Predicting NMR relaxation of proteins from molecular dynamics simulations with accurate methyl rotation barriers

A Combined Approach to Extract Rotational Dynamics of Globular Proteins Undergoing Liquid-Liquid Phase Separation

The formation of protein condensates (droplets) via liquid-liquid phase separation (LLPS) is a commonly observed phenomenon in vitro. Changing the environmental properties with cosolutes, molecular crowders, protein partners, temperature, pressure, etc. has been shown to favor or disfavor the formation of protein droplets by fine-tuning the water-water, water-protein, and protein-protein interactions. Therefore, these environmental properties and their spatiotemporal fine-tuning are likely to be important also in a cellular context at the existing protein expression levels. One of the key physicochemical properties of biomolecules impacted by molecular crowding is diffusion, which determines the viscoelastic behavior of the condensates. Here, we investigate the change in the rotational diffusion of γD-crystallin, undergoing LLPS in vitro in aqueous solutions in the absence and presence of cosolutes. We studied its rotational dynamics using molecular dynamics simulations (MD), electron paramagnetic resonance (EPR) spectroscopy, and fluorescence spectroscopy. MD simulations performed under dilute and crowded conditions show that the rotational diffusion of crystallin in water is retarded by 1 to 2 orders of magnitude in the condensed phase. To obtain the rotational dynamics in the dilute phase, we used fluorescence anisotropy and to extract the retardation factor in the condensed phase, we used spin-labeled γD-crystallin proteins as EPR viscosity nanoprobes. Aided by a viscosity nanoruler calibrated with solutions at increasing sucrose concentrations, we validated the rotational diffusion retardation predicted by MD simulations. This study underlines the predictive power of MD simulations and showcases the use of a sensitive EPR nanoprobe to extract the viscosity of biomolecular condensates.

The contribution of methyl groups to electron spin decoherence of nitroxides in glassy matrices

Long electron spin coherence lifetimes are crucial for high sensitivity and resolution in many pulse electron paramagnetic resonance (EPR) experiments aimed at measuring hyperfine and dipolar couplings, as well as in potential quantum sensing applications of molecular spin qubits. In immobilized systems, methyl groups contribute significantly to electron spin decoherence as a result of methyl torsional quantum tunneling. We examine the electron spin decoherence dynamics of the nitroxide radical 2,2,6,6-tetramethylpiperidin-1-oxyl (TEMPO) in both a methyl-free solvent and a methyl-containing solvent at cryogenic temperature. We model nitroxide and solvent methyl effects on decoherence using cluster correlation expansion (CCE) simulations extended to include methyl tunneling and compare the calculations to experimental data. We show that by using the methyl tunneling frequency as a fit parameter, experimental Hahn echo decays can be reproduced fairly well, allowing structural properties to be investigated in silico. In addition, we examine the Hahn echo of a hypothetical system with an unpaired electron and a single methyl to determine the effect of geometric configuration on methyl-driven electron spin decoherence. The simulations show that a methyl group contributes the most to electron spin decoherence if it is located between 2.5 and 6-7 Å from the electron spin, with its orientation being of secondary importance.

Investigating the effects of cysteine-118 oxidation on G12D KRas structure and dynamics: insights from MD simulations

Mutations of Ras proteins are believed to be among the most prominent causes of cancer. There is increasing evidence that the activity of Ras may be controlled by the redox state of cysteine residues located within the NKCD motif. This redox signaling is critical to both physiological and pathological processes and occurs when C118 is oxidized in a reversible manner. In this study, we used atomistic molecular dynamics simulations and Markov state models to investigate the structural and conformational effects of C118 oxidation on the oncogenic mutant KRas(G12D). While both mutants share common features and exhibit some distinct conformational states and fluctuations, we have found that the oxidized variant KRas(G12D/C118SOH) is more dynamic than the unoxidized counterpart, particularly in the switch II region. Additionally, C118 oxidation is found to alter the structure of the nucleotide-binding site and the switch regions as well as perturb the conformational equilibrium between Ras active and inactive states. These conformational preferences may alter the affinity to different effectors, resulting in selective downstream activation. Our results are anticipated to help future drug development efforts aimed at KRAS-related anticancer treatment.Communicated by Ramaswamy H. Sarma.

Molecular dynamics simulation of the effect of temperature on the conformation of ubiquitin protein

CONTENT

Ubiquitin, a ubiquitous small protein found in all living organisms, is crucial for tagging proteins earmarked for degradation and holds pivotal importance in biomedicine. Protein functionality is intricately linked to its structure. To comprehend the impact of diverse temperatures on ubiquitin protein structure, our study delved into the energy landscape, hydrogen bonding, and overall structural stability of ubiquitin protein at varying temperatures. Through meticulous analysis of root mean square deviation and root mean square fluctuation, we validated the robustness of the simulation conditions employed. Within our simulated system, the bonding energy and electrostatic potential energy exhibited linear augmentation, while the van der Waals energy demonstrated a linear decline. Additionally, our findings highlighted that the α-Helix secondary structure of the ubiquitin protein gradually transitions toward helix destabilization under high-temperature conditions. The secondary structure of ubiquitin protein experiences distinct changes under varying temperatures. The outcomes of our molecular simulations offer a theoretical framework that enhances our comprehension of how temperature impacts the structural stability of ubiquitin protein. These insights contribute not only to a deeper understanding of iniquity's behavior but also hold broader implications in the realm of biomedicine and beyond.

METHODS

All the MD simulations were performed using the GROMACS software with GROMOS96 force field and SPC for water. The ubiquitin protein was put in the center of a cubic box with a length of 8 nm, a setting that allowed > 0.8 nm in the minimal distance between the protein surface and the box wall. To remove the possible coordinate collision of the configurations, in the beginning, the steepest descent method was used until the maximum force between atoms was under 100 kJ/mol·nm with a 0.01 nm step size. Minimization was followed by 30 ps of position-restrained MD simulation. The protein was restrained to its initial position, and the solvent was freely equilibrated. The product phase was obtained with the whole system simulated for 10 ns without any restraint using an integral time step of 1 fs with different temperatures. The cutoff for short-range electronic interaction was set to 1.5 nm. The long-range interactions were treated with a particle-mesh Ewald (PME) method with a grid width of 1.2 nm.

Microsecond Timescale Conformational Dynamics of a Small-Molecule Ligand within the Active Site of a Protein

The possible internal dynamics of non-isotope-labeled small-molecule ligands inside a target protein is inherently difficult to capture. Whereas high crystallographic temperature factors can denote either static disorder or motion, even moieties with very low B-factors can be subject to vivid motion between symmetry-related sites. Here we report the experimental identification of internal μs timescale dynamics of a high-affinity, natural-abundance ligand tightly bound to the enzyme human carbonic anhydrase II (hCAII) even within a crystalline lattice. The rotamer jumps of the ligand's benzene group manifest themselves both, in solution and fast magic-angle spinning solid-state NMR 1 H R1ρ relaxation dispersion, for which we obtain further mechanistic insights from molecular-dynamics (MD) simulations. The experimental confirmation of rotameric jumps in bound ligands within proteins in solution or the crystalline state may improve understanding of host-guest interactions in biology and supra-molecular chemistry and may facilitate medicinal chemistry for future drug campaigns.

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.

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.

Nonequilibrium Modeling of the Elementary Step in PDZ3 Allosteric Communication

While allostery is of paramount importance for protein signaling and regulation, the underlying dynamical process of allosteric communication is not well understood. The PDZ3 domain represents a prime example of an allosteric single-domain protein, as it features a well-established long-range coupling between the C-terminal α₃-helix and ligand binding. In an intriguing experiment, Hamm and co-workers employed photoswitching of the α₃-helix to initiate a conformational change of PDZ3 that propagates from the C-terminus to the bound ligand within 200 ns. Performing extensive nonequilibrium molecular dynamics simulations, the modeling of the experiment reproduces the measured time scales and reveals a detailed picture of the allosteric communication in PDZ3. In particular, a correlation analysis identifies a network of contacts connecting the α₃-helix and the core of the protein, which move in a concerted manner. Representing a one-step process and involving direct α₃-ligand contacts, this cooperative transition is considered as the elementary step in the propagation of conformational change.

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.

Development and Validation of Fluorinated, Aromatic Amino Acid Parameters for Use with the AMBER ff15ipq Protein Force Field

We developed force field parameters for fluorinated, aromatic amino acids enabling molecular dynamics (MD) simulations of fluorinated proteins. These parameters are tailored to the AMBER ff15ipq protein force field and enable the modeling of 4, 5, 6, and 7F-tryptophan, 3F- and 3,5F-tyrosine, and 4F- or 4-CF3-phenylalanine. The parameters include 181 unique atomic charges derived using the implicitly polarized charge (IPolQ) scheme in the presence of SPC/Eb explicit water molecules and 9 unique bond, angle, or torsion terms. Our simulations of benchmark peptides and proteins maintain expected conformational propensities on the μs time scale. In addition, we have developed an open-source Python program to calculate fluorine relaxation rates from MD simulations. The extracted relaxation rates from protein simulations are in good agreement with experimental values determined by 19F NMR. Collectively, our results illustrate the power and robustness of the IPolQ lineage of force fields for modeling the structure and dynamics of fluorine-containing proteins at the atomic level.

Double Mutant of Chymotrypsin Inhibitor 2 Stabilized through Increased Conformational Entropy

The conformational heterogeneity of a folded protein can affect not only its function but also stability and folding. We recently discovered and characterized a stabilized double mutant (L49I/I57V) of the protein CI2 and showed that state-of-the-art prediction methods could not predict the increased stability relative to the wild-type protein. Here, we have examined whether changed native-state dynamics, and resulting entropy changes, can explain the stability changes in the double mutant protein, as well as the two single mutant forms. We have combined NMR relaxation measurements of the ps-ns dynamics of amide groups in the backbone and the methyl groups in the side chains with molecular dynamics simulations to quantify the native-state dynamics. The NMR experiments reveal that the mutations have different effects on the conformational flexibility of CI2: a reduction in conformational dynamics (and entropy estimated from this) of the native state of the L49I variant correlates with its decreased stability, while increased dynamics of the I57V and L49I/I57V variants correlates with their increased stability. These findings suggest that explicitly accounting for changes in native-state entropy might be needed to improve the predictions of the effect of mutations on protein stability.

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.

Using molecular dynamics trajectories to predict nuclear spin relaxation behaviour in large spin systems

Molecular dynamics (MD) trajectories provide useful insights into molecular structure and dynamics. However, questions persist about the quantitative accuracy of those insights. Experimental NMR spin relaxation rates can be used as tests, but only if relaxation superoperators can be efficiently computed from MD trajectories - no mean feat for the quantum Liouville space formalism where matrix dimensions quadruple with each added spin 1/2. Here we report a module for the Spinach software framework that computes Bloch-Redfield-Wangsness relaxation superoperators (including non-secular terms and cross-correlations) from MD trajectories. Predicted initial slopes of nuclear Overhauser effects for sucrose trajectories using advanced water models and a force field optimised for glycans are within 25% of experimental values.

SRLS Analysis of 15N-1H NMR Relaxation from the Protein S100A1: Dynamic Structure, Calcium Binding, and Related Changes in Conformational Entropy

We report on amide (N-H) NMR relaxation from the protein S100A1 analyzed with the slowly relaxing local structure (SRLS) approach. S100A1 comprises two calcium-binding "EF-hands" (helix-loop-helix motifs) connected by a linker. The dynamic structure of this protein, in both calcium-free and calcium-bound form, is described as the restricted local N-H motion coupled to isotropic protein tumbling. The restrictions are given by a rhombic potential, u (∼10 kT), the local motion by a diffusion tensor with rate constant D₂ (∼10⁹ s^-1), and principal axis tilted from the N-H bond at angle β (10-20°). This parameter combination provides a physically insightful picture of the dynamic structure of S100A1 from the N-H bond perspective. Calcium binding primarily affects the C-terminal EF-hand, among others slowing down the motion of helices III and IV approximately 10-fold. Overall, it brings about significant changes in the shape of the local potential, u, and the orientation of the local diffusion axis, β. Conformational entropy derived from u makes an unfavorable entropic contribution to the free energy of calcium binding estimated at 8.6 ± 0.5 kJ/mol. The N-terminal EF-hand undergoes moderate changes. These findings provide new insights into the calcium-binding process. The same data were analyzed previously with the extended model-free (EMF) method, which is a simple limit of SRLS. In that interpretation, the protein tumbles anisotropically. Locally, calcium binding increases ordering in the loops of S100A1 and conformational exchange (R_ex) in the helices of its N-terminal EF-hand. These are very unusual features. We show that they most likely stem from problematic data-fitting, oversimplifications inherent in EMF, and experimental imperfections. R_ex is shown to be mainly a fit parameter. By reanalyzing the experimental data with SRLS, which is largely free of these deficiencies, we obtain-as delineated above-physically-relevant structural, kinetic, geometric, and binding information.

A twist in the road less traveled: The AMBER ff15ipq-m force field for protein mimetics

We present a new force field, AMBER ff15ipq-m, for simulations of protein mimetics in applications from therapeutics to biomaterials. This force field is an expansion of the AMBER ff15ipq force field that was developed for canonical proteins and enables the modeling of four classes of artificial backbone units that are commonly used alongside natural α residues in blended or "heterogeneous" backbones: chirality-reversed D-α-residues, the Cα-methylated α-residue Aib, homologated β-residues (β3) bearing proteinogenic side chains, and two cyclic β residues (βcyc; APC and ACPC). The ff15ipq-m force field includes 472 unique atomic charges and 148 unique torsion terms. Consistent with the AMBER IPolQ lineage of force fields, the charges were derived using the Implicitly Polarized Charge (IPolQ) scheme in the presence of explicit solvent. To our knowledge, no general force field reported to date models the combination of artificial building blocks examined here. In addition, we have derived Karplus coefficients for the calculation of backbone amide J-coupling constants for β3Ala and ACPC β residues. The AMBER ff15ipq-m force field reproduces experimentally observed J-coupling constants in simple tetrapeptides and maintains the expected conformational propensities in reported structures of proteins/peptides containing the artificial building blocks of interest-all on the μs timescale. These encouraging results demonstrate the power and robustness of the IPolQ lineage of force fields in modeling the structure and dynamics of natural proteins as well as mimetics with protein-inspired artificial backbones in atomic detail.

NMR techniques in studying water in biotechnological systems

Different NMR methodologies have been considered in studying water as a part of the structure of heterogeneous biosystems. The current work mostly describes NMR techniques to investigate slow translational dynamics of molecules affecting anisotropic properties of polymers and biomaterials. With these approaches, information about organized structures and their stability could be obtained in conditions when external factors affect biomolecules. Such changes might include rearrangement of macromolecular conformations at fabrication of nano-scaffolds for tissue engineering applications. The changes in water-fiber interactions could be mirrored by the magnetic resonance methods in various relaxations, double-quantum filtered (DQF), 1D and 2D translational diffusion experiments. These findings effectively demonstrate the current state of NMR studies in applying these experiments to the various systems with the anisotropic properties. For fibrous materials, it is shown how NMR correlation experiments with two gradients (orthogonal or collinear) encode diffusion coefficients in anisotropic materials and how to estimate the permeability of cell walls. It is considered how the DQF NMR technique discovers anisotropic water in natural polymers with various cross-links. The findings clarify hydration sites, dynamic properties, and binding of macromolecules discovering the role of specific states in improving scaffold characteristics in tissue engineering processes. Showing the results in developing these NMR tools, this review focuses on the ways of extracting information about biophysical properties of biomaterials from the NMR data obtained.

13C NMR Relaxation Analysis of Protein GB3 for the Assessment of Side Chain Dynamics Predictions by Current AMBER and CHARMM Force Fields

Molecular simulations with seven current AMBER- and CHARMM-based force fields yield markedly differing internal bond vector autocorrelation function predictions for many of the 223 methine and methylene H-C bonds of the 56-residue protein GB3. To enable quantification of accuracy, ¹³C R₁, R₂, and heteronuclear NOE relaxation rates have been determined for the methine and stereochemically assigned methylene C^α and C^β positions. With only three experimental relaxation values for each bond vector, central to this analysis is the accuracy with which MD-derived autocorrelation curves can be represented by a 3-parameter equation which, in turn, maps onto the NMR relaxation values. In contrast to the more widely used extended Lipari-Szabo order parameter representation, 95% of these MD-derived internal autocorrelation curves for GB3 can be fitted to within 1.0% rmsd over the time frame from 30 ps to 4 ns by a biexponential Larmor frequency-selective representation (LF-S²). Applying the LF-S² representation to the experimental relaxation rates and uncertainties serves to determine the boundary range for the autocorrelation function of each bond vector consistent with the experimental data. Not surprisingly, all seven force fields predict the autocorrelation functions for the more motionally restricted ¹H^α-¹³C^α and ¹H^β-¹³C^β bond vectors with reasonable accuracy. However, for the ¹H^β-¹³C^β bond vectors exhibiting aggregate order parameter S² values less than 0.85, only 1% of the MD-derived predictions lie with 1 σ of the experimentally determined autocorrelation functions and only 7% within 2 σ. On the other hand, substantial residue type-specific improvements in predictive performance were observed among the recent AMBER force fields. This analysis indicates considerable potential for the use of ¹³C relaxation measurements in guiding the optimization of the side chain dynamics characteristics of protein molecular simulations.