Unraveling motion in proteins by combining NMR relaxometry and molecular dynamics simulations: A case study on ubiquitin.

Nuclear magnetic resonance (NMR) relaxation experiments shine light onto the dynamics of molecular systems in the picosecond to millisecond timescales. As these methods cannot provide an atomically resolved view of the motion of atoms, functional groups, or domains giving rise to such signals, relaxation techniques have been combined with molecular dynamics (MD) simulations to obtain mechanistic descriptions and gain insights into the functional role of side chain or domain motion. In this work, we present a comparison of five computational methods that permit the joint analysis of MD simulations and NMR relaxation experiments. We discuss their relative strengths and areas of applicability and demonstrate how they may be utilized to interpret the dynamics in MD simulations with the small protein ubiquitin as a test system. We focus on the aliphatic side chains given the rigidity of the backbone of this protein. We find encouraging agreement between experiment, Markov state models built in the χ1/χ2 rotamer space of isoleucine residues, explicit rotamer jump models, and a decomposition of the motion using ROMANCE. These methods allow us to ascribe the dynamics to specific rotamer jumps. Simulations with eight different combinations of force field and water model highlight how the different metrics may be employed to pinpoint force field deficiencies. Furthermore, the presented comparison offers a perspective on the utility of NMR relaxation to serve as validation data for the prediction of kinetics by state-of-the-art biomolecular force fields.

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.

Correlating histone acetylation with nucleosome core particle dynamics and function.

Epigenetic modifications of chromatin play a critical role in regulating the fidelity of the genetic code and in controlling the translation of genetic information into the protein components of the cell. One key posttranslational modification is acetylation of histone lysine residues. Molecular dynamics simulations, and to a smaller extent experiment, have established that lysine acetylation increases the dynamics of histone tails. However, a systematic, atomic resolution experimental investigation of how this epigenetic mark, focusing on one histone at a time, influences the structural dynamics of the nucleosome beyond the tails, and how this translates into accessibility of protein factors such as ligases and nucleases, has yet to be performed. Herein, using NMR spectroscopy of nucleosome core particles (NCPs), we evaluate the effects of acetylation of each histone on tail and core dynamics. We show that for histones H2B, H3, and H4, the histone core particle dynamics are little changed, even though the tails have increased amplitude motions. In contrast, significant increases to H2A dynamics are observed upon acetylation of this histone, with the docking domain and L1 loop particularly affected, correlating with increased susceptibility of NCPs to nuclease digestion and more robust ligation of nicked DNA. Dynamic light scattering experiments establish that acetylation decreases inter-NCP interactions in a histone-dependent manner and facilitates the development of a thermodynamic model for NCP stacking. Our data show that different acetylation patterns result in nuanced changes to NCP dynamics, modulating interactions with other protein factors, and ultimately controlling biological output.

Inhibitor-3 inhibits Protein Phosphatase 1 via a metal binding dynamic protein-protein interaction.

To achieve substrate specificity, protein phosphate 1 (PP1) forms holoenzymes with hundreds of regulatory and inhibitory proteins. Inhibitor-3 (I3) is an ancient inhibitor of PP1 with putative roles in PP1 maturation and the regulation of PP1 activity. Here, we show that I3 residues 27-68 are necessary and sufficient for PP1 binding and inhibition. In addition to a canonical RVxF motif, which is shared by nearly all PP1 regulators and inhibitors, and a non-canonical SILK motif, I3 also binds PP1 via multiple basic residues that bind directly in the PP1 acidic substrate binding groove, an interaction that provides a blueprint for how substrates bind this groove for dephosphorylation. Unexpectedly, this interaction positions a CCC (cys-cys-cys) motif to bind directly across the PP1 active site. Using biophysical and inhibition assays, we show that the I3 CCC motif binds and inhibits PP1 in an unexpected dynamic, fuzzy manner, via transient engagement of the PP1 active site metals. Together, these data not only provide fundamental insights into the mechanisms by which IDP protein regulators of PP1 achieve inhibition, but also shows that fuzzy interactions between IDPs and their folded binding partners, in addition to enhancing binding affinity, can also directly regulate enzyme activity.

Less is more: A simple methyl-TROSY based pulse scheme offers improved sensitivity in applications to high molecular weight complexes.

The HMQC pulse sequence and variants thereof have been exploited in studies of high molecular weight protein complexes, taking advantage of the fact that fast and slow relaxing magnetization components are sequestered along two distinct magnetization transfer pathways. Despite the simplicity of the HMQC scheme an even shorter version can be designed, based on elimination of the terminal refocusing period, as a further means of increasing signal. Here we present such an experiment, and show that significant sensitivity gains, in some cases by factors of two or more, are realized in studies of proteins varying in molecular masses from 100 kDa to 1 MDa.

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.

Optimizing frequency sampling in CEST experiments.

For the past decade chemical exchange saturation transfer (CEST) experiments have been successfully applied to study exchange processes in biomolecules involving sparsely populated, transiently formed conformers. Initial implementations focused on extensive sampling of the CEST frequency domain, requiring significant measurement times. Here we show that the lengthy sampling schemes often used are not optimal and that reduced frequency sampling schedules can be developed without a priori knowledge of the exchange parameters, that only depend on the chosen B1 field, and, to a lesser extent, on the intrinsic transverse relaxation rates of ground state spins. The reduced sampling approach described here can be used synergistically with other methods for reducing measurement times such as those that excite multiple frequencies in the CEST dimension simultaneously, or make use of non-uniform sampling of indirectly detected time domains, to further decrease measurement times. The proposed approach is validated by analysis of simulated and experimental datasets.

Explicit models of motions to analyze NMR relaxation data in proteins.

Nuclear Magnetic Resonance (NMR) is a tool of choice to characterize molecular motions. In biological macromolecules, pico- to nanosecond motions, in particular, can be probed by nuclear spin relaxation rates, which depend on the time fluctuations of the orientations of spin interaction frames. For the past 40 years, relaxation rates have been successfully analyzed using the Model-Free (MF) approach, which makes no assumption on the nature of motions and reports on the effective amplitude and timescale of the motions. However, obtaining a mechanistic picture of motions from this type of analysis is difficult at best, unless complemented with molecular dynamics (MD) simulations. In spite of their limited accuracy, such simulations can be used to obtain the information necessary to build explicit models of motions designed to analyze NMR relaxation data. Here, we present how to build such models, suited in particular to describe motions of methyl-bearing protein side chains and compare them with the MF approach. We show on synthetic data that explicit models of motions are more robust in the presence of rotamer jumps which dominate the relaxation in methyl groups of protein side chains. We expect this work to motivate the use of explicit models of motion to analyze MD and NMR data.

How wide is the window opened by high-resolution relaxometry on the internal dynamics of proteins in solution?

The dynamics of molecules in solution is usually quantified by the determination of timescale-specific amplitudes of motions. High-resolution nuclear magnetic resonance (NMR) relaxometry experiments-where the sample is transferred to low fields for longitudinal (T1) relaxation, and back to high field for detection with residue-specific resolution-seeks to increase the ability to distinguish the contributions from motion on timescales slower than a few nanoseconds. However, tumbling of a molecule in solution masks some of these motions. Therefore, we investigate to what extent relaxometry improves timescale resolution, using the "detector" analysis of dynamics. Here, we demonstrate improvements in the characterization of internal dynamics of methyl-bearing side chains by carbon-13 relaxometry in the small protein ubiquitin. We show that relaxometry data leads to better information about nanosecond motions as compared to high-field relaxation data only. Our calculations show that gains from relaxometry are greater with increasing correlation time of rotational diffusion.

Theoretical and computational framework for the analysis of the relaxation properties of arbitrary spin systems. Application to high-resolution relaxometry.

A wide variety of nuclear magnetic resonance experiments rely on the prediction and analysis of relaxation processes. Recently, innovative approaches have been introduced where the sample travels through a broad range of magnetic fields in the course of the experiment, such as dissolution dynamic nuclear polarization or high-resolution relaxometry. Understanding the relaxation properties of nuclear spin systems over orders of magnitude of magnetic fields is essential to rationalize the results of these experiments. For example, during a high-resolution relaxometry experiment, the absence of control of nuclear spin relaxation pathways during the sample transfers and relaxation delays leads to systematic deviations of polarization decays from an ideal mono-exponential decay with the pure longitudinal relaxation rate. These deviations have to be taken into account to describe quantitatively the dynamics of the system. Here, we present computational tools to (1) calculate analytical expressions of relaxation rates for a broad variety of spin systems and (2) use these analytical expressions to correct the deviations arising in high-resolution relaxometry experiments. These tools lead to a better understanding of nuclear spin relaxation, which is required to improve the sensitivity of many pulse sequences, and to better characterize motions in macromolecules.

Boosting the resolution of low-field [Formula: see text] relaxation experiments on intrinsically disordered proteins with triple-resonance NMR.

Improving our understanding of nanosecond motions in disordered proteins requires the enhanced sampling of the spectral density function obtained from relaxation at low magnetic fields. High-resolution relaxometry and two-field NMR measurements of relaxation have, so far, only been based on the recording of one- or two-dimensional spectra, which provide insufficient resolution for challenging disordered proteins. Here, we introduce a 3D-HNCO-based two-field NMR experiment for measurements of protein backbone [Formula: see text] amide longitudinal relaxation rates. The experiment provides accurate longitudinal relaxation rates at low field (0.33 T in our case) preserving the resolution and sensitivity typical for high-field NMR spectroscopy. Radiofrequency pulses applied on six different radiofrequency channels are used to manipulate the spin system at both fields. The experiment was demonstrated on the C-terminal domain of [Formula: see text] subunit of RNA polymerase from Bacillus subtilis, a protein with highly repetitive amino-acid sequence and very low dispersion of backbone chemical shifts.

Protein Dynamics from Accurate Low-Field Site-Specific Longitudinal and Transverse Nuclear Spin Relaxation.

Nuclear magnetic relaxation provides invaluable quantitative site-specific information on the dynamics of complex systems. Determining dynamics on nanosecond time scales requires relaxation measurements at low magnetic fields incompatible with high-resolution NMR. Here, we use a two-field NMR spectrometer to measure carbon-13 transverse and longitudinal relaxation rates at a field as low as 0.33 T (proton Larmor frequency 14 MHz) in specifically labeled side chains of the protein ubiquitin. The use of radiofrequency pulses enhances the accuracy of measurements as compared to high-resolution relaxometry approaches, where the sample is moved in the stray field of the superconducting magnet. Importantly, we demonstrate that accurate measurements at a single low magnetic field provide enough information to characterize complex motions on low nanosecond time scales, which opens a new window for the determination of site-specific nanosecond motions in complex systems such as proteins.

Understanding the methyl-TROSY effect over a wide range of magnetic fields.

The use of relaxation interference in the methyl Transverse Relaxation-Optimized SpectroscopY (TROSY) experiment has opened new avenues for the study of large proteins and protein assemblies in nuclear magnetic resonance. So far, the theoretical description of the methyl-TROSY experiment has been limited to the slow-tumbling approximation, which is correct for large proteins on high-field spectrometers. In a recent paper, favorable relaxation interference was observed in the methyl groups of a small protein at a magnetic field as low as 0.33 T, well outside the slow-tumbling regime. Here, we present a model to describe relaxation interference in methyl groups over a broad range of magnetic fields, not limited to the slow-tumbling regime. We predict that the type of multiple-quantum transition that shows favorable relaxation properties change with the magnetic field. Under the condition of fast methyl-group rotation, methyl-TROSY experiments can be recorded over the entire range of magnetic fields from a fraction of 1 T up to 100 T.

The structure of SDS22 provides insights into the mechanism of heterodimer formation with PP1.

Protein phosphatase 1 (PP1) dephosphorylates hundreds of key biological targets by associating with nearly 200 regulatory proteins to form highly specific holoenzymes. The vast majority of regulators are intrinsically disordered proteins (IDPs) and bind PP1 via short linear motifs within their intrinsically disordered regions. One of the most ancient PP1 regulators is SDS22, a protein that is conserved from yeast to mammals. Sequence analysis of SDS22 revealed that it is a leucine-rich repeat (LRR) protein, suggesting that SDS22, unlike nearly every other known PP1 regulator, is not an IDP but instead is fully structured. Here, the 2.9 Šresolution crystal structure of human SDS22 in space group P212121 is reported. SDS22 adopts an LRR fold with the horseshoe-like curvature typical for this family of proteins. The structure results in surfaces with distinct chemical characteristics that are likely to be critical for PP1 binding.

Time-Resolved Protein Side-Chain Motions Unraveled by High-Resolution Relaxometry and Molecular Dynamics Simulations.

Motions of proteins are essential for the performance of their functions. Aliphatic protein side chains and their motions play critical roles in protein interactions: for recognition and binding of partner molecules at the surface or serving as an entropy reservoir within the hydrophobic core. Here, we present a new NMR method based on high-resolution relaxometry and high-field relaxation to determine quantitatively both motional amplitudes and time scales of methyl-bearing side chains in the picosecond-to-nanosecond range. We detect a wide variety of motions in isoleucine side chains in the protein ubiquitin. We unambiguously identify slow motions in the low nanosecond range, which, in conjunction with molecular dynamics computer simulations, could be assigned to transitions between rotamers. Our approach provides unmatched detailed insight into the motions of aliphatic side chains in proteins and provides a better understanding of the nature and functional role of protein side-chain motions.

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.

Structure and Dynamics of an Intrinsically Disordered Protein Region That Partially Folds upon Binding by Chemical-Exchange NMR.

Many intrinsically disordered proteins (IDPs) and protein regions (IDRs) engage in transient, yet specific, interactions with a variety of protein partners. Often, if not always, interactions with a protein partner lead to partial folding of the IDR. Characterizing the conformational space of such complexes is challenging: in solution-state NMR, signals of the IDR in the interacting region become broad, weak, and often invisible, while X-ray crystallography only provides information on fully ordered regions. There is thus a need for a simple method to characterize both fully and partially ordered regions in the bound state of IDPs. Here, we introduce an approach based on monitoring chemical exchange by NMR to investigate the state of an IDR that folds upon binding through the observation of the free state of the protein. Structural constraints for the bound state are obtained from chemical shifts, and site-specific dynamics of the bound state are characterized by relaxation rates. The conformation of the interacting part of the IDR was determined and subsequently docked onto the structure of the folded partner. We apply the method to investigate the interaction between the disordered C-terminal region of Artemis and the DNA binding domain of Ligase IV. We show that we can accurately reproduce the structure of the core of the complex determined by X-ray crystallography and identify a broader interface. The method is widely applicable to the biophysical investigation of complexes of disordered proteins and folded proteins.

Caspase-6 Undergoes a Distinct Helix-Strand Interconversion upon Substrate Binding.

Caspases are cysteine aspartate proteases that are major players in key cellular processes, including apoptosis and inflammation. Specifically, caspase-6 has also been implicated in playing a unique and critical role in neurodegeneration; however, structural similarities between caspase-6 and other caspase active sites have hampered precise targeting of caspase-6. All caspases can exist in a canonical conformation, in which the substrate binds atop a ß-strand platform in the 130's region. This caspase-6 region can also adopt a helical conformation that has not been seen in any other caspases. Understanding the dynamics and interconversion between the helical and strand conformations in caspase-6 is critical to fully assess its unique function and regulation. Here, hydrogen/deuterium exchange mass spectrometry indicated that caspase-6 is inherently and dramatically more conformationally dynamic than closely related caspase-7. In contrast to caspase-7, which rests constitutively in the strand conformation before and after substrate binding, the hydrogen/deuterium exchange data in the L2' and 130's regions suggested that before substrate binding, caspase-6 exists in a dynamic equilibrium between the helix and strand conformations. Caspase-6 transitions exclusively to the canonical strand conformation only upon substrate binding. Glu-135, which showed noticeably different calculated pK a values in the helix and strand conformations, appears to play a key role in the interconversion between the helix and strand conformations. Because caspase-6 has roles in several neurodegenerative diseases, exploiting the unique structural features and conformational changes identified here may provide new avenues for regulating specific caspase-6 functions for therapeutic purposes.