Nuclear magnetic resonance provides a quantitative description of protein conformational flexibility on physiologically important time scales

Uncovering allostery and regulation in SORCIN through molecular dynamics simulations

Soluble resistance-related calcium-binding protein or Sorcin is an allosteric, calcium-binding Penta-EF hand (PEF) family protein implicated in multi-drug resistant cancers. Sorcin is known to bind chemotherapeutic molecules such as Doxorubicin. This study uses in-silico molecular dynamics simulations to explore the dynamics and allosteric behavior of Sorcin in the context of Ca2+ uptake and Doxorubicin binding. The results show that Ca2+ binding induces large, but reversible conformational changes in the Sorcin structure which manifest as rigid body reorientations that preserve the local secondary structure. A reciprocal allosteric handshake centered around the EF5 hand is found to be key in Sorcin dimer formation and stabilization. Binding of Doxorubicin results in rearrangement of allosteric communities which disrupts long-range allosteric information transfer from the N-terminal domain to the middle lobe. However, this binding does not result in secondary structure destabilization. Sorcin does not appear to have a distinct Ca2+ activated mode of Doxorubicin binding.Communicated by Ramaswamy H. Sarma.

Broadband Dynamics of Ubiquitin by Anionic and Cationic Nanoparticle Assisted NMR Spin Relaxation

The quantitative and comprehensive description of the internal dynamics of proteins is critical for understanding their function. Nanoparticle-assisted ¹⁵ N NMR spin relaxation spectroscopy is a new method for the observation of picosecond to microsecond dynamics of proteins when transiently interacting with the surface of the nanoparticles (NPs). The method is applied here to the protein ubiquitin in the presence of anionic and cationic silica NPs (SNPs) of different sizes. The backbone dynamics profiles are reproducible and strikingly similar to each other, indicating that specific protein-SNP interactions are unimportant. The dynamics profiles closely match the sub-nanosecond dynamics S² values observed by model-free analysis of standard ¹⁵ N relaxation of ubiquitin in free solution, indicating that the bulk of the ubiquitin backbone dynamics in solution is confined to sub-nanosecond timescales and, hence, it is dynamically more restrained than previous NMR studies have suggested.

Impact of protein dynamics on secondary structure prediction

Protein 3D structures support their biological functions. As the number of protein structures is negligible in regards to the number of available protein sequences, prediction methodologies relying only on protein sequences are essential tools. In this field, protein secondary structure prediction (PSSPs) is a mature area, and is considered to have reached a plateau. Nonetheless, proteins are highly dynamical macromolecules, a property that could impact the PSSP methods. Indeed, in a previous study, the stability of local protein conformations was evaluated demonstrating that some regions easily changed to another type of secondary structure. The protein sequences of this dataset were used by PSSPs and their results compared to molecular dynamics to investigate their potential impact on the quality of the secondary structure prediction. Interestingly, a direct link is observed between the quality of the prediction and the stability of the assignment to the secondary structure state. The more stable a local protein conformation is, the better the prediction will be. The secondary structure assignment not taken from the crystallized structures but from the conformations observed during the dynamics slightly increase the quality of the secondary structure prediction. These results show that evaluation of PSSPs can be done differently, but also that the notion of dynamics can be included in development of PSSPs and other approaches such as de novo approaches.

Determination of Protein ps-ns Motions by High-Resolution Relaxometry

Many of the functions of biomacromolecules can be rationalized by the characterization of their conformational energy landscapes: the structures of the dominant states, transitions between states and motions within states. Nuclear magnetic resonance (NMR) spectroscopy is the technique of choice to study internal motions in proteins. The determination of motions on picosecond to nanosecond timescales requires the measurement of nuclear spin relaxation rates at multiple magnetic fields. High sensitivity and resolution are obtained only at high magnetic fields, so that, until recently, site-specific relaxation rates in biomolecules were only measured over a narrow range of high magnetic fields. This limitation was particularly striking for the quantification of motions on nanosecond timescales, close to the correlation time for overall rotational diffusion. High-resolution relaxometry is an emerging technique to investigate picosecond-nanosecond motions of proteins. This approach uses a high-field NMR spectrometer equipped with a sample shuttle device, which allows for the measurement of the relaxation rate constants at low magnetic fields, while preserving the sensitivity and resolution of a high-field NMR spectrometer. The combined analysis of high-resolution relaxometry and standard high-field relaxation data provides a more accurate description of the dynamics of proteins, in particular in the nanosecond range. The purpose of this chapter is to describe how to perform high-resolution relaxometry experiments and how to analyze the rates measured with this technique.

Differential Enzyme Flexibility Probed Using Solid-State Nanopores

Enzymes and motor proteins are dynamic macromolecules that coexist in a number of conformations of similar energies. Protein function is usually accompanied by a change in structure and flexibility, often induced upon binding to ligands. However, while measuring protein flexibility changes between active and resting states is of therapeutic significance, it remains a challenge. Recently, our group has demonstrated that breadth of signal amplitudes in measured electrical signatures as an ensemble of individual protein molecules is driven through solid-state nanopores and correlates with protein conformational dynamics. Here, we extend our study to resolve subtle flexibility variation in dihydrofolate reductase mutants from unlabeled single molecules in solution. We first demonstrate using a canonical protein system, adenylate kinase, that both size and flexibility changes can be observed upon binding to a substrate that locks the protein in a closed conformation. Next, we investigate the influence of voltage bias and pore geometry on the measured electrical pulse statistics during protein transport. Finally, using the optimal experimental conditions, we systematically study a series of wild-type and mutant dihydrofolate reductase proteins, finding a good correlation between nanopore-measured protein conformational dynamics and equilibrium bulk fluorescence probe measurements. Our results unequivocally demonstrate that nanopore-based measurements reliably probe conformational diversity in native protein ensembles.

Simultaneous detection of intra- and inter-molecular paramagnetic relaxation enhancements in protein complexes

Paramagnetic relaxation enhancement (PRE) measurements constitute a powerful approach for detecting both permanent and transient protein-protein interactions. Typical PRE experiments require an intrinsic or engineered paramagnetic site on one of the two interacting partners; while a second, diamagnetic binding partner is labeled with stable isotopes (¹⁵N or ¹³C). Multiple paramagnetic labeled centers or reversed labeling schemes are often necessary to obtain sufficient distance restraints to model protein-protein complexes, making this approach time consuming and expensive. Here, we show a new strategy that combines a modified pulse sequence (¹H_N-Γ₂-CCLS) with an asymmetric labeling scheme to enable the detection of both intra- and inter-molecular PREs simultaneously using only one sample preparation. We applied this strategy to the non-covalent dimer of ubiquitin. Our method confirmed the previously identified binding interface for the transient di-ubiquitin complex, and at the same time, unveiled the internal structural dynamics rearrangements of ubiquitin upon interaction. In addition to reducing the cost of sample preparation and speed up PRE measurements, by detecting the intra-molecular PRE this new strategy will make it possible to measure and calibrate inter-molecular distances more accurately for both symmetric and asymmetric protein-protein complexes.

Conformational switch of the bacterial adhesin FimH in the absence of the regulatory domain: Engineering a minimalistic allosteric system

For many biological processes such as ligand binding, enzymatic catalysis, or protein folding, allosteric regulation of protein conformation and dynamics is fundamentally important. One example is the bacterial adhesin FimH, where the C-terminal pilin domain exerts negative allosteric control over binding of the N-terminal lectin domain to mannosylated ligands on host cells. When the lectin and pilin domains are separated under shear stress, the FimH-ligand interaction switches in a so-called catch-bond mechanism from the low- to high-affinity state. So far, it has been assumed that the pilin domain is essential for the allosteric propagation within the lectin domain that would otherwise be conformationally rigid. To test this hypothesis, we generated mutants of the isolated FimH lectin domain and characterized their thermodynamic, kinetic, and structural properties using isothermal titration calorimetry, surface plasmon resonance, nuclear magnetic resonance, and X-ray techniques. Intriguingly, some of the mutants mimicked the conformational and kinetic behaviors of the full-length protein and, even in absence of the pilin domain, conducted the cross-talk between allosteric sites and the mannoside-binding pocket. Thus, these mutants represent a minimalistic allosteric system of FimH, useful for further mechanistic studies and antagonist design.

Applications of NMR and computational methodologies to study protein dynamics

Overwhelming evidence now illustrates the defining role of atomic-scale protein flexibility in biological events such as allostery, cell signaling, and enzyme catalysis. Over the years, spin relaxation nuclear magnetic resonance (NMR) has provided significant insights on the structural motions occurring on multiple time frames over the course of a protein life span. The present review article aims to illustrate to the broader community how this technique continues to shape many areas of protein science and engineering, in addition to being an indispensable tool for studying atomic-scale motions and functional characterization. Continuing developments in underlying NMR technology alongside software and hardware developments for complementary computational approaches now enable methodologies to routinely provide spatial directionality and structural representations traditionally harder to achieve solely using NMR spectroscopy. In addition to its well-established role in structural elucidation, we present recent examples that illustrate the combined power of selective isotope labeling, relaxation dispersion experiments, chemical shift analyses, and computational approaches for the characterization of conformational sub-states in proteins and enzymes.

The Exact NOE as an Alternative in Ensemble Structure Determination

The structure-function paradigm is increasingly replaced by the structure-dynamics-function paradigm. All protein activity is steered by the interplay between enthalpy and entropy. Conformational dynamics serves as a proxy of conformational entropy. Therefore, it is essential to study not only the average conformation but also the spatial sampling of a protein on all timescales. To this purpose, we have established a protocol for determining multiple-state ensembles of proteins based on exact nuclear Overhauser effects (eNOEs). We have recently extended our previously reported eNOE data set for the protein GB3 by a very large set of backbone and side-chain residual dipolar couplings and three-bond J couplings. Here, we demonstrate that at least four structural states are required to represent the complete data set by dissecting the contributions to the CYANA target function, which quantifies restraint violations in structure calculation. We present a four-state ensemble of GB3, which largely preserves the characteristics obtained from eNOEs only. Due to the abundance of the input data, the ensemble and χ(1) angles in particular are well suited for cross-validation of the input data and comparison to x-ray structures. Principal component analysis is used to automatically identify and validate relevant states of the ensembles. Overall, our findings suggest that eNOEs are a valuable alternative to traditional NMR probes in spatial elucidation of proteins.

Structure Calculation and Reconstruction of Discrete-State Dynamics from Residual Dipolar Couplings

Residual dipolar couplings (RDCs) acquired by nuclear magnetic resonance (NMR) spectroscopy are an indispensable source of information in investigation of molecular structures and dynamics. Here, we present a comprehensive strategy for structure calculation and reconstruction of discrete-state dynamics from RDC data that is based on the singular value decomposition (SVD) method of order tensor estimation. In addition to structure determination, we provide a mechanism of producing an ensemble of conformations for the dynamical regions of a protein from RDC data. The developed methodology has been tested on simulated RDC data with ±1 Hz of error from an 83 residue α protein (PDB ID 1A1Z ) and a 213 residue α/β protein DGCR8 (PDB ID 2YT4 ). In nearly all instances, our method reproduced the structure of the protein including the conformational ensemble to within less than 2 Å. On the basis of our investigations, arc motions with more than 30° of rotation are identified as internal dynamics and are reconstructed with sufficient accuracy. Furthermore, states with relative occupancies above 20% are consistently recognized and reconstructed successfully. Arc motions with a magnitude of 15° or relative occupancy of less than 10% are consistently unrecognizable as dynamical regions within the context of ±1 Hz of error.

Investigating protein conformational energy landscapes and atomic resolution dynamics from NMR dipolar couplings: a review

Nuclear magnetic resonance spectroscopy is exquisitely sensitive to protein dynamics. In particular inter-nuclear dipolar couplings, that become measurable in solution when the protein is dissolved in a dilute liquid crystalline solution, report on all conformations sampled up to millisecond timescales. As such they provide the opportunity to describe the Boltzmann distribution present in solution at atomic resolution, and thereby to map the conformational energy landscape in unprecedented detail. The development of analytical methods and approaches based on numerical simulation and their application to numerous biologically important systems is presented.

Ensemble Calculation for Intrinsically Disordered Proteins Using NMR Parameters

Intrinsically disordered proteins (IDPs) perform their function despite their lack of well-defined tertiary structure. Residual structure has been observed in IDPs, commonly described as transient/dynamic or expressed in terms of fractional populations. In order to understand how the protein primary sequence dictates the dynamic and structural properties of IDPs and in general to understand how IDPs function, atomic-level descriptions are needed. Nuclear magnetic resonance spectroscopy provides information about local and long-range structure in IDPs at amino acid specific resolution and can be used in combination with ensemble descriptions to represent the dynamic nature of IDPs. In this chapter we describe sample-and-select approaches for ensemble modelling of local structural propensities in IDPs with specific emphasis on validation of these ensembles.

New opportunities for tensor-free calculations of residual dipolar couplings for the study of protein dynamics

Residual dipolar couplings (RDCs) can provide exquisitely detailed information about the structure and dynamics of proteins. It is challenging, however, to extract such information from RDC measurements in conformationally heterogeneous states of proteins because of the complex relationship between RDCs and protein structures. To obtain new insights into this problem, we discuss methods of calculating the RDCs that do not require the definition of an alignment tensor. These methods can help in particular in the search of effective ways to use RDCs to characterise disordered or partially disordered states of proteins.

Towards a true protein movie: a perspective on the potential impact of the ensemble-based structure determination using exact NOEs

Confined by the Boltzmann distribution of the energies of the states, a multitude of structural states are inherent to biomolecules. For a detailed understanding of a protein's function, its entire structural landscape at atomic resolution and insight into the interconversion between all the structural states (i.e. dynamics) are required. Whereas dedicated trickery with NMR relaxation provides aspects of local dynamics, and 3D structure determination by NMR is well established, only recently have several attempts been made to formulate a more comprehensive description of the dynamics and the structural landscape of a protein. Here, a perspective is given on the use of exact NOEs (eNOEs) for the elucidation of structural ensembles of a protein describing the covered conformational space.

Nanosecond time scale motions in proteins revealed by high-resolution NMR relaxometry

Understanding the molecular determinants underlying protein function requires the characterization of both structure and dynamics at atomic resolution. Nuclear relaxation rates allow a precise characterization of protein dynamics at the Larmor frequencies of spins. This usually limits the sampling of motions to a narrow range of frequencies corresponding to high magnetic fields. At lower fields one cannot achieve sufficient sensitivity and resolution in NMR. Here, we use a fast shuttle device where the polarization builds up and the signals are detected at high field, while longitudinal relaxation takes place at low fields 0.5 < B₀ < 14.1 T. The sample is propelled over a distance up to 50 cm by a blowgun-like system in about 50 ms. The analysis of nitrogen-15 relaxation in the protein ubiquitin over such a wide range of magnetic fields offers unprecedented insights into molecular dynamics. Some key regions of the protein feature structural fluctuations on nanosecond time scales, which have so far been overlooked in high-field relaxation studies. Nanosecond motions in proteins may have been underestimated by traditional high-field approaches, and slower supra-τ_c motions that have no effect on relaxation may have been overestimated. High-resolution relaxometry thus opens the way to a quantitative characterization of nanosecond motions in proteins.

Advances in the REDCAT software package

Background

Residual Dipolar Couplings (RDCs) have emerged in the past two decades as an informative source of experimental restraints for the study of structure and dynamics of biological macromolecules and complexes. The REDCAT software package was previously introduced for the analysis of molecular structures using RDC data. Here we report additional features that have been included in this software package in order to expand the scope of its analyses. We first discuss the features that enhance REDCATs user-friendly nature, such as the integration of a number of analyses into one single operation and enabling convenient examination of a structural ensemble in order to identify the most suitable structure. We then describe the new features which expand the scope of RDC analyses, performing exercises that utilize both synthetic and experimental data to illustrate and evaluate different features with regard to structure refinement and structure validation.

Results

We establish the seamless interaction that takes place between REDCAT, VMD, and Xplor-NIH in demonstrations that utilize our newly developed REDCAT-VMD and XplorGUI interfaces. These modules enable visualization of RDC analysis results on the molecular structure displayed in VMD and refinement of structures with Xplor-NIH, respectively. We also highlight REDCAT’s Error-Analysis feature in reporting the localized fitness of a structure to RDC data, which provides a more effective means of recognizing local structural anomalies. This allows for structurally sound regions of a molecule to be identified, and for any refinement efforts to be focused solely on locally distorted regions.

Conclusions

The newly engineered REDCAT software package, which is available for download via the WWW from http://ifestos.cse.sc.edu, has been developed in the Object Oriented C++ environment. Our most recent enhancements to REDCAT serve to provide a more complete RDC analysis suite, while also accommodating a more user-friendly experience, and will be of great interest to the community of researchers and developers since it hides the complications of software development.

Revealing the properties of plant defensins through dynamics

Defensins are potent, ancient natural antibiotics that are present in organisms ranging from lower organisms to humans. Although the structures of several defensins have been well characterized, the dynamics of only a few have been studied. This review discusses the diverse dynamics of two plant defensins for which the structure and dynamics have been characterized, both in the free state and in the presence of target membranes. Multiple motions are observed in loops and in secondary structure elements and may be related to twisting or breathing of the α-helix and β-sheet. This complex behavior is altered in the presence of an interface and is responsive to the presence of the putative target. The stages of membrane recognition and disruption can be mapped over a large time scale range, demonstrating that defensins in solution exist as an ensemble of different conformations, a subset of which is selected upon membrane binding. Therefore, studies on the dynamics have revealed that defensins interact with membranes through a mechanism of conformational selection.

Correlation between local structural dynamics of proteins inferred from NMR ensembles and evolutionary dynamics of homologues of known structure

Conformational changes in proteins are extremely important for their biochemical functions. Correlation between inherent conformational variations in a protein and conformational differences in its homologues of known structure is still unclear. In this study, we have used a structural alphabet called Protein Blocks (PBs). PBs are used to perform abstraction of protein 3-D structures into a 1-D strings of 16 alphabets (a-p) based on dihedral angles of overlapping pentapeptides. We have analyzed the variations in local conformations in terms of PBs represented in the ensembles of 801 protein structures determined using NMR spectroscopy. In the analysis of concatenated data over all the residues in all the NMR ensembles, we observe that the overall nature of inherent local structural variations in NMR ensembles is similar to the nature of local structural differences in homologous proteins with a high correlation coefficient of .94. High correlation at the alignment positions corresponding to helical and β-sheet regions is only expected. However, the correlation coefficient by considering only the loop regions is also quite high (.91). Surprisingly, segregated position-wise analysis shows that this high correlation does not hold true to loop regions at the structurally equivalent positions in NMR ensembles and their homologues of known structure. This suggests that the general nature of local structural changes is unique; however most of the local structural variations in loop regions of NMR ensembles do not correlate to their local structural differences at structurally equivalent positions in homologues.

A general method for constructing atomic-resolution RNA ensembles using NMR residual dipolar couplings: the basis for interhelical motions revealed

The ability to modulate alignment and measure multiple independent sets of NMR residual dipolar couplings (RDCs) has made it possible to characterize internal motions in proteins at atomic resolution and with time scale sensitivity ranging from picoseconds up to milliseconds. The application of such methods to the study of RNA dynamics, however, remains fundamentally limited by the inability to modulate alignment and by strong couplings between internal and overall motions that complicate the quantitative interpretation of RDCs. Here, we address this problem by showing that RNA alignment can be generally modulated, in a controlled manner, by variable elongation of A-form helices and that the information contained within the measured RDCs can be extracted even in the presence of strong couplings between motions and overall alignment via structure-based prediction of alignment. Using this approach, four RDC data sets, and a broad conformational pool obtained from a 8.2 μs molecular dynamics simulation, we successfully construct and validate an atomic resolution ensemble of human immunodeficiency virus type I transactivation response element RNA. This ensemble reveals local motions in and around the bulge involving changes in stacking and hydrogen-bonding interactions, which are undetectable by traditional spin relaxation and drive global changes in interhelical orientation. This new approach broadens the scope of using RDCs in characterizing the dynamics of nucleic acids.

The dynamic structure of thrombin in solution

The backbone dynamics of human α-thrombin inhibited at the active site serine were analyzed using R(1), R(2), and heteronuclear NOE experiments, variable temperature TROSY 2D [(1)H-(15)N] correlation spectra, and R(ex) measurements. The N-terminus of the heavy chain, which is formed upon zymogen activation and inserts into the protein core, is highly ordered, as is much of the double beta-barrel core. Some of the surface loops, by contrast, remain very dynamic with order parameters as low as 0.5 indicating significant motions on the ps-ns timescale. Regions of the protein that were thought to be dynamic in the zymogen and to become rigid upon activation, in particular the γ-loop, the 180s loop, and the Na(+) binding site have order parameters below 0.8. Significant R(ex) was observed in most of the γ-loop, in regions proximal to the light chain, and in the β-sheet core. Accelerated molecular dynamics simulations yielded a molecular ensemble consistent with measured residual dipolar couplings that revealed dynamic motions up to milliseconds. Several regions, including the light chain and two proximal loops, did not appear highly dynamic on the ps-ns timescale, but had significant motions on slower timescales.

Review: Use of residual dipolar couplings to determine the structure of carbohydrates

Solution nuclear magnetic resonance spectroscopy is especially useful in the carbohydrate field. The measurement of residual dipolar couplings provides long-range structural information, a valuable complement for the structural study of carbohydrates either in its free form or in the bound state to proteins. They permit to deduce the geometry and the flexibility of the glycosidic linkages, which have a major influence on the conformation of carbohydrates and their overall shape. This article reviews the current application of the residual dipolar couplings methodology to carbohydrates.

Determination of structural fluctuations of proteins from structure-based calculations of residual dipolar couplings

Residual dipolar couplings (RDCs) have the potential of providing detailed information about the conformational fluctuations of proteins. It is very challenging, however, to extract such information because of the complex relationship between RDCs and protein structures. A promising approach to decode this relationship involves structure-based calculations of the alignment tensors of protein conformations. By implementing this strategy to generate structural restraints in molecular dynamics simulations we show that it is possible to extract effectively the information provided by RDCs about the conformational fluctuations in the native states of proteins. The approach that we present can be used in a wide range of alignment media, including Pf1, charged bicelles and gels. The accuracy of the method is demonstrated by the analysis of the Q factors for RDCs not used as restraints in the calculations, which are significantly lower than those corresponding to existing high-resolution structures and structural ensembles, hence showing that we capture effectively the contributions to RDCs from conformational fluctuations.

On the calculation of ³Jαβ-coupling constants for side chains in proteins

Structural knowledge about proteins is mainly derived from values of observables, measurable in NMR spectroscopic or X-ray diffraction experiments, i.e. absorbed or scattered intensities, through theoretically derived relationships between structural quantities such as atom positions or torsional angles on the one hand and observable quantities such as squared structure factor amplitudes, NOE intensities or (3) J-coupling constants on the other. The standardly used relation connecting (3) J-couplings to torsional angles is the Karplus relation, which is used in protein structure refinement as well as in the evaluation of simulated properties of proteins. The accuracy of the simple and generalised Karplus relations is investigated using side-chain structural and (3) J (αβ)-coupling data for three different proteins, Plastocyanin, Lysozyme, and FKBP, for which such data are available. The results show that the widely used Karplus relations are only a rough estimate for the relation between (3) J (αβ)-couplings and the corresponding χ(1)-angle in proteins.

An improved structural characterisation of reduced French bean plastocyanin based on NMR data and local-elevation molecular dynamics simulation

Deriving structural information about a protein from NMR experimental data is still a non-trivial challenge to computational biochemistry. This is because of the low ratio of the number of independent observables to the number of molecular degrees of freedom, the approximations involved in the different relationships between particular observable quantities and molecular conformation, and the averaged character of the experimental data. For example, protein (3)J-coupling data are seldom used for structure refinement because of the multiple-valuedness and limited accuracy of the Karplus relationship linking a (3)J-coupling to a torsional angle. Moreover, sampling of the large conformational space is still problematic. Using the 99-residue protein plastocyanin as an example we investigated whether use of a thermodynamically calibrated force field, inclusion of solvent degrees of freedom, and application of adaptive local-elevation sampling that accounts for conformational averaging produces a more realistic representation of the ensemble of protein conformations than standard single-structure refinement in a non-explicit solvent using restraints that do not account for averaging and are partly based on non-observed data. Yielding better agreement with observed experimental data, the protein conformational ensemble is less restricted than when using standard single-structure refinement techniques, which are likely to yield a picture of the protein which is too rigid.

Standard tensorial analysis of local ordering in proteins from residual dipolar couplings

Residual dipolar couplings (RDCs) in proteins arise from independent external medium-related and internal protein-related ordering of the spin-bearing probe. Griesinger et al. developed a method for treating RDCs in proteins. The global ordering is given in the standard manner by a rank 2 tensor specified in a known molecular frame, MF. The local ordering is described by the spherical harmonic ensemble averages, <Y(2m)(θ, φ)>, m = 0, ±1, ±2, also given in MF. From these quantities, a method we call mf-RDC derives the squared generalized order parameter (S(rdc)(2)), the amplitude (direction) of the anisotropic disorder, η (Φ′), and an approximation, (N−H)(eff), to the average probe orientation, i.e., to the local director. (N−H)(eff) is determined through a frame transformation where <Y(20)> is maximized. Φ′ is associated with a subsequent frame transformation where <Y(22) + Y(2−2)> is maximized. The mf-RDC method was applied previously to N−H and C−C(methyl) sites in ubiquitin. In this study, we convert the respective <Y(2m)(θ, φ)>'s into a Saupe tensor, which is diagonalized. This is the standard procedure. It yields the eigenvalues, S(xx), S(yy), and S(zz), and the Principal Axis System (PAS) of the rank 2 local ordering tensor, S(l). S(rdc)(2), η, and Φ′ can be recast as S(xx), S(yy), and S(zz). The mf-RDC frame transformations are not the same as the conventional Wigner rotation. The standard tensorial analysis provides new information. The contribution of local ordering rhombicity to S(rdc)(2) is evaluated. For the α-helix of ubiquitin, the main local ordering axis is assigned as C(i−1)(α) − C(i)(α); for the methyl sites, it is associated with the C−C(methyl) axis, as in mf-RDC. Ordering strength correlates with methyl type. The strength (rhombicity) of S(l) associated with picosecond−nanosecond local motions is reduced moderately (substantially) by nanosecond−millisecond local motions. A scheme for analyzing experimental RDCs based on the standard tensorial perspective, which allows for arbitrary orientation of the local director in the protein and of the PAS of S(l) in the probe, is formulated.

Synergistic applications of MD and NMR for the study of biological systems

Modern biological sciences are becoming more and more multidisciplinary. At the same time, theoretical and computational approaches gain in reliability and their field of application widens. In this short paper, we discuss recent advances in the areas of solution nuclear magnetic resonance (NMR) spectroscopy and molecular dynamics (MD) simulations that were made possible by the combination of both methods, that is, through their synergistic use. We present the main NMR observables and parameters that can be computed from simulations, and how they are used in a variety of complementary applications, including dynamics studies, model-free analysis, force field validation, and structural studies.

Crowding induces differences in the diffusion of thermophilic and mesophilic proteins: a new look at neutron scattering results

The dynamical basis underlying the increased thermal stability of thermophilic proteins remains uncertain. Here, we challenge the new paradigm established by neutron scattering experiments in solution, in which the adaptation of thermophilic proteins to high temperatures lies in the lower sensitivity of their flexibility to temperature changes. By means of a combination of molecular dynamics and Brownian dynamics simulations, we report a reinterpretation of those experiments and show evidence that under crowding conditions, such as in vivo, thermophilic and homolog mesophilic proteins have diffusional properties with different thermal behavior.

Understanding biomolecular motion, recognition, and allostery by use of conformational ensembles

We review the role conformational ensembles can play in the analysis of biomolecular dynamics, molecular recognition, and allostery. We introduce currently available methods for generating ensembles of biomolecules and illustrate their application with relevant examples from the literature. We show how, for binding, conformational ensembles provide a way of distinguishing the competing models of induced fit and conformational selection. For allostery we review the classic models and show how conformational ensembles can play a role in unravelling the intricate pathways of communication that enable allostery to occur. Finally, we discuss the limitations of conformational ensembles and highlight some potential applications for the future.

Determination of Conformational Equilibria in Proteins Using Residual Dipolar Couplings

In order to carry out their functions, proteins often undergo significant conformational fluctuations that enable them to interact with their partners. The accurate characterization of these motions is key in order to understand the mechanisms by which macromolecular recognition events take place. Nuclear magnetic resonance spectroscopy offers a variety of powerful methods to achieve this result. We discuss a method of using residual dipolar couplings as replica-averaged restraints in molecular dynamics simulations to determine large amplitude motions of proteins, including those involved in the conformational equilibria that are established through interconversions between different states. By applying this method to ribonuclease A, we show that it enables one to characterize the ample fluctuations in interdomain orientations expected to play an important functional role.

Protein dynamics: whispering within

Dynamic communication between atoms within folded proteins is potentially important for function, but its measurement has been a challenge. Now, a combined NMR and modelling study provides insights on the presence and strengths of such correlations.

Characterizing weak protein-protein complexes by NMR residual dipolar couplings

Protein-protein interactions occur with a wide range of affinities from tight complexes characterized by femtomolar dissociation constants to weak, and more transient, complexes of millimolar affinity. Many of the weak and transiently formed protein-protein complexes have escaped characterization due to the difficulties in obtaining experimental parameters that report on the complexes alone without contributions from the unbound, free proteins. Here, we review recent developments for characterizing the structures of weak protein-protein complexes using nuclear magnetic resonance spectroscopy with special emphasis on the utility of residual dipolar couplings.