Heteronuclear Adiabatic Relaxation Dispersion (HARD) for quantitative analysis of conformational dynamics in proteins

Investigating the role of conformational heterogeneity in FUS-RRM fibrillation

The Fused in Sarcoma (FUS) protein, previously implicated in neurodegenerative diseases, contains N- and C-terminal LC-rich regions, a zinc finger motif flanked by two RG-rich regions, and a single RNA-recognition motif (RRM). FUS-RRM monomers undergo amyloid-like aggregation, however, the detailed molecular insights into the fibrillation process are yet to be deciphered. Here, we investigated the conformational heterogeneity of FUS-RRM using NMR relaxation-dispersion experiments. We observed that the monomer (M) exists in a dynamic exchange with an excited state (ES), which gets perturbed by altering the pH. Although the overall fold of the FUS-RRM remains unperturbed at the lower pH, aggregation kinetics increase. The data suggests a coupling of the conformational heterogeneity to aggregation kinetics wherein a perturbation to ES probably acts as a switch that controls the fibrillation process under physiological and stress conditions. These results add to the understanding of the fibrillation process, thereby paving the way for a better understanding of the role of FUS in neurodegenerative diseases.

Unbiased clustering of residues undergoing synchronous motions in proteins using NMR spin relaxation data

Biological macromolecules are dynamic entities that transition between various conformational states, often playing a vital role in biological functions. Their inherent flexibility spans a broad range of timescales. Motions occurring within the microsecond to millisecond range are especially important, as they are integral to processes such as enzyme catalysis, folding, ligand binding, and allostery. NMR Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion measurements are the preferred method for characterizing macromolecular motions at atomic resolution. However, it is still uncertain whether the functional motions of multiple residues in macromolecules need to be coordinated and/or synchronized within the protein matrix in order to perform the desired function. Here, we illustrate an unbiased method to analyze NMR relaxation dispersion and identify dynamic clusters of residues that fluctuate on similar timescales within proteins. The method requires relaxation dispersion data for backbone amides or side-chain methyl groups, which are globally fitted using the Bloch-McConnell equations for each pair of residues. The goodness of the pairwise fitting serves as a metric to construct two-dimensional synchronous dynamics (SyncDyn) maps, allowing us to identify residue clusters whose dynamics are influenced by ligand binding. We applied our method to the catalytic subunit of the cAMP-dependent protein kinase A (PKAC) and the T17A mutant of ribonuclease A (RNAse A). The SyncDyn maps for PKA-C showed distinct clusters of residues located in critical allosteric sites. Nucleotide binding activates the movement of residues at the interface between the two lobes and also those distal to the active site. In the case of RNAse A, the SyncDyn maps show that residues fluctuating with the same time scale are interspersed in both lobes of the enzyme. Overall, our approach eliminates arbitrary manual selection of residues for dynamic clustering and objectively identifies all possible residue pairs that fluctuate synchronously, i.e. on the same timescale.

On the geometric phase effects on time evolution of the density matrix during modulated radiofrequency pulses

In this work the effect of the geometric phase on time evolution of the density matrix was evaluated during nonadiabatic radiofrequency (RF) pulses with Sine amplitude modulation (AM) and Cosine frequency modulation (FM) functions of the RAFF (Relaxations Along a Fictitious Field) family, and the polarization between two energy level ½ spin system coupled by dipolar interaction was evaluated during the application of RF irradiation. The dependencies of the diagonal density matrix elements and the polarization on the rotational correlation times and the time during RF pulses were evaluated. The general treatment of the density matrix elements along with the polarization generated during RF pulses was unavailable thus far, and for the first time was here derived for the nonadiabatic case of the RAFF pulses. The current formalism could be extended to other AM and FM RF waveforms, including the adiabatic RF pulses which are widely used in magnetic resonance (MR). We demonstrate that the sub-geometric phases (SGP) influence the density matrix elements and thus the polarization generated during the application of RF AM and FM pulses. The corrections to describe the SGP influence of the density matrix elements developed in this work could be essential for determination of MR fundamental parameters necessary for evaluation of tissue contrasts in vivo in MRI and for protein dynamics characterization in high resolution NMR, where AM and FM RF pulses are frequently utilized.

Complete solution for rotating frame relaxation functions during adiabatic pulses

During adiabatic full passage (AFP) radiofrequency (RF) pulses the relaxation functions are conventionally treated in the Tilting Doubly Rotating Frame (TDRF), or the second rotating frame (SRF) of reference. Such a description is adequate when during the adiabatic passage the magnetization M is perfectly aligned with the time dependent effective magnetic field, B(1)eff(t), leading to T1ρ(t) relaxation, or evolves on a plane perpendicular to B(1)eff(t), leading to T2ρ(t) relaxation. Time evolution of B(1)eff(t) results in formation of a fictitious magnetic field, which is typically neglected during the AFP pulses operating in adiabatic regime, i.e., given that the adiabatic condition |γ-1dα(1)(t)/dt| ≪ B(1)eff(t) is well satisfied. Here α(1)(t) is the angle between B(1)eff(t) and the axis of quantization of the first rotating frame (FRF) z', and dα(1)(t)/dt is the angular velocity. When the fictitious field component cannot be neglected, for the adequate description of relaxation during AFP pulses the solutions for the relaxation functions in a multi-fold rotating frame are necessary. Such a general treatment is currently unavailable for adiabatic RF pulses. Here, we obtain the solution for the relaxation functions in the Tilting Triply Rotating Frame (TTRF) during the Hyperbolic Secant (HS) pulses of the HSn family, HS1 and HS4, where n is the stretching factor. We show that the contribution to the relaxations originating from the non-negligible magnitude of the fictitious field depends on the pulse modulation functions of the AFP pulses and the parameters of the pulses. The corrections to describe the relaxations are given, which may be relevant in specific experimental setups especially for high-resolution NMR.

Differential conformational dynamics in two type-A RNA-binding domains drive the double-stranded RNA recognition and binding

Trans-activation response (TAR) RNA-binding protein (TRBP) has emerged as a key player in the RNA interference pathway, wherein it binds to different pre-microRNAs (miRNAs) and small interfering RNAs (siRNAs), each varying in sequence and/or structure. We hypothesize that TRBP displays dynamic adaptability to accommodate heterogeneity in target RNA structures. Thus, it is crucial to ascertain the role of intrinsic and RNA-induced protein dynamics in RNA recognition and binding. We have previously elucidated the role of intrinsic and RNA-induced conformational exchange in the double-stranded RNA-binding domain 1 (dsRBD1) of TRBP in shape-dependent RNA recognition. The current study delves into the intrinsic and RNA-induced conformational dynamics of the TRBP-dsRBD2 and then compares it with the dsRBD1 study carried out previously. Remarkably, the two domains exhibit differential binding affinity to a 12-bp dsRNA owing to the presence of critical residues and structural plasticity. Furthermore, we report that dsRBD2 depicts constrained conformational plasticity when compared to dsRBD1. Although, in the presence of RNA, dsRBD2 undergoes induced conformational exchange within the designated RNA-binding regions and other residues, the amplitude of the motions remains modest when compared to those observed in dsRBD1. We propose a dynamics-driven model of the two tandem domains of TRBP, substantiating their contributions to the versatility of dsRNA recognition and binding.

The Landau-Zener-Stückelberg-Majorana transition in the T2 ≪ T1 limit

Landau-Zener-Stückelberg-Majorana (LZSM) transitions occur between quantum states when parameters in the system's Hamiltonian are varied continuously and rapidly. In magnetic resonance, losses in adiabatic rapid passage can be understood using the physics of LZSM transitions. Most treatments of LZSM transitions ignore the T2 dephasing of coherences, however. Motivated by ongoing work in magnetic resonance force microscopy, we employ the Bloch equations, coordinate transformation, and the Magnus expansion to derive expressions for the final magnetization following a rapid field sweep at fixed irradiation intensity that include T2 losses. Our derivation introduces an inversion-function, Fourier transform method for numerically evaluating highly oscillatory integrals. Expressions for the final magnetization are given for low and high irradiation intensity, valid in the T2≪T1 limit. Analytical results are compared to numerical simulations and nuclear magnetic resonance experiments. Our relatively straightforward calculation reproduces semiquantitatively the well known LZSM result in the T2→0 limit.

On the geometric phases during radio frequency pulses with sine and cosine amplitude and frequency modulation

In this work, we describe the formation of geometric phases during nonadiabatic frequency swept (FS) radio frequency (RF) pulses with sine amplitude modulation and cosine frequency modulation functions. The geometric phases during the FS pulse were analyzed using a Schrödinger equation formalism, and the unified analytical expression for the geometric phase was derived. We present the solutions for sub-geometric phase components incorporated in spinor wavefunctions for the RF Hamiltonian of spin ½ nuclei. We demonstrate that the geometric phases during sine/cosine RF pulses are opposite in signs for different initial conditions of the spinor and that geometric phases can accumulate in correspondence to different magnetization trajectories. The derived formalism could be extended for the evaluation of the geometric phases during a wide class of amplitude- and frequency-modulated pulses used in MRI and in high-resolution NMR.

An NMR portrait of functional and dysfunctional allosteric cooperativity in cAMP-dependent protein kinase A

The cAMP-dependent protein kinase A (PKA) is the archetypical eukaryotic kinase. The catalytic subunit (PKA-C) structure is highly conserved among the AGC-kinase family. PKA-C is a bilobal enzyme with a dynamic N-lobe, harbouring the Adenosine-5'-triphosphate (ATP) binding site and a more rigid helical C-lobe. The substrate-binding groove resides at the interface of the two lobes. A distinct feature of PKA-C is the positive binding cooperativity between nucleotide and substrate. Several PKA-C mutations lead to the development of adenocarcinomas, myxomas, and other rare forms of liver tumours. Nuclear magnetic resonance (NMR) spectroscopy shows that these mutations disrupt the allosteric communication between the two lobes, causing a drastic decrease in binding cooperativity. The loss of cooperativity correlates with changes in substrate fidelity and reduced kinase affinity for the endogenous protein kinase inhibitor (PKI). The similarity between PKI and the inhibitory sequence of the kinase regulatory subunits suggests that the overall mechanism of regulation of the kinase may be disrupted. We surmise that a reduced or obliterated cooperativity may constitute a common trait for both orthosteric and allosteric mutations of PKA-C that may lead to dysregulation and disease.

Inherent conformational plasticity in dsRBDs enables interaction with topologically distinct RNAs

Many double-stranded RNA-binding domains (dsRBDs) interact with topologically distinct dsRNAs in biological pathways pivotal to viral replication, cancer causation, neurodegeneration, and so on. We hypothesized that the adaptability of dsRBDs is essential to target different dsRNA substrates. A model dsRBD and a few dsRNAs, slightly different in shape from each other, were used to test the systematic shape dependence of RNA on the dsRBD-binding using nuclear magnetic resonance (NMR) spectroscopy and molecular modeling. NMR-based titrations showed a distinct binding pattern for the dsRBD with the topologically distinct dsRNAs. The line broadening upon RNA binding was observed to cluster in the residues lying in close proximity, thereby suggesting an RNA-induced conformational exchange in the dsRBD. Further, while the intrinsic microsecond dynamics observed in the apo-dsRBD were found to quench upon binding with the dsRNA, the microsecond dynamics got induced at residues spatially proximal to quench sites upon binding with the dsRNA. This apparent relay of conformational exchange suggests the significance of intrinsic dynamics to help adapt the dsRBD to target various dsRNA-shapes. The conformational pool visualized in MD simulations for the apo-dsRBD reported here has also been observed to sample the conformations seen previously for various dsRBDs in apo- and in dsRNA-bound state structures, further suggesting the conformational adaptability of the dsRBDs. These investigations provide a dynamic basis for the substrate promiscuity for dsRBD proteins.

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.

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.

Multiple frequency saturation pulses reduce CEST acquisition time for quantifying conformational exchange in biomolecules

Exchange between conformational states is required for biomolecular catalysis, allostery, and folding. A variety of NMR experiments have been developed to quantify motional regimes ranging from nanoseconds to seconds. In this work, we describe an approach to speed up the acquisition of chemical exchange saturation transfer (CEST) experiments that are commonly used to probe millisecond to second conformational exchange in proteins and nucleic acids. The standard approach is to obtain CEST datasets through the acquisition of a series of 2D correlation spectra where each experiment utilizes a single saturation frequency to ¹H, ¹⁵N or ¹³C. These pseudo 3D datasets are time consuming to collect and are further lengthened by reduced signal to noise stemming from the long saturation pulse. In this article, we show how usage of a multiple frequency saturation pulse (i.e., MF-CEST) changes the nature of data collection from series to parallel, and thus decreases the total acquisition time by an integer factor corresponding to the number of frequencies in the pulse. We demonstrate the applicability of MF-CEST on a Src homology 2 (SH2) domain from phospholipase Cγ and the secondary active transport protein EmrE as model systems by collecting ¹³C methyl and ¹⁵N backbone datasets. MF-CEST can also be extended to additional sites within proteins and nucleic acids. The only notable drawback of MF-CEST as applied to backbone ¹⁵N experiments occurs when a large chemical shift difference between the major and minor populations is present (typically greater than ~ 8 ppm). In these cases, ambiguity may arise between the chemical shift of the minor population and the multiple frequency saturation pulse. Nevertheless, this drawback does not occur for methyl group MF-CEST experiments or in cases where somewhat smaller chemical shift differences occur are present.

General expressions for R1ρ relaxation for N-site chemical exchange and the special case of linear chains

Exploration of dynamic processes in proteins and nucleic acids by spin-locking NMR experiments has been facilitated by the development of theoretical expressions for the R_1ρ relaxation rate constant covering a variety of kinetic situations. Herein, we present a generalized approximation to the chemical exchange, R_ex, component of R_1ρ for arbitrary kinetic schemes, assuming the presence of a dominant major site population, derived from the negative reciprocal trace of the inverse Bloch-McConnell evolution matrix. This approximation is equivalent to first-order truncation of the characteristic polynomial derived from the Bloch-McConnell evolution matrix. For three- and four-site chemical exchange, the first-order approximations are sufficient to distinguish different kinetic schemes. We also introduce an approach to calculate R_1ρ for linear N-site schemes, using the matrix determinant lemma to reduce the corresponding 3N×3N Bloch-McConnell evolution matrix to a 3×3 matrix. The first- and second order-expansions of the determinant of this 3×3 matrix are closely related to previously derived equations for two-site exchange. The second-order approximations for linear N-site schemes can be used to obtain more accurate approximations for non-linear N-site schemes, such as triangular three-site or star four-site topologies. The expressions presented herein provide powerful means for the estimation of R_ex contributions for both low (CEST-limit) and high (R_1ρ-limit) radiofrequency field strengths, provided that the population of one state is dominant. The general nature of the new expressions allows for consideration of complex kinetic situations in the analysis of NMR spin relaxation data.

Evaluating the influence of initial magnetization conditions on extracted exchange parameters in NMR relaxation experiments: applications to CPMG and CEST

Transient excursions of native protein states to functionally relevant higher energy conformations often occur on the μs-ms timescale. NMR spectroscopy has emerged as an important tool to probe such processes using techniques such as Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion and Chemical Exchange Saturation Transfer (CEST). The extraction of kinetic and structural parameters from these measurements is predicated upon mathematical modeling of the resulting relaxation profiles, which in turn relies on knowledge of the initial magnetization conditions at the start of the CPMG/CEST relaxation elements in these experiments. Most fitting programs simply assume initial magnetization conditions that are given by equilibrium populations, which may be incorrect in certain implementations of experiments. In this study we have quantified the systematic errors in extracted parameters that are generated from analyses of CPMG and CEST experiments using incorrect initial boundary conditions. We find that the errors in exchange rates (k ex ) and populations (p E ) are typically small (<10 %) and thus can be safely ignored in most cases. However, errors become larger and cannot be fully neglected (20-40 %) as k ex falls near the lower limit of each method or when short CPMG/CEST relaxation elements are used in these experiments. The source of the errors can be rationalized and their magnitude given by a simple functional form. Despite the fact that errors tend to be small, it is recommended that the correct boundary conditions be implemented in fitting programs so as to obtain as robust estimates of exchange parameters as possible.

Geometric Approximation: A New Computational Approach To Characterize Protein Dynamics from NMR Adiabatic Relaxation Dispersion Experiments

A new computational strategy is reported that provides a fast approximation of numerical solutions of differential equations in general. The method is demonstrated with the analysis of NMR adiabatic relaxation dispersion experiments to reveal biomolecular dynamics. When an analytical solution to the theoretical equations describing a physical process is not available, the new approach can significantly accelerate the computational speed of the conventional numerical integration up to 10(5) times. NMR adiabatic relaxation dispersion experiments enhanced with optimized proton-decoupled pulse sequences, although extremely powerful, have previously been refractory to quantitative analysis. Both simulations and experimental validation demonstrate detectable "slow" (microsecond to millisecond) conformational exchange rates from 10(2) to 10(5) s(-1). This greatly expanded time-scale range enables the characterization of a wide array of conformational fluctuations for individual residues, which correlate with biomolecular function and were previously inaccessible. Moreover, the new computational method can be potentially generalized for analysis of new types of relaxation dispersion experiments to characterize the various dynamics of biomolecular systems.

Chemical exchange in biomacromolecules: past, present, and future

The perspective reviews quantitative investigations of chemical exchange phenomena in proteins and other biological macromolecules using NMR spectroscopy, particularly relaxation dispersion methods. The emphasis is on techniques and applications that quantify the populations, interconversion kinetics, and structural features of sparsely populated conformational states in equilibrium with a highly populated ground state. Applications to folding, molecular recognition, catalysis, and allostery by proteins and nucleic acids are highlighted.

Measuring dynamic and kinetic information in the previously inaccessible supra-τ(c) window of nanoseconds to microseconds by solution NMR spectroscopy

Nuclear Magnetic Resonance (NMR) spectroscopy is a powerful tool that has enabled experimentalists to characterize molecular dynamics and kinetics spanning a wide range of time-scales from picoseconds to days. This review focuses on addressing the previously inaccessible supra-tc window (defined as τ(c) < supra-τ(c) < 40 μs; in which tc is the overall tumbling time of a molecule) from the perspective of local inter-nuclear vector dynamics extracted from residual dipolar couplings (RDCs) and from the perspective of conformational exchange captured by relaxation dispersion measurements (RD). The goal of the first section is to present a detailed analysis of how to extract protein dynamics encoded in RDCs and how to relate this information to protein functionality within the previously inaccessible supra-τ(c) window. In the second section, the current state of the art for RD is analyzed, as well as the considerable progress toward pushing the sensitivity of RD further into the supra-τ(c) scale by up to a factor of two (motion up to 25 μs). From the data obtained with these techniques and methodology, the importance of the supra-τ(c) scale for protein function and molecular recognition is becoming increasingly clearer as the connection between motion on the supra-τ(c) scale and protein functionality from the experimental side is further strengthened with results from molecular dynamics simulations.