. Agonist binding shows the receptor in equilibrium between two inactive states and a pre-active form, increasingly populated with higher ligand efficacy. Nanobody coupling leads to a fully active ternary receptor complex present in amounts correlating directly with agonist efficacy, consistent with partial agonism. While for different agonists the helix 6 environment in the active-state ternary complexes resides in a well-defined conformation, showing little conformational mobility, the environment of the highly conserved NPxxY motif on helix 7 remains dynamic adopting diverse, agonist-specific conformations, implying a further role of this region in receptor function. An inactive nanobody-coupled ternary receptor form is also observed.

Methyl TROSY spectroscopy: A versatile NMR approach to study challenging biological systems

A major goal in structural biology is to unravel how molecular machines function in detail. To that end, solution-state NMR spectroscopy is ideally suited as it is able to study biological assemblies in a near natural environment. Based on methyl TROSY methods, it is now possible to record high-quality data on complexes that are far over 100 kDa in molecular weight. In this review, we discuss the theoretical background of methyl TROSY spectroscopy, the information that can be extracted from methyl TROSY spectra and approaches that can be used to assign methyl resonances in large complexes. In addition, we touch upon insights that have been obtained for a number of challenging biological systems, including the 20S proteasome, the RNA exosome, molecular chaperones and G-protein-coupled receptors. We anticipate that methyl TROSY methods will be increasingly important in modern structural biology approaches, where information regarding static structures is complemented with insights into conformational changes and dynamic intermolecular interactions.

Dynamic design: manipulation of millisecond timescale motions on the energy landscape of cyclophilin A

Proteins need to interconvert between many conformations in order to function, many of which are formed transiently, and sparsely populated. Particularly when the lifetimes of these states approach the millisecond timescale, identifying the relevant structures and the mechanism by which they interconvert remains a tremendous challenge. Here we introduce a novel combination of accelerated MD (aMD) simulations and Markov state modelling (MSM) to explore these 'excited' conformational states. Applying this to the highly dynamic protein CypA, a protein involved in immune response and associated with HIV infection, we identify five principally populated conformational states and the atomistic mechanism by which they interconvert. A rational design strategy predicted that the mutant D66A should stabilise the minor conformations and substantially alter the dynamics, whereas the similar mutant H70A should leave the landscape broadly unchanged. These predictions are confirmed using CPMG and R1ρ solution state NMR measurements. By efficiently exploring functionally relevant, but sparsely populated conformations with millisecond lifetimes in silico, our aMD/MSM method has tremendous promise for the design of dynamic protein free energy landscapes for both protein engineering and drug discovery.

Exchange saturation transfer and associated NMR techniques for studies of protein interactions involving high-molecular-weight systems

A brief overview of theoretical and experimental aspects of the Dark state Exchange Saturation Transfer (DEST) and lifetime line broadening ([Formula: see text]) NMR methodologies is presented from a physico-chemical perspective. We describe how the field-dependence of [Formula: see text] can be used for determining the exchange regime on the transverse spin relaxation time-scale. Some limitations of DEST/[Formula: see text] methodology in applications to molecular systems with intermediate molecular weights are discussed, and the means of overcoming these limitations via the use of closely related exchange NMR techniques is presented. Finally, several applications of DEST/[Formula: see text] methodology are described from a methodological viewpoint, with an emphasis on providing examples of how kinetic and relaxation parameters of exchange can be reliably extracted from the experimental data in each particular case.

Local unfolding of the HSP27 monomer regulates chaperone activity

The small heat-shock protein HSP27 is a redox-sensitive molecular chaperone that is expressed throughout the human body. Here, we describe redox-induced changes to the structure, dynamics, and function of HSP27 and its conserved α-crystallin domain (ACD). While HSP27 assembles into oligomers, we show that the monomers formed upon reduction are highly active chaperones in vitro, but are susceptible to self-aggregation. By using relaxation dispersion and high-pressure nuclear magnetic resonance (NMR) spectroscopy, we observe that the pair of β-strands that mediate dimerisation partially unfold in the monomer. We note that numerous HSP27 mutations associated with inherited neuropathies cluster to this dynamic region. High levels of sequence conservation in ACDs from mammalian sHSPs suggest that the exposed, disordered interface present in free monomers or oligomeric subunits may be a general, functional feature of sHSPs.

The small heat-shock protein HSP27 occurs predominantly in oligomeric forms, which makes its structural characterisation challenging. Here the authors employ CPMG and high-pressure NMR with native mass spectrometry and biophysical assays to show that the active monomeric form of HSP27 is substantially disordered and highly chaperone-active.

Microsecond Protein Dynamics from Combined Bloch-McConnell and Near-Rotary-Resonance R1p Relaxation-Dispersion MAS NMR

Studying protein dynamics on microsecond-to-millisecond (μs-ms) time scales can provide important insight into protein function. In magic-angle-spinning (MAS) NMR, μs dynamics can be visualized by R 1 ρ rotating-frame relaxation dispersion experiments in different regimes of radio-frequency field strengths: at low RF field strength, isotropic-chemical-shift fluctuation leads to "Bloch-McConnell-type" relaxation dispersion, while when the RF field approaches rotary resonance conditions bond angle fluctuations manifest as increased R 1 ρ rate constants ("Near-Rotary-Resonance Relaxation Dispersion", NERRD). Here we explore the joint analysis of both regimes to gain comprehensive insight into motion in terms of geometric amplitudes, chemical-shift changes, populations and exchange kinetics. We use a numerical simulation procedure to illustrate these effects and the potential of extracting exchange parameters, and apply the methodology to the study of a previously described conformational exchange process in microcrystalline ubiquitin.

Chemical Exchange

The phenomenon of chemical or conformational exchange in NMR spectroscopy has enabled detailed characterization of time-dependent aspects of biomolecular function, including folding, molecular recognition, allostery, and catalysis, on timescales from microsecond to second. Importantly, NMR methods based on a variety of spin relaxation parameters have been developed that provide quantitative information on interconversion kinetics, thermodynamic properties, and structural features of molecular states populated to a fraction of a percent at equilibrium and otherwise unobservable by other NMR approaches. The ongoing development of more sophisticated experimental techniques and the necessity to apply these methods to larger and more complex molecular systems engenders a corresponding need for theoretical advances describing such techniques and facilitating data analysis in applications. This review surveys current aspects of the theory of chemical exchange, as utilized in ZZ-exchange; Hahn and Carr-Purcell-Meiboom-Gill (CPMG) spin-echo; and R_1ρ, chemical exchange saturation transfer (CEST), and dark state saturation transfer (DEST) spin-locking experiments. The review emphasizes theoretical results for kinetic topologies with more than two interconverting states, both to obtain compact analytical forms suitable for data analysis and to establish conditions for distinguishability between alternative kinetic schemes.

General Expressions for Carr-Purcell-Meiboom-Gill Relaxation Dispersion for N-Site Chemical Exchange

The Carr-Purcell-Meiboom-Gill (CPMG) nuclear magnetic resonance experiment is widely used to characterize chemical exchange phenomena in biological macromolecules. Theoretical expressions for the nuclear spin relaxation rate constant for two-site chemical exchange during CPMG pulse trains valid for all time scales are well-known as are descriptions of N-site exchange in the fast limit. We have obtained theoretical expressions for N-site exchange outside of the fast limit by using approximations to an average Liouvillian describing the decay of magnetization during a CPMG pulse train. We obtain general expressions for CPMG experiments for any N-site scheme and all experimentally accessible time scales. For sufficiently slow chemical exchange, we obtain closed-form expressions for the relaxation rate constant and a general characteristic polynomial for arbitrary kinetic schemes. Furthermore, we highlight features that qualitatively characterize CPMG curves obtained for various N-site kinetic topologies, quantitatively characterize CPMG curves obtained from systems in various N-site exchange situations, and test distinguishability of kinetic models.

NMR probing of invisible excited states using selectively labeled RNAs

Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion NMR experiments are invaluable for probing sparsely and transiently populated biomolecular states that cannot be directly detected by traditional NMR experiments and that are invisible by other biophysical approaches. A notable gap for RNA is the absence of CPMG experiments for measurement of methine base ¹H and methylene C5' chemical shifts of ribose moieties in the excited state, partly because of complications from homonuclear ¹³C-¹³C scalar couplings. Here we present site-specific ¹³C labeling that makes possible the design of pulse sequences for recording accurate ¹H-¹³C MQ and SQ CPMG experiments for ribose methine H1'-C1' and H2'-C2', base and ribose ¹H CPMG, as well as a new ¹H-¹³C TROSY-detected methylene (CH₂) C5' CPMG relaxation pulse schemes. We demonstrate the utility of these experiments for two RNAs, the A-Site RNA known to undergo exchange and the IRE RNA suspected of undergoing exchange on microseconds to millisecond time-scale. We anticipate the new labeling approaches will facilitate obtaining structures of invisible states and provide insights into the relevance of such states for RNA-drug interactions.

Deciphering the Dynamic Interaction Profile of an Intrinsically Disordered Protein by NMR Exchange Spectroscopy

Intrinsically disordered proteins (IDPs) display a large number of interaction modes including folding-upon-binding, binding without major structural transitions, or binding through highly dynamic, so-called fuzzy, complexes. The vast majority of experimental information about IDP binding modes have been inferred from crystal structures of proteins in complex with short peptides of IDPs. However, crystal structures provide a mainly static view of the complexes and do not give information about the conformational dynamics experienced by the IDP in the bound state. Knowledge of the dynamics of IDP complexes is of fundamental importance to understand how IDPs engage in highly specific interactions without concomitantly high binding affinity. Here, we combine rotating-frame R_1ρ, Carr-Purcell-Meiboom Gill relaxation dispersion as well as chemical exchange saturation transfer to decipher the dynamic interaction profile of an IDP in complex with its partner. We apply the approach to the dynamic signaling complex formed between the mitogen-activated protein kinase (MAPK) p38α and the intrinsically disordered regulatory domain of the MAPK kinase MKK4. Our study demonstrates that MKK4 employs a subtle combination of interaction modes in order to bind to p38α, leading to a complex displaying significantly different dynamics across the bound regions.

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.

Application of geometric approximation to the CPMG experiment: Two- and three-site exchange

The Carr-Purcell-Meiboom-Gill (CPMG) experiment is one of the most classical and well-known relaxation dispersion experiments in NMR spectroscopy, and it has been successfully applied to characterize biologically relevant conformational dynamics in many cases. Although the data analysis of the CPMG experiment for the 2-site exchange model can be facilitated by analytical solutions, the data analysis in a more complex exchange model generally requires computationally-intensive numerical analysis. Recently, a powerful computational strategy, geometric approximation, has been proposed to provide approximate numerical solutions for the adiabatic relaxation dispersion experiments where analytical solutions are neither available nor feasible. Here, we demonstrate the general potential of geometric approximation by providing a data analysis solution of the CPMG experiment for both the traditional 2-site model and a linear 3-site exchange model. The approximate numerical solution deviates less than 0.5% from the numerical solution on average, and the new approach is computationally 60,000-fold more efficient than the numerical approach. Moreover, we find that accurate dynamic parameters can be determined in most cases, and, for a range of experimental conditions, the relaxation can be assumed to follow mono-exponential decay. The method is general and applicable to any CPMG RD experiment (e.g. N, C', C^α, H^α, etc.) The approach forms a foundation of building solution surfaces to analyze the CPMG experiment for different models of 3-site exchange. Thus, the geometric approximation is a general strategy to analyze relaxation dispersion data in any system (biological or chemical) if the appropriate library can be built in a physically meaningful domain.

Measurement of Ligand-Target Residence Times by 1H Relaxation Dispersion NMR Spectroscopy

A ligand-observed ¹H NMR relaxation experiment is introduced for measuring the binding kinetics of low-molecular-weight compounds to their biomolecular targets. We show that this approach, which does not require any isotope labeling, is applicable to ligand–target systems involving proteins and nucleic acids of variable molecular size. The experiment is particularly useful for the systematic investigation of low affinity molecules with residence times in the micro- to millisecond time regime.

Protein dynamics and function from solution state NMR spectroscopy

It is well-established that dynamics are central to protein function; their importance is implicitly acknowledged in the principles of the Monod, Wyman and Changeux model of binding cooperativity, which was originally proposed in 1965. Nowadays the concept of protein dynamics is formulated in terms of the energy landscape theory, which can be used to understand protein folding and conformational changes in proteins. Because protein dynamics are so important, a key to understanding protein function at the molecular level is to design experiments that allow their quantitative analysis. Nuclear magnetic resonance (NMR) spectroscopy is uniquely suited for this purpose because major advances in theory, hardware, and experimental methods have made it possible to characterize protein dynamics at an unprecedented level of detail. Unique features of NMR include the ability to quantify dynamics (i) under equilibrium conditions without external perturbations, (ii) using many probes simultaneously, and (iii) over large time intervals. Here we review NMR techniques for quantifying protein dynamics on fast (ps-ns), slow (μs-ms), and very slow (s-min) time scales. These techniques are discussed with reference to some major discoveries in protein science that have been made possible by NMR spectroscopy.

NMR Methods to Study Dynamic Allostery

Nuclear magnetic resonance (NMR) spectroscopy provides a unique toolbox of experimental probes for studying dynamic processes on a wide range of timescales, ranging from picoseconds to milliseconds and beyond. Along with NMR hardware developments, recent methodological advancements have enabled the characterization of allosteric proteins at unprecedented detail, revealing intriguing aspects of allosteric mechanisms and increasing the proportion of the conformational ensemble that can be observed by experiment. Here, we present an overview of NMR spectroscopic methods for characterizing equilibrium fluctuations in free and bound states of allosteric proteins that have been most influential in the field. By combining NMR experimental approaches with molecular simulations, atomistic-level descriptions of the mechanisms by which allosteric phenomena take place are now within reach.

Protein Allostery and Conformational Dynamics

The functions of many proteins are regulated through allostery, whereby effector binding at a distal site changes the functional activity (e.g., substrate binding affinity or catalytic efficiency) at the active site. Most allosteric studies have focused on thermodynamic properties, in particular, substrate binding affinity. Changes in substrate binding affinity by allosteric effectors have generally been thought to be mediated by conformational transitions of the proteins or, alternatively, by changes in the broadness of the free energy basin of the protein conformational state without shifting the basin minimum position. When effector binding changes the free energy landscape of a protein in conformational space, the change affects not only thermodynamic properties but also dynamic properties, including the amplitudes of motions on different time scales and rates of conformational transitions. Here we assess the roles of conformational dynamics in allosteric regulation. Two cases are highlighted where NMR spectroscopy and molecular dynamics simulation have been used as complementary approaches to identify residues possibly involved in allosteric communication. Perspectives on contentious issues, for example, the relationship between picosecond-nanosecond local and microsecond-millisecond conformational exchange dynamics, are presented.

Conformational Reorganization Coupled to the Ionization of Internal Lys Residues in Proteins

Ionizable groups buried in the hydrophobic interior of proteins are essential for energy transduction and catalysis. Because the protein interior is usually neither as polar nor as polarizable as water, these groups tend to have anomalous pKa values, and their ionization tends to be coupled to conformational reorganization. To elucidate mechanisms of energy transduction in proteins, it is necessary to understand the structural determinants of the pKa values of these buried groups, including the range and character of the conformational reorganization that the ionization of these buried groups can elicit. The L25K and L125K variants of staphylococcal nuclease (SNase) were used to characterize the diverse types of structural reorganization that can be promoted by the ionization of buried groups. NMR relaxation dispersion and ZZ-exchange experiments were used to identify the locations and measure the time scales and extent of pH-dependent conformational exchange in these two proteins. The buried Lys-25 and Lys-125 residues titrate with pKa of 6.3 and 6.2, respectively. The L25K protein fluctuates between the native state and an ensemble of locally unfolded states on the 400 μs to 7 ms time scale. On the 100 to 500 ms time scale the native state exchanges with a subglobally unfolded state in which the β-barrel is partially reorganized. The equilibrium between the native state and this alternative state is highly pH dependent; at pH values below the pKa of Lys-25 the state with the partially reorganized β-barrel is the dominant state. In contrast, the L125K protein only exhibited pH-independent fluctuation in the microsecond to millisecond time scale in the region near Lys-125. The study illustrates how diverse and how localized the coupling between conformational reorganization and ionization of buried groups can be. The pH-sensitive exchange between the fully native and subglobally or locally unfolded states in time scales well into hundreds of milliseconds will challenge all computational methods for structure-based calculations of pKa values.

Relaxation dispersion NMR spectroscopy for the study of protein allostery

Allosteric transmission of information between distant sites in biological macromolecules often involves collective transitions between active and inactive conformations. Nuclear magnetic resonance (NMR) spectroscopy can yield detailed information on these dynamics. In particular, relaxation dispersion techniques provide structural, dynamic, and mechanistic information on conformational transitions occurring on the millisecond to microsecond timescales. In this review, we provide an overview of the theory and analysis of Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion NMR experiments and briefly describe their application to the study of allosteric dynamics in the homeodomain from the PBX transcription factor (PBX-HD). CPMG NMR data show that local folding (helix/coil) transitions in one part of PBX-HD help to communicate information between two distant binding sites. Furthermore, the combination of CPMG and other spin relaxation data show that this region can also undergo local misfolding, reminiscent of conformational ensemble models of allostery.