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.

Small-molecule autocatalysis drives compartment growth, competition and reproduction.

Sustained autocatalysis coupled to compartment growth and division is a key step in the origin of life, but an experimental demonstration of this phenomenon in an artificial system has previously proven elusive. We show that autocatalytic reactions within compartments-when autocatalysis, and reactant and solvent exchange outpace product exchange-drive osmosis and diffusion, resulting in compartment growth. We demonstrate, using the formose reaction compartmentalized in aqueous droplets in an emulsion, that compartment volume can more than double. Competition for a common reactant (formaldehyde) causes variation in droplet growth rate based on the composition of the surrounding droplets. These growth rate variations are partially transmitted after selective division of the largest droplets by shearing, which converts growth-rate differences into differences in droplet frequency. This shows how a combination of properties of living systems (growth, division, variation, competition, rudimentary heredity and selection) can arise from simple physical-chemical processes and may have paved the way for the emergence of evolution by natural selection.

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.

Multivalent interactions of the disordered regions of XLF and XRCC4 foster robust cellular NHEJ and drive the formation of ligation-boosting condensates in vitro.

In mammalian cells, DNA double-strand breaks are predominantly repaired by non-homologous end joining (NHEJ). During repair, the Ku70/80 heterodimer (Ku), XRCC4 in complex with DNA Ligase 4 (X4L4), and XLF form a flexible scaffold that holds the broken DNA ends together. Insights into the architectural organization of the NHEJ scaffold and its regulation by the DNA-dependent protein kinase catalytic subunit (DNA-PKcs) have recently been obtained by single-particle cryo-electron microscopy analysis. However, several regions, especially the C-terminal regions (CTRs) of the XRCC4 and XLF scaffolding proteins, have largely remained unresolved in experimental structures, which hampers the understanding of their functions. Here, we used magnetic resonance techniques and biochemical assays to comprehensively characterize the interactions and dynamics of the XRCC4 and XLF CTRs at atomic resolution. We show that the CTRs of XRCC4 and XLF are intrinsically disordered and form a network of multivalent heterotypic and homotypic interactions that promotes robust cellular NHEJ activity. Importantly, we demonstrate that the multivalent interactions of these CTRs led to the formation of XLF and X4L4 condensates in vitro which can recruit relevant effectors and critically stimulate DNA end ligation. Our work highlights the role of disordered regions in the mechanism and dynamics of NHEJ and lays the groundwork for the investigation of NHEJ protein disorder and its associated condensates inside cells with implications in cancer biology, immunology and the development of genome editing strategies.

Efficient 18.8 T MAS-DNP NMR reveals hidden side chains in amyloid fibrils.

Amyloid fibrils are large and insoluble protein assemblies composed of a rigid core associated with a cross-ß arrangement rich in ß-sheet structural elements. It has been widely observed in solid-state NMR experiments that semi-rigid protein segments or side chains do not yield easily observable NMR signals at room temperature. The reasons for the missing peaks may be due to the presence of unfavorable dynamics that interfere with NMR experiments, which result in very weak or unobservable NMR signals. Therefore, for amyloid fibrils, semi-rigid and dynamically disordered segments flanking the amyloid core are very challenging to study. Here, we show that high-field dynamic nuclear polarization (DNP), an NMR hyperpolarization technique typically performed at low temperatures, can circumvent this issue because (i) the low-temperature environment (~ 100 K) slows down the protein dynamics to escape unfavorable detection regime, (ii) DNP improves the overall NMR sensitivity including those of flexible side chains, and (iii) efficient cross-effect DNP biradicals (SNAPol-1) optimized for high-field DNP (≥ 18.8 T) are employed to offer high sensitivity and resolution suitable for biomolecular NMR applications. By combining these factors, we have successfully established an impressive enhancement factor of ε ~ 50 on amyloid fibrils using an 18.8 T/ 800 MHz magnet. We have compared the DNP efficiencies of M-TinyPol, NATriPol-3, and SNAPol-1 biradicals on amyloid fibrils. We found that SNAPol-1 (with ε ~ 50) outperformed the other two radicals. The MAS DNP experiments revealed signals of flexible side chains previously inaccessible at conventional room-temperature experiments. These results demonstrate the potential of MAS-DNP NMR as a valuable tool for structural investigations of amyloid fibrils, particularly for side chains and dynamically disordered segments otherwise hidden at room temperature.

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.

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.

Convergent views on disordered protein dynamics from NMR and computational approaches.

Intrinsically disordered proteins (IDPs) or intrinsically disordered regions (IDRs) is a class of biologically important proteins exhibiting specific biophysical characteristics. They lack a hydrophobic core, and their conformational behavior is strongly influenced by electrostatic interactions. IDPs and IDRs are highly dynamic, and a characterization of the motions of IDPs and IDRs is essential for their physically correct description. NMR together with molecular dynamics simulations are the methods best suited to such a task because they provide information about dynamics of proteins with atomistic resolution. Here, we present a study of motions of a disordered C-terminal domain of the delta subunit of RNA polymerase from Bacillus subtilis. Positively and negatively charged residues in the studied domain form transient electrostatic contacts critical for the biological function. Our study is focused on investigation of ps-ns dynamics of backbone of the delta subunit based on analysis of amide 15N NMR relaxation data and molecular dynamics simulations. In order to extend an informational content of NMR data to lower frequencies, which are more sensitive to slower motions, we combined standard (high-field) NMR relaxation experiments with high-resolution relaxometry. Altogether, we collected data reporting the relaxation at 12 different magnetic fields, resulting in an unprecedented data set. Our results document that the analysis of such data provides a consistent description of dynamics and confirms the validity of so far used protocols of the analysis of dynamics of IDPs also for a partially folded protein. In addition, the potential to access detailed description of motions at the timescale of tens of ns with the help of relaxometry data is discussed. Interestingly, in our case, it appears to be mostly relevant for a region involved in the formation of temporary contacts within the disordered region, which was previously proven to be biologically important.

How does it really move? Recent progress in the investigation of protein nanosecond dynamics by NMR and simulation.

Nuclear magnetic resonance (NMR) spin relaxation experiments currently probe molecular motions on timescales from picoseconds to nanoseconds. The detailed interpretation of these motions in atomic detail benefits from complementarity with the results from molecular dynamics (MD) simulations. In this mini-review, we describe the recent developments in experimental techniques to study the backbone dynamics from 15N relaxation and side-chain dynamics from 13C relaxation, discuss the different analysis approaches from model-free to dynamics detectors, and highlight the many ways that NMR relaxation experiments and MD simulations can be used together to improve the interpretation and gain insights into protein dynamics.

Detection of Metabolite-Protein Interactions in Complex Biological Samples by High-Resolution Relaxometry: Toward Interactomics by NMR.

Metabolomics, the systematic investigation of metabolites in biological fluids, cells, or tissues, reveals essential information about metabolism and diseases. Metabolites have functional roles in a myriad of biological processes, as substrates and products of enzymatic reactions but also as cofactors and regulators of large numbers of biochemical mechanisms. These functions involve interactions of metabolites with macromolecules. Yet, methods to systematically investigate these interactions are still scarce to date. In particular, there is a need for techniques suited to identify and characterize weak metabolite-macromolecule interactions directly in complex media such as biological fluids. Here, we introduce a method to investigate weak interactions between metabolites and macromolecules in biological fluids. Our approach is based on high-resolution NMR relaxometry and does not require any invasive procedure or separation step. We show that we can detect interactions between small and large molecules in human blood serum and quantify the size of the complex. Our work opens the way for investigations of metabolite (or other small molecules)-protein interactions in biological fluids for interactomics or pharmaceutical applications.

Sequential assignment of NMR spectra of peptides at natural isotopic abundance with zero- and ultra-low-field total correlation spectroscopy (ZULF-TOCSY).

A novel method dubbed ZULF-TOCSY results from the combination of Zero and Ultra-Low Field (ZULF) with high-field, high-resolution NMR, leading to a generalization of the concept of total correlation spectroscopy (TOCSY). ZULF-TOCSY is a new building block for NMR methods, which has the unique property that the polarization is evenly distributed among all NMR-active nuclei such as 1H, 13C, 15N, 31P, etc., provided that they belong to the same coupling network, and provided that their relaxation is not too fast at low fields, as may occur in macromolecules. Here, we show that ZULF-TOCSY correlations can be observed for peptides at natural isotopic abundance, such as the protected hexapeptide Boc-Met-enkephalin. The analysis of ZULF-TOCSY spectra readily allows one to make sequential assignments, thus offering an alternative to established heteronuclear 2D experiments like HMBC. For Boc-Met-enkephalin, we show that ZULF-TOCSY allows one to observe all expected cross-peaks between carbonyl carbons and α-CH protons, while the popular HMBC method provides insufficient information.

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.

Total Correlation Spectroscopy across All NMR-Active Nuclei by Mixing at Zero Field.

Multidimensional nuclear magnetic resonance (NMR) is based on a combination of well-established building blocks for polarization transfer. These blocks are used to design correlation experiments through one or a few chemical bonds or through space. Here, we introduce a building block that enables polarization transfer across all NMR-active nuclei in a coupled network of spins: isotropic mixing at zero and ultralow field (ZULF). Exploiting mixing under ZULF-NMR conditions, heteronuclear TOtal Correlation SpectroscopY (TOCSY) experiments were developed to highlight coupled spin networks. We demonstrate 1H-13C and 1H-15N correlations in ZULF-TOCSY spectra of labeled amino acids, which allow one to obtain cross-peaks among all heteronuclei belonging to the same coupled network, even when the direct interaction between them is negligible. We also demonstrate the potential of ZULF-TOCSY to analyze complex mixtures on a growth medium of isotope-labeled biomolecules. ZULF-TOCSY enables the quick identification of individual compounds in the mixture by their coupled spin networks. The ZULF-TOCSY method will lead to the development of a new toolbox of experiments to analyze complex mixtures by NMR.

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.

Sensitivity-enhanced three-dimensional and carbon-detected two-dimensional NMR of proteins using hyperpolarized water.

Signal enhancements of up to two orders of magnitude in protein NMR can be achieved by employing HDO as a vector to introduce hyperpolarization into folded or intrinsically disordered proteins. In this approach, hyperpolarized HDO produced by dissolution-dynamic nuclear polarization (D-DNP) is mixed with a protein solution waiting in a high-field NMR spectrometer, whereupon amide proton exchange and nuclear Overhauser effects (NOE) transfer hyperpolarization to the protein and enable acquisition of a signal-enhanced high-resolution spectrum. To date, the use of this strategy has been limited to 1D and 1H-15N 2D correlation experiments. Here we introduce 2D 13C-detected D-DNP, to reduce exchange-induced broadening and other relaxation penalties that can adversely affect proton-detected D-DNP experiments. We also introduce hyperpolarized 3D spectroscopy, opening the possibility of D-DNP studies of larger proteins and IDPs, where assignment and residue-specific investigation may be impeded by spectral crowding. The signal enhancements obtained depend in particular on the rates of chemical and magnetic exchange of the observed residues, thus resulting in non-uniform 'hyperpolarization-selective' signal enhancements. The resulting spectral sparsity, however, makes it possible to resolve and monitor individual amino acids in IDPs of over 200 residues at acquisition times of just over a minute. We apply the proposed experiments to two model systems: the compactly folded protein ubiquitin, and the intrinsically disordered protein (IDP) osteopontin (OPN).

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.

Surprising absence of strong homonuclear coupling at low magnetic field explored by two-field nuclear magnetic resonance spectroscopy.

Strong coupling of nuclear spins, which is achieved when their scalar coupling 2πJ is greater than or comparable to the difference Δω in their Larmor precession frequencies in an external magnetic field, gives rise to efficient coherent longitudinal polarization transfer. The strong coupling regime can be achieved when the external magnetic field is sufficiently low, as Δω is reduced proportional to the field strength. In the present work, however, we demonstrate that in heteronuclear spin systems these simple arguments may not hold, since heteronuclear spin-spin interactions alter the Δω value. The experimental method that we use is two-field nuclear magnetic resonance (NMR), exploiting sample shuttling between the high field, at which NMR spectra are acquired, and the low field, where strong couplings are expected and at which NMR pulses can be applied to affect the spin dynamics. By using this technique, we generate zero-quantum spin coherences by means of a nonadiabatic passage through a level anticrossing and study their evolution at the low field. Such zero-quantum coherences mediate the polarization transfer under strong coupling conditions. Experiments performed with a 13C-labeled amino acid clearly show that the coherent polarization transfer at the low field is pronounced in the 13C spin subsystem under proton decoupling. However, in the absence of proton decoupling, polarization transfer by coherent processes is dramatically reduced, demonstrating that heteronuclear spin-spin interactions suppress the strong coupling regime, even when the external field is low. A theoretical model is presented, which can model the reported experimental results.