Protein Side-chain Dynamics Research Articles

Analytical Framework to Understand the Origins of Methyl Side-Chain Dynamics in Protein Assemblies.

Side-chain motions play an important role in understanding protein structure, dynamics, protein-protein, and protein-ligand interactions. However, our understanding of protein side-chain dynamics is currently limited by the lack of analytical tools. Here, we present a novel analytical framework employing experimental nuclear magnetic resonance (NMR) relaxation measurements at atomic resolution combined with molecular dynamics (MD) simulation to characterize with a high level of detail the methyl side-chain dynamics in insoluble protein assemblies, using amyloid fibrils formed by the prion HET-s. We use MD simulation to interpret experimental results, where rotameric hops, including methyl group rotation and χ1/χ2 rotations, cannot be completely described with a single correlation time but rather sample a broad distribution of correlation times, resulting from continuously changing local structure in the fibril. Backbone motion similarly samples a broad range of correlation times, from ∼100 ps to μs, although resulting from mostly different dynamic processes; nonetheless, we find that the backbone is not fully decoupled from the side-chain motion, where changes in side-chain dynamics influence backbone motion and vice versa. While the complexity of side-chain motion in protein assemblies makes it very challenging to obtain perfect agreement between experiment and simulation, our analytical framework improves the interpretation of experimental dynamics measurements for complex protein assemblies.

Comprehensive analysis of relaxation decays from high-resolution relaxometry

Relaxometry consists in measuring relaxation rates over orders of magnitude of magnetic fields to probe motions of complex systems. High-resolution relaxometry (HRR) experiments can be performed on conventional high-field NMR magnets equipped with a sample shuttle. During the experiment, the sample shuttle transfers the sample between the high-field magnetic center and a chosen position in the stray field for relaxation during a variable delay, thus using the stray field as a variable field. As the relaxation delay occurs outside of the probe, HRR experiments cannot rely on the control of cross-relaxation pathways, which is standard in high-field relaxation pulse sequences. Thus, decay rates are not pure relaxation rates, which may impair a reliable description of the dynamics. Previously, we took into account cross-relaxation effects in the analysis of high-resolution relaxometry data by applying a correction factor to relaxometry decay rates in order to estimate relaxation rates. These correction factors were obtained from the iterative simulation of the relaxation decay while the sample lies outside of the probe and a preceding analysis of relaxation rates which relies on the approximation of a priori multi-exponential decays by mono-exponential functions. However, an analysis protocol matching directly experimental and simulated relaxometry decays should be more self consistent and more generally applicable as it can accommodate deviations from mono-exponential decays. Here, we introduce Matching INtensities for the Optimization of Timescales and Amplitudes of motions Under Relaxometry (MINOTAUR), a framework for the analysis of high-resolution relaxometry that takes as input the intensity decays at all fields. This approach uses the full relaxation matrix to calculate intensity decays, allowing complex relaxation pathways to be taken into account. Therefore, it eliminates the need for a correction of decay rates and for fitting multi-exponential decays with mono-exponential functions. The MINOTAUR software is designed as a flexible framework where relaxation matrices and spectral density functions corresponding to various models of motions can be defined on a case-by-case basis. The agreement with our previous analyses of protein side-chain dynamics from carbon-13 relaxation is excellent, while providing a more robust analysis tool. We expect MINOTAUR to become the tool of choice for the analysis of high-resolution relaxometry.

Explicit Models of Motion to Understand Protein Side-Chain Dynamics.

Nuclear magnetic relaxation is widely used to probe protein dynamics. For decades, most analyses of relaxation in proteins have relied successfully on the model-free approach, forgoing mechanistic descriptions of motion. Model-free types of correlation functions cannot describe a large carbon-13 relaxation dataset in protein side chains. Here, we use molecular dynamics simulations to design explicit models of motion and solve Fokker-Planck diffusion equations. These models of motion provide better agreement with relaxation data, mechanistic insight, and a direct link to configuration entropy.

Proton TOCSY NMR relaxation rates quantitate protein side chain mobility in the Pin1 WW domain

Protein side chain dynamics play a vital role in many biological processes, but differentiating mobile from rigid side chains remains a technical challenge in structural biology. Solution NMR spectroscopy is ideally suited for this but suffers from limited signal-to-noise, signal overlap, and a need for fractional 13C or 2H labeling. Here we introduce a simple strategy measuring initial 1H relaxation rates during a 1H TOCSY sequence like DIPSI-2, which can be appended to the beginning of any multi-dimensional NMR sequence that begins on 1H. The TOCSY RF field compels all 1H atoms to behave similarly under the influence of strong coupling and rotating frame cross-relaxation, so that differences in relaxation rates are due primarily to side chain mobility. We apply the scheme to a thermostable mutant Pin1 WW domain and demonstrate that the observed 1H relaxation rates correlate well with two independent NMR measures of side-chain dynamics, cross-correlated 13C relaxation rates in 13CβH2 methylene groups and maximum observable 3J couplings sensitive to the χ1 side chain dihedral angle (3JHα,Hβ, 3JN,Hβ, and 3JCO,Hβ). The most restricted side chains belong to Trp26 and Asn40, which are closely packed to constitute the folding center of the WW domain. None of the other conserved aromatic residues is as immobile as the first tryptophan side chain of the WW domain. The proposed 1H relaxation methodology should make it relatively easy to measure side chain dynamics on uniformly 15N- or 13C-labeled proteins, so long as chemical shift assignments are obtainable.

Probing Side-Chain Dynamics in Proteins by NMR Relaxation of Isolated 13C Magnetization Modes in 13CH3 Methyl Groups.

The dynamics of methyl-bearing side chains in proteins were probed by 13C relaxation measurements of a number of 13C magnetization modes in selectively 13CH3-labeled methyl groups of proteins. We first show how 13C magnetization modes in a 13CH3 spin-system can be isolated using acute-angle 1H radio-frequency pulses. The parameters of methyl-axis dynamics, a measure of methyl-axis ordering (Saxis2) and the correlation time of fast local methyl-axis motions (τf), derived from 13C relaxation in 13CH3 groups are compared with their counterparts obtained from 13C relaxation in 13CHD2 methyl isotopomers. We show that in high-molecular-weight proteins, excellent correlations are obtained between the [13CHD2]-derived Saxis2 values and those extracted from relaxation of the 13C magnetization of the I = 1/2 manifold in 13CH3 methyls. In smaller proteins, a certain degree of anticorrelation is observed between the Saxis2 and τf values obtained from 13C relaxation of the I = 1/2 manifold magnetization in 13CH3 methyls. These parameters can be partially decorrelated by inclusion in the analysis of relaxation data of the I = 3/2 manifold 13C magnetization.

Magic-Angle-Pulse Driven Separation of Degenerate 1 H Transitions in Methyl Groups of Proteins: Application to Studies of Methyl Axis Dynamics.

Dynamics of protein side chains is one of the principal determinants of conformational entropy in protein structures and molecular recognition events. We describe NMR experiments that rely on the use of magic-angle pulses for efficient isolation of degenerate 1 H transitions of the I=3/2 manifold of 13 CH3 methyl groups, and serve as 'building blocks' for the measurement of transverse spin relaxation rates of the fast- and slow-relaxing 1 H transitions - the primary quantitative reporters of methyl axis dynamics in selectively {13 CH3 }-methyl-labelled, highly deuterated proteins. The magic-angle-pulse driven experiments are technically simpler and, in the absence of relaxation, predicted to be 2.3-fold more sensitive than previously developed analogous schemes. Validation of the methodology on a sample of {13 CH3 }-labeled ubiquitin demonstrates quantitative agreement between order parameters of methyl three-fold symmetry axis obtained with magic-angle-pulse driven experiments and other established NMR techniques, paving the way for studies of methyl axis dynamics in human DNAJB6b chaperone, a protein that undergoes exchange with high-molecular-weight oligomeric species.

Site-specific 2D IR spectroscopy: a general approach for the characterization of protein dynamics with high spatial and temporal resolution.

The conformational heterogeneity and dynamics of protein side chains contribute to function, but investigating exactly how is hindered by experimental challenges arising from the fast timescales involved and the spatial heterogeneity of protein structures. The potential of two-dimensional infrared (2D IR) spectroscopy for measuring conformational heterogeneity and dynamics with unprecedented spatial and temporal resolution has motivated extensive effort to develop amino acids with functional groups that have frequency-resolved absorptions to serve as probes of their protein microenvironments. We demonstrate the full advantage of the approach by selective incorporation of the probe p-cyanophenylalanine at six distinct sites in a Src homology 3 domain and the application of 2D IR spectroscopy to site-specifically characterize heterogeneity and dynamics and their contribution to cognate ligand binding. The approach revealed a wide range of microenvironments and distinct responses to ligand binding, including at the three adjacent, conserved aromatic residues that form the recognition surface of the protein. Molecular dynamics simulations performed for all the labeled proteins provide insight into the underlying heterogeneity and dynamics. Similar application of 2D IR spectroscopy and site-selective probe incorporation will allow for the characterization of heterogeneity and dynamics of other proteins, how heterogeneity and dynamics are affected by solvation and local structure, and how they might contribute to biological function.

How accurately do force fields represent protein side chain ensembles?

Although the protein backbone is the most fundamental part of the structure, the fine-tuning of side-chain conformations is important for protein function, for example, in protein-protein and protein-ligand interactions, and also in enzyme catalysis. While several benchmarks testing the performance of protein force fields for side chain properties have already been published, they often considered only a few force fields and were not tested against the same experimental observables; hence, they are not directly comparable. In this work, we explore the ability of twelve force fields, which are different flavors of AMBER, CHARMM, OPLS, or GROMOS, to reproduce average rotamer angles and rotamer populations obtained from extensive NMR studies of the 3 J and residual dipolar coupling constants for two small proteins: ubiquitin and GB3. Based on a total of 196 μs sampling time, our results reveal that all force fields identify the correct side chain angles, while the AMBER and CHARMM force fields clearly outperform the OPLS and GROMOS force fields in estimating rotamer populations. The three best force fields for representing the protein side chain dynamics are AMBER 14SB, AMBER 99SB*-ILDN, and CHARMM36. Furthermore, we observe that the side chain ensembles of buried amino acid residues are generally more accurately represented than those of the surface exposed residues.

Basic experiments in 2H static NMR for the characterization of protein side-chain dynamics.

The focus of this review is the basic methodology for applications of static deuteron NMR for studies of dynamics in the side chains of proteins. We review experimental approaches for the measurements of static line shapes and relaxation rates as well as signal enhancement strategies using the multiple echo acquisition scheme. Further, we describe computational strategies for modeling jump and diffusive motions underlying experimental data. Applications are chosen from studies of amyloid fibrils comprising the amyloid-β protein.

NMR Relaxation and Molecular Dynamics Simulations of Side Chain Dynamics in Proteins

Molecular dynamics (MD) simulations and nuclear magnetic resonance (NMR) spin relaxation experiments have become increasingly powerful to study protein dynamics at atomic resolution due to steady improvements in physical models and computation power. Good agreement between generalized Lipari-Szabo (S2NH) order parameters derived from experiment and simulation is now observed for the backbone dynamics of a number of proteins. Unfortunately, the agreement for side chains, as e.g. probed by S2CH3 for methyl-containing side chains, is much poorer. In this work we discuss several issues with methyl side chains that need to be addressed to close the gap between NMR and MD. Accounting for protein tumbling is one very important factor to obtain a good agreement. In our hands, the application of improved water force fields with an appropriate way of including anisotropic overall protein tumbling improves the prediction of experimentally measured dynamic observables by MD simulations. We demonstrate these aspects for T4 lysozyme as a representative example. Our results guide the way for extracting from the NMR relaxation data the most accurate parameters that describe protein side chain dynamics and report on conformational entropy. Additionally, we reparametrized side chain dihedral angle energy barriers for methyl rotation in the Amber99SB∗-ILDN force field. We demonstrate that this leads to a much more realistic dynamics of methyl groups and is another important feature to close the gap between spectral densities from NMR relaxation and MD simulation.

Ultrafast Reorientational Dynamics of Leucine at the Air-Water Interface.

Ultrafast dynamics of protein side chains are involved in important biological processes such as ligand binding, protein folding, and hydration. In addition, the dynamics of a side chain can report on local environments within proteins. While protein side chain dynamics have been probed for proteins in solution with nuclear magnetic resonance and infrared methods for decades, information about side chain dynamics at interfaces is lacking. At the same time, the dynamics and motions of side chains can be particularly important for interfacial binding and protein-driven surface manipulation. We here demonstrate that ultrafast reorientation dynamics of leucine amino acids at interfaces can be recorded in situ and in real time using polarization- and time-resolved pump-probe sum frequency generation (SFG). Combined with molecular dynamics simulations, time-resolved SFG was used to probe the reorientation of the isopropyl methyl groups of l-leucine at the air-water interface. The data show that the methyl units reorient diffusively at an in plane rate of Dφ = 0.07 rad(2)/ps and an out of plane rate of Dθ = 0.05 rad(2)/ps.

Effect of Short- and Long-Range Interactions on Trp Rotamer Populations Determined by Site-Directed Tryptophan Fluorescence of Tear Lipocalin

In the lipocalin family, the conserved interaction between the main α-helix and the β-strand H is an ideal model to study protein side chain dynamics. Site-directed tryptophan fluorescence (SDTF) has successfully elucidated tryptophan rotamers at positions along the main alpha helical segment of tear lipocalin (TL). The rotamers assigned by fluorescent lifetimes of Trp residues corroborate the restriction expected based on secondary structure. Steric conflict constrains Trp residues to two (t, g −) of three possible χ1 (t, g −, g +) canonical rotamers. In this study, investigation focused on the interplay between rotamers for a single amino acid position, Trp 130 on the α-helix and amino acids Val 113 and Leu 115 on the H strand, i.e. long range interactions. Trp130 was substituted for Phe by point mutation (F130W). Mutations at positions 113 and 115 with combinations of Gly, Ala, Phe residues alter the rotamer distribution of Trp130. Mutations, which do not distort local structure, retain two rotamers (two lifetimes) populated in varying proportions. Replacement of either long range partner with a small amino acid, V113A or L115A, eliminates the dominance of the t rotamer. However, a mutation that distorts local structure around Trp130 adds a third fluorescence lifetime component. The results indicate that the energetics of long-range interactions with Trp 130 further tune rotamer populations. Diminished interactions, evident in W130G113A115, result in about a 22% increase of α-helix content. The data support a hierarchic model of protein folding. Initially the secondary structure is formed by short-range interactions. TL has non-native α-helix intermediates at this stage. Then, the long-range interactions produce the native fold, in which TL shows α-helix to β-sheet transitions. The SDTF method is a valuable tool to assess long-range interaction energies through rotamer distribution as well as the characterization of low-populated rotameric states of functionally important excited protein states.

A Simple Method to Measure Protein Side-Chain Mobility Using NMR Chemical Shifts

Protein side-chain motions are involved in many important biological processes including enzymatic catalysis, allosteric regulation, and the mediation of protein-protein, protein-DNA, protein-RNA, and protein-cofactor interactions. NMR spectroscopy has long been used to provide insights into the motions of side-chain groups. Currently, the method of choice for studying side-chain dynamics by NMR is the measurement of methyl (2)H autorelaxation. Methyl (2)H autorelaxation exhibits simple relaxation mechanisms and can be straightforwardly converted to meaningful dynamic parameters. However, methyl groups can only be found in 6 of 19 side-chain bearing amino acids. Consequently, only a sparse assessment of protein side-chain dynamics is possible. Therefore, there is a significant interest in developing novel methods of studying side-chain motions that can be applied to all types of side-chains. Here, we show how side-chain chemical shifts can be used to determine the magnitude of fast side-chain motions in proteins. The chemical shift method is applicable to all side-chain bearing residues and does not require any additional measurements beyond standard NMR experiments for backbone and side-chain assignments.

Toward the Characterization of Fractional Stochastic Processes Underlying Methyl Dynamics in Proteins

In this article, we investigate the multiple-scale structure of methyl side chain dynamics in proteins. We show that the orientational correlation functions of CH(3) methyl groups are well described by a fractional Brownian dynamics model. Typical angular correlation functions involved in NMR relaxation were computed from MD simulations performed on two different proteins. These correlation functions were shown to be very well fitted by a fractional Ornstein-Uhlenbeck process in the presence of effective local potentials at the C-H and C-C methyl bonds. In addition, our analysis highlights the presence of the asymptotic power law decay of the waiting time probability density of the stochastic process involved, thereby illustrating the connection between approaches based on fractional diffusion equations and the continuous time random walk.

Probing Side-Chain Dynamics in Proteins by the Measurement of Nine Deuterium Relaxation Rates Per Methyl Group

We demonstrate the feasibility of the measurement of up to nine deuterium spin relaxation rates in 13CHD2 and 13CH2D methyl isotopomers of small proteins. In addition to five measurable 2H relaxation rates in a 13CH2D methyl group (Millet, O.; Muhandiram, D. R.; Skrynnikov, N. R.; Kay, L. E. J. Am. Chem. Soc. 2002, 124, 6439-48), the measurement of additional four rates of (nearly) single-exponentially decaying magnetization terms in methyl groups of the 13CHD2 variety is reported. Consistency relationships between 2H spin relaxation rates measured in the two different types of methyl groups are derived and verified experimentally for a subset of methyl-containing side chains in the protein ubiquitin. A detailed comparison of methyl-bearing side-chain dynamics parameters obtained from relaxation measurements in 13CH2D and 13CHD2 methyls of ubiquitin at 10, 27, and 40 °C reveals that transverse 2H relaxation rates in 13CHD2 groups are reliable and accurate reporters of the amplitudes of methyl 3-fold axis motions (S(axis)2) for protein molecules with global molecular tumbling times τ(C) >~9 ns. For smaller molecules, simple correction of transverse 2H relaxation rates in 13CHD2 groups is sufficient for the derivation of robust measures of order. Residue-specific distributions of S(axis)2 are consistent with atomic-detail molecular dynamics (MD) results. Both 13CHD2- and 13CH2D-derived S(axis)2 values are in good overall agreement with those obtained from 1 μs MD simulations at all the three temperatures, although some differences in the site-specific temperature dependence between MD- and 2H-relaxation-derived S(axis)2 values are observed.

A tribute to Lewis E Kay on his 50th birthday

It is a great pleasure for us to introduce this special issue of the Journal of Biomolecular NMR on the occasion of Prof. Lewis E. Kay’s 50th birthday. We are grateful to the Editors of the Journal of Biomolecular NMR for accepting our proposal. In particular, we thank Prof. Martin Billeter for editing this issue, and Dr. Ad Bax for advice and support. We believe that Lewis merits this special issue of Journal of Biomolecular NMR for his innovative contributions to biomolecular NMR spectroscopy, as well as for his role as inspirer for a large group of young research professionals. The following short list of examples serves to illustrate how the work of Lewis Kay has helped to advance our field: Lewis has consistently been a pioneer in the development of novel methods essential to increasing the size of proteins that may be studied by NMR. In the days when assigning chemical shifts of a protein with 150 amino acids was a major endeavour, the Kay lab––in collaboration with Prof. Cheryl Arrowsmith––combined advances in gradientenhanced spectroscopy, protein deuteration and pulse sequence design to establish the resonance assignments for a 37 kDa complex. As these techniques became more broadly used, his lab forged ahead with clever biochemical tricks for incorporating protonated methyl groups in otherwise deuterated proteins, and developed methyl TROSY experiments that permit well-resolved spectra to be obtained for high molecular weight complexes, extending to 1 MDa. Lewis has been a leader in using NMR to measure fast timescale macromolecular dynamics, starting with his contributions to inverse-detected N relaxation experiments. His deuterium spin relaxation methodologies have had a huge impact on our ability to characterize side chain dynamics in proteins. In addition, the Kay lab has extensively developed and applied new methodologies for studying low-populated states of proteins and their roles in biology. Building on transverse relaxation dispersion experiments, the Kay lab has introduced approaches to elucidate the threeK. H. Gardner (&) Department of Biochemistry, UT Southwestern Medical Center, 5323 Harry Hines Blvd., Dallas, TX 75390-8816, USA e-mail: Kevin.Gardner@UTSouthwestern.edu

Probing Protein Side Chain Dynamics Via 13C NMR Relaxation

Protein side chain dynamics is associated with protein stability, folding, and intermolecular interactions. Detailed dynamics information is crucial for the understanding of protein function and biochemical and biophysical properties, which can be obtained using NMR relaxation techniques. In this review, (13)C relaxation of methine, methylene and methyl groups with and without (1)H decoupling are described briefly for a better understanding of how spin relaxation is associated with motional (dynamics) parameters. Developments in the measurement and interpretation of (13)C auto-relaxation and cross-correlated relaxation data are presented too. Finally, recent progress in the use of (13)C relaxation to probe the dynamics of protein side chains is detailed mainly for the dynamics of non-deuterated proteins on picoseconds-nanosecond timescales.

Conservation of Side-Chain Dynamics Within a Protein Family

The question of protein dynamics and its relevance to function is currently a topic of great interest. Proteins are particularly dynamic at the side-chain level on the time scale of picoseconds to nanoseconds. Here, we present a comparison of NMR-monitored side-chain motion between three PDZ domains of approximately 30% sequence identity and show that the side-chain dynamics display nontrivial conservation. Methyl (2)H relaxation was carried out to determine side-chain order parameters (S(2)), which were found to be more similar than naively expected from sequence, local packing, or a combination of the two. Thus, the dynamics of a rather distant homologue appears to be an excellent predictor of a protein's side-chain dynamics and, on average, better than current structure-based methods. Fast side-chain dynamics therefore display a high level of organization associated with global fold. Beyond simple conservation, the analysis herein suggests that the pattern of side-chain flexibility has significant contributions from nonlocal elements of the PDZ fold, such as correlated motions, and that the conserved dynamics may directly support function.

Protein Side-Chain Dynamics and Residual Conformational Entropy

Changes in residual conformational entropy of proteins can be significant components of the thermodynamics of folding and binding. Nuclear magnetic resonance (NMR) spin relaxation is the only experimental technique capable of probing local protein entropy, by inference from local internal conformational dynamics. To assess the validity of this approach, the picosecond-to-nanosecond dynamics of the arginine side-chain N(epsilon)-H(epsilon) bond vectors of Escherichia coli ribonuclease H (RNase H) were determined by NMR spin relaxation and compared to the mechanistic detail provided by molecular dynamics (MD) simulations. The results indicate that arginine N(epsilon) spin relaxation primarily reflects persistence of guanidinium salt bridges and correlates well with simulated side-chain conformational entropy. In particular cases, the simulations show that the aliphatic part of the arginine side chain can retain substantial disorder while the guanidinium group maintains its salt bridges; thus, the N(epsilon)-H(epsilon) bond-vector orientation is conserved and side-chain flexibility is concealed from N(epsilon) spin relaxation. The MD simulations and an analysis of a rotamer library suggest that dynamic decoupling of the terminal moiety from the remainder of the side chain occurs for all five amino acids with more than two side-chain dihedral angles (R, K, E, Q, and M). Dynamic decoupling thus may represent a general biophysical strategy for minimizing the entropic penalties of folding and binding.

Protein Side-Chain Dynamics As Observed by Solution- and Solid-State NMR Spectroscopy: A Similarity Revealed

In this paper, we seek to compare the internal dynamics of a small globular protein, SH3 domain from alpha-spectrin, in solution and in a crystalline state. The comparison involves side-chain methyl 13C R1 relaxation rates that are highly sensitive to local dynamics in the vicinity of the methyl site. To conduct the relaxation measurements, protein samples have been prepared using specially labeled alpha-ketoisovalerate precursors, resulting in selective incorporation of the 1H-13C spin pair in one or both methyl groups of the valine and leucine side chains. The sparse labeling pattern in an otherwise deuterated sample makes it possible to record high-resolution 13C, 1H solid-state spectra using magic angle spinning experiment with a MAS frequency of 22 kHz. Furthermore, this labeling scheme avoids proton-driven 13C-13C spin-diffusion effects, thus allowing for accurate measurements of 13C R1 relaxation in the individual methyl groups. While the relaxation response from a polycrystalline sample is generally expected to be multiexponential, we demonstrate both theoretically and experimentally that in this particular case the relaxation profiles are, in excellent approximation, monoexponential. In fact, solid-state relaxation data can be interpreted in a model-free fashion, similar to solution data. Direct comparison between the experimentally measured solid and solution rates reveals a strong correlation, r = 0.94. Furthermore, when solution rates are corrected for the effect of the overall molecular tumbling (quantified on the basis of the solution 15N relaxation data), the results are in one-to-one agreement with the solid-state rates. This finding indicates that methyl dynamics in the solution and solid samples are quantitatively similar. More broadly, it suggests that the entire dynamic network, including motions of side chains in the protein hydrophobic core and backbone motions, is similar. This result opens interesting possibilities for combined interpretation of solid- and solution-state relaxation data, potentially leading to a detailed characterization of internal protein dynamics on a wide range of time scales.