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

Exploring weak ligand-protein interactions by relaxometry of long-lived spin order

Relaxation times of nuclear spins often serve as a valuable source of information on the dynamics of various biochemical processes. Measuring relaxation as a function of the external magnetic field turned out to be extremely useful for the studies of weak ligand-protein interactions. We demonstrate that observing the relaxation of the long-lived spin order instead of longitudinal magnetization extends the capability of this approach. We studied the field-dependent relaxation of the longitudinal magnetization and the singlet order (SO) of methylene protons in alanine-glycine dipeptide and citrate in the presence of human serum albumin (HSA). As a result, SO relaxation proved to be more sensitive to ligand-protein interaction, providing higher relaxation contrast for various HSA concentrations. To assess the parameters of the binding process in more details, we utilized a simple analytical relaxation model to fit the experimental field dependences for both SO and T1 relaxation. We also tested the validity of our approach in the experiments with trimethylsilylpropanoic acid (TSP) used as a competitor in ligand binding with HSA.

A set of cross-correlated relaxation experiments to probe the correlation time of two different and complementary spin pairs

Intrinsically disordered proteins (IDPs) defy the conventional structure-function paradigm by lacking a well-defined tertiary structure and exhibiting inherent flexibility. This flexibility leads to distinctive spin relaxation modes, reflecting isolated and specific motions within individual peptide planes. In this work, we propose a new pulse sequence to measure the longitudinal 13C' CSA-13C'-13Cα DD CCR rate [Formula: see text] and present a novel 3D version of the transverse [Formula: see text] CCR rate, adopting the symmetrical reconversion approach. We combined these rates with the analogous ΓxyN/NH and ΓzN/NH CCR rates to derive residue-specific correlation times for both spin-pairs within the same peptide plane. The presented approach offers a straightforward and intuitive way to compare the correlation times of two different and complementary spin vectors, anticipated to be a valuable aid to determine IDPs backbone dihedral angles distributions. We performed the proposed experiments on two systems: a folded protein ubiquitin and Coturnix japonica osteopontin, a prototypical IDP. Comparative analyses of the results show that the correlation times of different residues vary more for IDPs than globular proteins, indicating that the dynamics of IDPs is largely heterogeneous and dominated by local fluctuations.

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.

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.

Fitting Force Field Parameters to NMR Relaxation Data

We present an approach to optimize force field parameters using time-dependent data from NMR relaxation experiments. To do so, we scan parameters in the dihedral angle potential energy terms describing the rotation of the methyl groups in proteins and compare NMR relaxation rates calculated from molecular dynamics simulations with the modified force fields to deuterium relaxation measurements of T4 lysozyme. We find that a small modification of C^γ methyl groups improves the agreement with experiments both for the protein used to optimize the force field and when validating using simulations of CI2 and ubiquitin. We also show that these improvements enable a more effective a posteriori reweighting of the MD trajectories. The resulting force field thus enables more direct comparison between simulations and side-chain NMR relaxation data and makes it possible to construct ensembles that better represent the dynamics of proteins in solution.

Genetically encoded non-canonical amino acids reveal asynchronous dark reversion of chromophore, backbone and side-chains in EL222

Photoreceptors containing the light-oxygen-voltage (LOV) domain elicit biological responses upon excitation of their flavin mononucleotide (FMN) chromophore by blue light. The mechanism and kinetics of dark-state recovery are not well understood. Here we incorporated the non-canonical amino acid p-cyanophenylalanine (CNF) by genetic code expansion technology at forty-five positions of the bacterial transcription factor EL222. Screening of light-induced changes in infrared (IR) absorption frequency, electric field and hydration of the nitrile groups identified residues CNF31 and CNF35 as reporters of monomer/oligomer and caged/decaged equilibria, respectively. Time-resolved multi-probe UV/Visible and IR spectroscopy experiments of the lit-to-dark transition revealed four dynamical events. Predominantly, rearrangements around the A'α helix interface (CNF31 and CNF35) precede FMN-cysteinyl adduct scission, folding of α-helices (amide bands), and relaxation of residue CNF151. This study illustrates the importance of characterizing all parts of a protein and suggests a key role for the N-terminal A'α extension of the LOV domain in controlling EL222 photocycle length. This article is protected by copyright. All rights reserved.

DHFR Mutants Modulate Their Synchronized Dynamics with the Substrate by Shifting Hydrogen Bond Occupancies

Antibiotic resistance is a global health problem in which mutations occurring in functional proteins render drugs ineffective. The working mechanisms of the arising mutants are seldom apparent; a methodology to decipher these mechanisms systematically would render devising therapies to control the arising mutational pathways possible. Here we utilize C_α-C_β bond vector relaxations obtained from moderate length MD trajectories to determine conduits for functionality of the resistance conferring mutants of Escherichia coli dihydrofolate reductase. We find that the whole enzyme is synchronized to the motions of the substrate, irrespective of the mutation introducing gain-of-function or loss-of function. The total coordination of the motions suggests changes in the hydrogen bond dynamics with respect to the wild type as a possible route to determine and classify the mode-of-action of individual mutants. As a result, nine trimethoprim-resistant point mutations arising frequently in evolution experiments are categorized. One group of mutants that display the largest occurrence (L28R, W30G) work directly by modifying the dihydrofolate binding region. Conversely, W30R works indirectly by the formation of the E139-R30 salt bridge which releases energy resulting from tight binding by distorting the binding cavity. A third group (D27E, F153S, I94L) arising as single, resistance invoking mutants in evolution experiment trajectories allosterically and dynamically affects a hydrogen bonding motif formed at residues 59-69-71 which in turn modifies the binding site dynamics. The final group (I5F, A26T, R98P) consists of those mutants that have properties most similar to the wild type; these only appear after one of the other mutants is fixed on the protein structure and therefore display clear epistasis. Thus, we show that the binding event is governed by the entire enzyme dynamics while the binding site residues play gating roles. The adjustments made in the total enzyme in response to point mutations are what make quantifying and pinpointing their effect a hard problem. Here, we show that hydrogen bond dynamics recorded on sub-μs time scales provide the necessary fingerprints to decipher the various mechanisms at play.

Probing Methyl Group Dynamics in Proteins by NMR Cross-Correlated Dipolar Relaxation and Molecular Dynamics Simulations

Nuclear magnetic resonance (NMR) spin relaxation is the most informative approach to experimentally probe the internal dynamics of proteins on the picosecond to nanosecond time scale. At the same time, molecular dynamics (MD) simulations of biological macromolecules are steadily improving through better physical models, enhanced sampling methods, and increased computational power, and they provide exquisite information about flexibility and its role in protein stability and molecular interactions. Many examples have shown that MD is now adept in probing protein backbone motion, but improvements are still required toward a quantitative description of the dynamics of side chains, for example, probed by the dynamics of methyl groups. Thus far, the comparison of computation with experiment for side chain dynamics has primarily focused on the relaxation of ¹³C and ²H nuclei induced by autocorrelated variation of spin interactions. However, the cross-correlation of ¹³C-¹H dipolar interactions in methyl groups offers an attractive alternative. Here, we establish a computational framework to extract cross-correlation relaxation parameters of methyl groups in proteins from all-atom MD simulations. To demonstrate the utility of the approach, cross-correlation relaxation rates of ubiquitin are computed from MD simulations performed with the AMBER99SB*-ILDN and CHARMM36 force fields. Simulation results were found to agree well with those obtained by experiment. Moreover, the data obtained with the two force fields are highly consistent.

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.

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.

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.

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 nano-second 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 time-scale 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.

Conformational Dynamics of Intrinsically Disordered Proteins Regulate Biomolecular Condensate Chemistry

Motions in biomolecules are critical for biochemical reactions. In cells, many biochemical reactions are executed inside of biomolecular condensates formed by ultradynamic intrinsically disordered proteins. A deep understanding of the conformational dynamics of intrinsically disordered proteins in biomolecular condensates is therefore of utmost importance but is complicated by diverse obstacles. Here we review emerging data on the motions of intrinsically disordered proteins inside of liquidlike condensates. We discuss how liquid–liquid phase separation modulates internal motions across a wide range of time and length scales. We further highlight the importance of intermolecular interactions that not only drive liquid–liquid phase separation but appear as key determinants for changes in biomolecular motions and the aging of condensates in human diseases. The review provides a framework for future studies to reveal the conformational dynamics of intrinsically disordered proteins in the regulation of biomolecular condensate chemistry.

How Much Entropy Is Contained in NMR Relaxation Parameters?

Solution-state NMR relaxation experiments are the cornerstone to study internal protein dynamics at an atomic resolution on time scales that are faster than the overall rotational tumbling time τ_R. Since the motions described by NMR relaxation parameters are connected to thermodynamic quantities like conformational entropies, the question arises how much of the total entropy is contained within this tumbling time. Using all-atom molecular dynamics simulations of the T4 lysozyme, we found that entropy buildup is rather fast for the backbone, such that the majority of the entropy is indeed contained in the short-time dynamics. In contrast, the contribution of the slow dynamics of side chains on time scales beyond τ_R on the side-chain conformational entropy is significant and should be taken into account for the extraction of accurate thermodynamic properties.

Observation of Sub-Microsecond Protein Methyl-Side Chain Dynamics by Nanoparticle-Assisted NMR Spin Relaxation

Amino-acid side-chain properties in proteins are key determinants of protein function. NMR spin relaxation of side chains is an important source of information about local protein dynamics and flexibility. However, traditional solution NMR relaxation methods are most sensitive to sub-nanosecond dynamics lacking information on slower ns-μs time-scale motions. Nanoparticle-assisted NMR spin relaxation (NASR) of methyl-side chains is introduced here as a window into these ns-μs dynamics. NASR utilizes the transient and nonspecific interactions between folded proteins and slowly tumbling spherical nanoparticles (NPs), whereby the increase of the relaxation rates reflects motions on time scales from ps all the way to the overall tumbling correlation time of the NPs ranging from hundreds of ns to μs. The observed motional amplitude of each methyl group can then be expressed by a model-free NASR S² order parameter. The method is demonstrated for ²H-relaxation of CH₂D methyl moieties and cross-correlated relaxation of CH₃ groups for proteins Im7 and ubiquitin in the presence of anionic silica-nanoparticles. Both types of relaxation experiments, dominated by either quadrupolar or dipolar interactions, yield highly consistent results. Im7 shows additional dynamics on the intermediate time scales taking place in a functionally important loop, whereas ubiquitin visits the majority of its conformational substates on the sub-ns time scale. These experimental observations are in good agreement with 4-10 μs all-atom molecular dynamics trajectories. NASR probes side-chain dynamics on a much wider range of motional time scales than previously possible, thereby providing new insights into the interplay between protein structure, dynamics, and molecular interactions that govern protein function.

Fitting Side-Chain NMR Relaxation Data Using Molecular Simulations

Proteins display a wealth of dynamical motions that can be probed using both experiments and simulations. We present an approach to integrate side-chain NMR relaxation measurements with molecular dynamics simulations to study the structure and dynamics of these motions. The approach, which we term ABSURDer (average block selection using relaxation data with entropy restraints), can be used to find a set of trajectories that are in agreement with relaxation measurements. We apply the method to deuterium relaxation measurements in T4 lysozyme and show how it can be used to integrate the accuracy of the NMR measurements with the molecular models of protein dynamics afforded by the simulations. We show how fitting of dynamic quantities leads to improved agreement with static properties and highlight areas needed for further improvements of the approach.

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.

Methodological advancements for characterising protein side chains by NMR spectroscopy

The surface of proteins is covered by side chains of polar amino acids that are imperative for modulating protein functionality through the formation of noncovalent intermolecular interactions. However, despite their tremendous importance, the unique structures of protein side chains require tailored approaches for investigation by nuclear magnetic resonance spectroscopy and so have traditionally been understudied compared with the protein backbone. Here, we review substantial recent methodological advancements within nuclear magnetic resonance spectroscopy to address this issue. Specifically, we consider advancements that provide new insight into methyl-bearing side chains, show the potential of using non-natural amino acids and reveal the actions of charged side chains. Combined, the new methods promise unprecedented characterisations of side chains that will further elucidate protein function.

Charge-Free, Stabilizing Amide-π Interactions Can Be Used to Control Collagen Triple-Helix Self-Assembly

There is a noted lack of understood, controllable interactions for directing the organization of collagen triple helices. While the field has had success using charge-pair interactions and cation-π interactions in helix design, these alone are not adequate for achieving the degree of specificity desirable for these supramolecular structures. Furthermore, because of the reliance on electrostatic interactions, designed heterotrimeric systems have been heavily charged, a property undesirable in some applications. Amide-π interactions are a comparatively understudied class of charge-free interactions, which could potentially be harnessed for triple-helix design. Herein, we propose, validate, and utilize pairwise amino acid amide-π interactions in collagen triple-helix design. Glutamine-phenylalanine pairs, when arranged in an axial geometry, are found to exhibit a moderately stabilizing effect, while in the lateral geometry, this pair is destabilizing. Together this allows glutamine-phenylalanine pairs to effectively set the register of triple helices. In contrast, interactions between asparagine and phenylalanine appear to have little effect on triple-helical stability. After deconvoluting the contributions of these amino acids to triple-helix stability, we demonstrate these new glutamine-phenylalanine interactions in the successful design of a heterotrimeric triple helix. The results of all of these analyses are used to update our collagen triple-helix thermal stability prediction algorithm, Scoring function for Collagen Emulating Peptides' Temperature of Transition (SCEPTTr).

How to assess the structural dynamics of transcription factors by integrating sparse NMR and EPR constraints with molecular dynamics simulations

We review recent advances in modeling structural ensembles of transcription factors from nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) spectroscopic data, integrated with molecular dynamics (MD) simulations. We focus on approaches that confirm computed conformational ensembles by sparse constraints obtained from magnetic resonance. This combination enables the deduction of functional and structural protein models even if nuclear Overhauser effects (NOEs) are too scarce for conventional structure determination. We highlight recent insights into the folding-upon-DNA binding transitions of intrinsically disordered transcription factors that could be assessed using such integrative approaches.

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.

Relaxometry models compared with Bayesian techniques: ganglioside micelle example

In this work a methodology to perform Bayesian model-comparison is developed and exemplified in the analysis of nuclear magnetic relaxation dispersion (NMRD) experiments of water in a ganglioside micelle system. NMRD is a powerful tool to probe slow dynamics in complex liquids. There are many interesting systems that can be studied with NMRD, such as ionic and lyotropic liquids or electrolytes. However, to progress in the understanding of the studied systems, relatively detailed theoretical NMRD-models are required. To improve the models, they need to be carefully compared, in addition to physico-chemical considerations of molecular and spin dynamics. The comparison is performed by computing the Bayesian evidence in terms of a thermodynamic integral solved with Markov chain Monte Carlo. The result leads to a conclusion of two micelle water-pools, and rules out both less and more parameters, i.e., one and three pools. On the other hand, if only the quality of the fits is considered (i.e., mean square deviation or χ2) a three water-pool model is the best. The latter can be expected since with more adjustable parameters a better fit is more likely. Bayesian evidence is needed to rank the uncertainty of the models, and in order to explain the outcome a notation of Ockham-entropy is defined. The two approximate selection tools, Akaike and Baysian information criterions, may lead to wrong conclusions compared to the full integration. This methodology is expected to be one of several important tools in NMRD model development; however, it is completely general and should find awakened use in many research areas.

Molecular Dynamics Simulations with NAMD2

X-ray diffraction crystallography is the primary technique to determine the three-dimensional structures of biomolecules. Although a robust method, X-ray crystallography is not able to access the dynamical behavior of macromolecules. To do so, we have to carry out molecular dynamics simulations taking as an initial system the three-dimensional structure obtained from experimental techniques or generated using homology modeling. In this chapter, we describe in detail a tutorial to carry out molecular dynamics simulations using the program NAMD2. We chose as a molecular system to simulate the structure of human cyclin-dependent kinase 2.

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.

Structural and dynamic origins of ESR lineshapes in spin-labeled GB1 domain: the insights from spin dynamics simulations based on long MD trajectories

Site-directed spin labeling (SDSL) ESR is a valuable tool to probe protein systems that are not amenable to characterization by x-ray crystallography, NMR or EM. While general principles that govern the shape of SDSL ESR spectra are known, its precise relationship with protein structure and dynamics is still not fully understood. To address this problem, we designed seven variants of GB1 domain bearing R1 spin label and recorded the corresponding MD trajectories (combined length 180 μs). The MD data were subsequently used to calculate time evolution of the relevant spin density matrix and thus predict the ESR spectra. The simulated spectra proved to be in good agreement with the experiment. Further analysis confirmed that the spectral shape primarily reflects the degree of steric confinement of the R1 tag and, for the well-folded protein such as GB1, offers little information on local backbone dynamics. The rotameric preferences of R1 side chain are determined by the type of the secondary structure at the attachment site. The rotameric jumps involving dihedral angles χ1 and χ2 are sufficiently fast to directly influence the ESR lineshapes. However, the jumps involving multiple dihedral angles tend to occur in (anti)correlated manner, causing smaller-than-expected movements of the R1 proxyl ring. Of interest, ESR spectra of GB1 domain with solvent-exposed spin label can be accurately reproduced by means of Redfield theory. In particular, the asymmetric character of the spectra is attributable to Redfield-type cross-correlations. We envisage that the current MD-based, experimentally validated approach should lead to a more definitive, accurate picture of SDSL ESR experiments.

Determining isoleucine side-chain rotamer-sampling in proteins from 13C chemical shift

A framework is presented to derive the conformational sampling of isoleucine side chains from nuclear magnetic resonance ¹³C chemical shifts.

Chemical shifts are often the only nuclear magnetic resonance parameter that can be obtained for challenging macromolecular systems. Here we present a framework to derive the conformational sampling of isoleucine side chains from ¹³C chemical shifts and demonstrate that side-chain conformations in a low-populated folding intermediate can be determined.

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.

Functional protein dynamics on uncharted time scales detected by nanoparticle-assisted NMR spin relaxation

Protein function depends critically on intrinsic internal dynamics, which is manifested in distinct ways, such as loop motions that regulate protein recognition and catalysis. Under physiological conditions, dynamic processes occur on a wide range of time scales from subpicoseconds to seconds. Commonly used NMR spin relaxation in solution provides valuable information on very fast and slow motions but is insensitive to the intermediate nanosecond to microsecond range that exceeds the protein tumbling correlation time. Presently, very little is known about the nature and functional role of these motions. It is demonstrated here how transverse spin relaxation becomes exquisitely sensitive to these motions at atomic resolution when studying proteins in the presence of nanoparticles. Application of this novel cross-disciplinary approach reveals large-scale dynamics of loops involved in functionally critical protein-protein interactions and protein-calcium ion recognition that were previously unobservable.

Reducing bias in the analysis of solution-state NMR data with dynamics detectors

Nuclear magnetic resonance (NMR) is sensitive to dynamics on a wide range of correlation times. Recently, we have shown that analysis of relaxation rates via fitting to a correlation function with a small number of exponential terms could yield a biased characterization of molecular motion in solid-state NMR due to limited sensitivity of experimental data to certain ranges of correlation times. We introduced an alternative approach based on "detectors" in solid-state NMR, for which detector responses characterize motion for a range of correlation times and reduce potential bias resulting from the use of simple models for the motional correlation functions. Here, we show that similar bias can occur in the analysis of solution-state NMR relaxation data. We have thus adapted the detector approach to solution-state NMR, specifically separating overall tumbling motion from internal motions and accounting for contributions of chemical exchange to transverse relaxation. We demonstrate that internal protein motions can be described with detectors when the overall motion and the internal motions are statistically independent. We illustrate the detector analysis on ubiquitin with typical relaxation data sets recorded at a single high magnetic field or at multiple high magnetic fields and compare with results of model-free analysis. We also compare our methodology to LeMaster's method of dynamics analysis.