Rotational Dynamics of Proteins from Spin Relaxation Times and Molecular Dynamics Simulations

Structure-Based Experimental Datasets for Benchmarking Protein Simulation Force Fields [Article v0.1]

This review article provides an overview of structurally oriented experimental datasets that can be used to benchmark protein force fields, focusing on data generated by nuclear magnetic resonance (NMR) spectroscopy and room temperature (RT) protein crystallography. We discuss what the observables are, what they tell us about structure and dynamics, what makes them useful for assessing force field accuracy, and how they can be connected to molecular dynamics simulations carried out using the force field one wishes to benchmark. We also touch on statistical issues that arise when comparing simulations with experiment. We hope this article will be particularly useful to computational researchers and trainees who develop, benchmark, or use protein force fields for molecular simulations.

Hydrogen-bond induced non-linear size dependence of lysozyme under the influence of aqueous glyceline

Natural deep eutectic solvents (NADESs) are environmentally friendly green solvents and hold great promise in the pharmaceutical industry. The secondary structure of a protein, lysozyme, follows a non-monotonous behavior in aqueous glyceline (choline chloride + glycerol) as the wt. % of water is increased. However, it is unclear how the hydration affects the stability of the protein in a non-linear way. In this work, we have performed all-atom molecular dynamic simulations for 1 μs with the lysozyme protein in an aqueous glyceline deep eutectic solvent (DES) by varying the wt. % of water. The simulated radius of gyration, Rg, values can qualitatively reproduce the protein behavior such that the Rg increases initially with an increase in wt. % of water, reaches the peak at 40 wt. %, and then gradually decreases with dilution. Several other properties, including root mean square deviation, root-mean square fluctuation, secondary structure of the protein, and solvent accessible surface area, are examined to explore the NADES effect on the protein structure. Next, we analyze the hydrogen bond profile of intra-protein and among various interspecies, e.g., protein-DES, DES-DES, protein-water, and water-water. The variation in protein-protein hydrogen bonds with concentrations can qualitatively explain the non-linear conformational dependence of the protein. The radial distribution function analyses show various microscopic structures formed due to the DES and water interaction, which play a critical role in protein behavior. This study indicates that at lower wt. % of water, the protein is constrained in a strong hydrogen bond network formed by glycerol and water molecules, resulting in a lower Rg. As the wt. % of water increases, the protein-water interaction drives the protein to expand, reflecting an increasing Rg. At sufficiently higher wt. % of water, the DES constituent and the water molecules interact strongly with the protein, resulting in a decrease in Rg. Overall, the investigation offers a microscopic insight into the protein conformation in DES.

Water Migration through Enzyme Tunnels Is Sensitive to the Choice of Explicit Water Model

The utilization of tunnels and water transport within enzymes is crucial for their catalytic function as water molecules can stabilize bound substrates and help with unbinding processes of products and inhibitors. Since the choice of water models for molecular dynamics simulations was shown to determine the accuracy of various calculated properties of the bulk solvent and solvated proteins, we have investigated if and to what extent water transport through the enzyme tunnels depends on the selection of the water model. Here, we focused on simulating enzymes with various well-defined tunnel geometries. In a systematic investigation using haloalkane dehalogenase as a model system, we focused on the well-established TIP3P, OPC, and TIP4P-Ew water models to explore their impact on the use of tunnels for water molecule transport. The TIP3P water model showed significantly faster migration, resulting in the transport of approximately 2.5 times more water molecules compared to that of the OPC and 1.7 times greater than that of the TIP4P-Ew. Finally, the transport was 1.4-fold more pronounced in TIP4P-Ew than in OPC. The increase in migration of TIP3P water molecules was mainly due to faster transit times through dehalogenase tunnels. We observed similar behavior in two different enzymes with buried active sites and different tunnel network topologies, i.e., alditol oxidase and cytochrome P450, indicating that our findings are likely not restricted to a particular enzyme family. Overall, this study showcases the critical importance of water models in comprehending the use of enzyme tunnels for small molecule transport. Given the significant role of water availability in various stages of the catalytic cycle and the solvation of substrates, products, and drugs, choosing an appropriate water model may be crucial for accurate simulations of complex enzymatic reactions, rational enzyme design, and predicting drug residence times.

Rapid Interpretation of Protein Backbone Rotation Dynamics Directly from Spin Relaxation Data

Besides their structure, dynamics is pivotal for protein functions, particularly for intrinsically disordered proteins (IDPs) that do not fold into a fixed 3D structure. However, the detection of protein dynamics is difficult for IDPs and other disordered biomolecules. NMR spin relaxation rates are sensitive to the rapid rotations of chemical bonds, but their interpretation is arduous for IDPs or molecular assemblies with a complex dynamic landscape. Here we demonstrate numerically that the dynamics of a wide range of proteins, from short peptides to partially disordered proteins and peptides in micelles, can be characterized by calculating the total effective correlation times of protein backbone N-H bond rotations, τeff, from experimentally measured transverse 15N spin relaxation rates, R2, using a linear relation. Our results enable the determination of magnetic-field-independent and intuitively understandable parameters describing protein dynamics at different regions of the sequence directly from experiments. A practical advance of the approach is demonstrated by analyzing partially disordered proteins in which rotations of disordered regions occur with timescales of 1-2 ns, independent of their size, suggesting that rotations of disordered and folded regions are uncoupled in these proteins.

Field-domain rapid-scan EPR at 240GHz for studies of protein functional dynamics at room temperature

We present field-domain rapid-scan (RS) electron paramagnetic resonance (EPR) at 8.6T and 240GHz. To enable this technique, we upgraded a home-built EPR spectrometer with an FPGA-enabled digitizer and real-time processing software. The software leverages the Hilbert transform to recover the in-phase (I) and quadrature (Q) channels, and therefore the raw absorptive and dispersive signals, χ' and χ'', from their combined magnitude (I2+Q2). Averaging a magnitude is simpler than real-time coherent averaging and has the added benefit of permitting long-timescale signal averaging (up to at least 2.5×106 scans) because it eliminates the effects of source-receiver phase drift. Our rapid-scan (RS) EPR provides a signal-to-noise ratio that is approximately twice that of continuous wave (CW) EPR under the same experimental conditions, after scaling by the square root of acquisition time. We apply our RS EPR as an extension of the recently reported time-resolved Gd-Gd EPR (TiGGER) [Maity et al., 2023], which is able to monitor inter-residue distance changes during the photocycle of a photoresponsive protein through changes in the Gd-Gd dipolar couplings. RS, opposed to CW, returns field-swept spectra as a function of time with 10ms time resolution, and thus, adds a second dimension to the static field transients recorded by TiGGER. We were able to use RS TiGGER to track time-dependent and temperature-dependent kinetics of AsLOV2, a light-activated phototropin domain found in oats. The results presented here combine the benefits of RS EPR with the improved spectral resolution and sensitivity of Gd chelates at high magnetic fields. In the future, field-domain RS EPR at high magnetic fields may enable studies of other real-time kinetic processes with time resolutions that are otherwise difficult to access in the solution state.

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.

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.

Probing the dynamic landscape of peptides in molecular assemblies by synergized NMR experiments and MD simulations

Peptides or proteins containing small biomolecular aggregates, such as micelles, bicelles, droplets and nanodiscs, are pivotal in many fields ranging from structural biology to pharmaceutics. Monitoring dynamics of such systems has been limited by the lack of experimental methods that could directly detect their fast (picosecond to nanosecond) timescale dynamics. Spin relaxation times from NMR experiments are sensitive to such motions, but their interpretation for biomolecular aggregates is not straightforward. Here we show that the dynamic landscape of peptide-containing molecular assemblies can be determined by a synergistic combination of solution state NMR experiments and molecular dynamics (MD) simulations. Solution state NMR experiments are straightforward to implement without an excessive amount of sample, while direct combination of spin relaxation data to MD simulations enables interpretation of dynamic landscapes of peptides and other aggregated molecules. To demonstrate this, we interpret NMR data from transmembrane, peripheral, and tail anchored peptides embedded in micelles. Our results indicate that peptides and detergent molecules do not rotate together as a rigid body, but peptides rotate in a viscous medium composed of detergent micelle. Spin relaxation times also provide indirect information on peptide conformational ensembles. This work gives new perspectives on peptide dynamics in complex biomolecular assemblies.

Additively manufactured, solid object structures for adjustable image contrast in Magnetic Resonance Imaging

The choice of materials challenges the development of Magnetic Resonance Imaging (MRI) phantoms and, to date, is mainly limited to water-filled compartments or gel-based components. Recently, solid materials have been introduced through additive manufacturing (AM) to mimic complex geometrical structures. Nonetheless, no such manufactured solid materials are available with controllable MRI contrast to mimic organ substructures or lesion heterogeneities. Here, we present a novel AM design that allows MRI contrast manipulation by varying the partial volume contribution to a ROI/voxel of MRI-visible material within an imaging object. Two sets of 11 cubes and three replicates of a spherical tumour model were designed and printed using AM. Most samples presented varying MRI-contrast in standard MRI sequences, based mainly on spin density and partial volume signal variation. A smooth and continuous MRI-contrast gradient could be generated in a single-compartment tumour model. This concept supports the development of more complex MRI phantoms that mimic the appearance of heterogeneous tumour tissues.

Accurate Simulations of Lipid Monolayers Require a Water Model with Correct Surface Tension

Lipid monolayers provide our lungs and eyes their functionality and serve as proxy systems in biomembrane research. Therefore, lipid monolayers have been studied intensively including using molecular dynamics simulations, which are able to probe their lateral structure and interactions with, e.g., pharmaceuticals or nanoparticles. However, such simulations have struggled in describing the forces at the air-water interface. Particularly, the surface tension of water and long-range van der Waals interactions have been considered critical, but their importance in monolayer simulations has been evaluated only separately. Here, we combine the recent C36/LJ-PME lipid force field that includes long-range van der Waals forces with water models that reproduce experimental surface tensions to elucidate the importance of these contributions in monolayer simulations. Our results suggest that a water model with correct surface tension is necessary to reproduce experimental surface pressure-area isotherms and monolayer phase behavior. The latter includes the liquid expanded and liquid condensed phases, their coexistence, and the opening of pores at the correct area per lipid upon expansion. Despite these improvements of the C36/LJ-PME with certain water models, the standard cutoff-based CHARMM36 lipid model with the 4-point OPC water model still provides the best agreement with experiments. Our results emphasize the importance of using high-quality water models in applications and parameter development in molecular dynamics simulations of biomolecules.

Bootstrap Aggregation for Model Selection in the Model-free Formalism

The ability to make robust inferences about the dynamics of biological macromolecules using NMR spectroscopy depends heavily on the application of appropriate theoretical models for nuclear spin relaxation. Data analysis for NMR laboratory-frame relaxation experiments typically involves selecting one of several model-free spectral density functions using a bias-corrected fitness test. Here, advances in statistical model selection theory, termed bootstrap aggregation or bagging, are applied to ¹⁵N spin relaxation data, developing a multimodel inference solution to the model-free selection problem. The approach is illustrated using data sets recorded at four static magnetic fields for the bZip domain of the S. cerevisiae transcription factor GCN4.

Ferreira T, Ollila OHS, Miettinen MS. Using Open Data to Rapidly Benchmark Biomolecular Simulations: Phospholipid Conformational Dynamics

Molecular dynamics (MD) simulations are widely used to monitor time-resolved motions of biomacromolecules, although it often remains unknown how closely the conformational dynamics correspond to those occurring in real life. Here, we used a large set of open-access MD trajectories of phosphatidylcholine (PC) lipid bilayers to benchmark the conformational dynamics in several contemporary MD models (force fields) against nuclear magnetic resonance (NMR) data available in the literature: effective correlation times and spin-lattice relaxation rates. We found none of the tested MD models to fully reproduce the conformational dynamics. That said, the dynamics in CHARMM36 and Slipids are more realistic than in the Amber Lipid14, OPLS-based MacRog, and GROMOS-based Berger force fields, whose sampling of the glycerol backbone conformations is too slow. The performance of CHARMM36 persists when cholesterol is added to the bilayer, and when the hydration level is reduced. However, for conformational dynamics of the PC headgroup, both with and without cholesterol, Slipids provides the most realistic description because CHARMM36 overestimates the relative weight of ∼1 ns processes in the headgroup dynamics. We stress that not a single new simulation was run for the present work. This demonstrates the worth of open-access MD trajectory databanks for the indispensable step of any serious MD study: benchmarking the available force fields. We believe this proof of principle will inspire other novel applications of MD trajectory databanks and thus aid in developing biomolecular MD simulations into a true computational microscope-not only for lipid membranes but for all biomacromolecular systems.

Heterogeneous dynamics in partially disordered proteins

Importance of disordered protein regions is increasingly recognized in biology, but their characterization remains challenging due to the lack of suitable experimental and theoretical methods. NMR experiments can detect multiple timescale dynamics and structural details of disordered protein regions, but their detailed interpretation is often difficult. Here we combine protein backbone 15N spin relaxation data with molecular dynamics (MD) simulations to detect not only heterogeneous dynamics of large partially disordered proteins but also their conformational ensembles. We observed that the rotational dynamics of folded regions in partially disordered proteins is dominated by similar rigid body rotation as in globular proteins, thereby being largely independent of flexible disordered linkers. Disordered regions, on the other hand, exhibit complex rotational motions with multiple timescales below ∼30 ns which are difficult to detect from experimental data alone, but can be captured by MD simulations. Combining MD simulations and backbone 15N spin relaxation data, measured applying segmental isotopic labeling with salt-inducible split intein, we resolved the conformational ensemble and dynamics of partially disordered periplasmic domain of TonB protein from Helicobacter pylori containing 250 residues. To demonstrate the universality of our approach, it was applied also to the partially disordered region of chicken Engrailed 2. Our results pave the way in understanding how TonB transfers energy from inner membrane to the outer membrane receptors in Gram-negative bacteria, as well as the function of other proteins with disordered domains.

NMR Studies of Bicontinuous Liquid Crystalline Phases of Cubic Symmetry: Interpretation of Frequency-Dependent Relaxation Rates

Extensive deuterium NMR relaxation data are presented for two specifically deuterium labeled surfactants forming bicontinuous cubic phases with water. ²H spin-lattice (R₁) and spin-spin (R₂) relaxation rates were measured over an extended frequency range from 2 to 60 MHz. The data are interpreted with an existing theoretical framework for spin relaxation in bicontinuous cubic phases, which takes its starting point in the description of bicontinuous phases using periodic minimal surfaces. We show that the theory succeeds in accounting for the data and that the defining parameters of the theory, correlation times and order parameters, are in agreement with related data in other surfactant phase situations. Specifically, we obtain the surfactant self-diffusion coefficient over the minimal surface in one unit cell and show that it is in agreement with the corresponding macroscopic NMR diffusion data. By measuring two additional NMR relaxation parameters for each carbon on the surfactant hydrocarbon tail, we demonstrate how order parameter and correlation time profiles can be obtained. Finally, we analyze published molecular dynamics trajectories for a bicontinuous cubic phase. The analysis provides further support for the theoretical framework used to interpret relaxation data.

Orientational Switch of the Lipase A Enzyme at the Oil-Water Interface: An Order of Magnitude Increase in Turnover Rate with a Single Surfactant Tag Explained

Interfacially active lipases can be immobilized at a biphasic interface to enhance turnover recyclability and to facilitate product separation. Extensive coarse-grained molecular dynamics simulations of lipase A (LipA) from Bacillus subtilis show a bimodal orientational distribution of the enzyme at an oil-water interface, arising from its ellipsoidal Janus particle-like character. The relative orientational preference can be tuned by pH. The simulations rationalize a rare experimental observation of an order of magnitude increase in the turnover rate of this lipase upon its noncovalent tagging by a single surfactant molecule at the interface, compared to its rate in bulk water. The adsorption free energy, the interfacial activation, a decrease in the number of orientational fluctuations, and an increased rate of translational diffusion, to all of which the Janus character of LipA contributes, are the factors responsible for this enhancement. This study can spur further investigations of the Janus behavior of enzymes to enhance their activity as well as to stabilize the biphasic emulsion needed for interfacial catalysis.

Rotational Diffusion of Membrane Proteins in Crowded Membranes

Membrane proteins travel along cellular membranes and reorient themselves to form functional oligomers and protein-lipid complexes. Following the Saffman-Delbrück model, protein radius sets the rate of this diffusive motion. However, it is unclear how this model, derived for ideal and dilute membranes, performs under crowded conditions of cellular membranes. Here, we study the rotational motion of membrane proteins using molecular dynamics simulations of coarse-grained membranes and 2-dimensional Lennard-Jones fluids with varying levels of crowding. We find that the Saffman-Delbrück model captures the size-dependency of rotational diffusion under dilute conditions where protein-protein interactions are negligible, whereas stronger scaling laws arise under crowding. Together with our recent work on lateral diffusion, our results reshape the description of protein dynamics in native membrane environments: The translational and rotational motions of proteins with small transmembrane domains are rapid, whereas larger proteins or protein complexes display substantially slower dynamics.

NMR Structure and Dynamics of TonB Investigated by Scar-Less Segmental Isotopic Labeling Using a Salt-Inducible Split Intein

The growing understanding of partially unfolded proteins increasingly points to their biological relevance in allosteric regulation, complex formation, and protein design. However, the structural characterization of disordered proteins remains challenging. NMR methods can access both the dynamics and structures of such proteins, yet suffering from a high degeneracy of NMR signals. Here, we overcame this bottleneck utilizing a salt-inducible split intein to produce segmentally isotope-labeled samples with the native sequence, including the ligation junction. With this technique, we investigated the NMR structure and conformational dynamics of TonB from Helicobacter pylori in the presence of a proline-rich low complexity region. Spin relaxation experiments suggest that the several nano-second time scale dynamics of the C-terminal domain (CTD) is almost independent of the faster pico-to-nanosecond dynamics of the low complexity central region (LCCR). Our results demonstrate the utility of segmental isotopic labeling for proteins with heterogenous dynamics such as TonB and could advance NMR studies of other partially unfolded proteins.

Structure and Dynamics of Spherical and Rodlike Alkyl Ethoxylate Surfactant Micelles Investigated Using NMR Relaxation and Atomistic Molecular Dynamics Simulations

Predicting and controlling the properties of amphiphile aggregate mixtures require understanding the arrangements and dynamics of the constituent molecules. To explore these topics, we study molecular arrangements and dynamics in alkyl ethoxylate nonionic surfactant micelles by combining NMR relaxation measurements with large-scale atomistic molecular dynamics simulations. We calculate parameters that determine relaxation rates directly from simulated trajectories, without introducing specific functional forms to describe the dynamics. NMR relaxation rates, which depend on relative motions of interacting atom pairs, are influenced by wide distributions of dynamic time scales. We find that relative motions of neighboring atom pairs are rapid and liquidlike but are subject to structural constraints imposed by micelle morphology. Relative motions of distant atom pairs are slower than nearby atom pairs because changes in distances and angles are smaller when the moving atoms are further apart. Large numbers of atom pairs undergoing these slow relative motions contribute to predominantly negative cross-relaxation rates. For spherical micelles, but not for cylindrical micelles, cross-relaxation rates are positive only for surfactant tail atoms connected to the hydrophilic headgroup. This effect is related to the lower packing density of these atoms at the hydrophilic-hydrophobic boundary in spherical vs cylindrical arrangements, with correspondingly rapid and less constrained motion of atoms at the boundary.

Side-Chain Dynamics of the Trifluoroacetone Cysteine Derivative Characterized by 19F NMR Relaxation and Molecular Dynamics Simulations

¹⁹F NMR spectroscopy is a powerful tool for the study of the structures, dynamics, and interactions of proteins bearing cysteine residues chemically modified with a trifluoroacetone group (CYF residue). ¹⁹F NMR relaxation rates for the fluoromethyl group of CYF residues are sensitive to overall rotational tumbling of proteins, fast rotation about the CF₃ methyl axis, and the internal motion of the CYF side-chain. To develop a quantitative understanding of these various motional contributions, we used the model-free approach to extend expressions for ¹⁹F- T₂ NMR relaxation to include side-chain motions for the CYF residue. We complemented the NMR studies with atomic views of methyl rotation and side-chain motions using molecular dynamics simulations. This combined methodology allows for quantitative separation of the contributions of fast pico- to nanosecond dynamics from micro- to millisecond exchange processes to the ¹⁹F line width and highlights the utility of the CYF residue as a sensitive reporter of side-chain environment and dynamics in proteins.

NMR structure of the C-terminal domain of TonB protein from Pseudomonas aeruginosa

The TonB protein plays an essential role in the energy transduction system to drive active transport across the outer membrane (OM) using the proton-motive force of the cytoplasmic membrane of Gram-negative bacteria. The C-terminal domain (CTD) of TonB protein is known to interact with the conserved TonB box motif of TonB-dependent OM transporters, which likely induces structural changes in the OM transporters. Several distinct conformations of differently dissected CTDs of Escherichia coli TonB have been previously reported. Here we determined the solution NMR structure of a 96-residue fragment of Pseudomonas aeruginosa TonB (PaTonB-96). The structure shows a monomeric structure with the flexible C-terminal region (residues 338-342), different from the NMR structure of E. coli TonB (EcTonB-137). The extended and flexible C-terminal residues are confirmed by 15N relaxation analysis and molecular dynamics simulation. We created models for the PaTonB-96/TonB box interaction and propose that the internal fluctuations of PaTonB-96 makes it more accessible for the interactions with the TonB box and possibly plays a role in disrupting the plug domain of the TonB-dependent OM transporters.

Narrowing the gap between experimental and computational determination of methyl group dynamics in proteins

A synergistic analysis of methyl NMR relaxation data and MD simulations identifies ways to improve studies of protein dynamics.