A general approach for prediction of motional EPR spectra from Molecular Dynamics (MD) simulations: application to spin labelled protein

Predicting and interpreting EPR spectra of POPC lipid bilayers with transmembrane α-helical peptides from all-atom molecular dynamics simulations

This study reports a large-scale all-atom MD simulation of POPC lipid bilayers in the presence of different concentrations of the transmembrane peptide acetyl-K2(LA)12K2-amide ((LA)12) and doped with 5-PC paramagnetic spin probes used in EPR studies. We apply a combined MD-EPR simulation methodology for the prediction of EPR spectra directly and completely from MD trajectories. This approach serves three major purposes. Firstly, comparing predicted EPR spectra with experimental ones, which are highly sensitive to motions, provides an ultimate test bed for the force fields currently employed for modeling lipid bilayer systems with embedded proteins or peptides. Secondly, simulations of EPR spectra directly from the atomistic MD models simplify the interpretation of the EPR line shapes and their changes induced by the presence of peptides in the lipid bilayer. These changes are directly linked to the dynamics and order of spin probes and POPC host molecules. Lastly and importantly, we demonstrate how the MD-EPR methodology can be employed to test the validity and limitations of the widely used approach for the estimation of the order parameter of lipids directly from the EPR experimental line shapes.

Unravelling Guest Dynamics in Crystalline Molecular Organics Using 2H Solid-State NMR and Molecular Dynamics Simulation

2H solid-state NMR and atomistic molecular dynamics (MD) simulations are used to understand the disorder of guest solvent molecules in two cocrystal solvates of the pharmaceutical furosemide. Traditional approaches to interpreting the NMR data fail to provide a coherent model of molecular behavior and indeed give misleading kinetic data. In contrast, the direct prediction of the NMR properties from MD simulation trajectories allows the NMR data to be correctly interpreted in terms of combined jump-type and libration-type motions. Time-independent component analysis of the MD trajectories provides additional insights, particularly for motions that are invisible to NMR. This allows a coherent picture of the dynamics of molecules restricted in molecular-sized cavities to be determined.

The 'hidden side' of spin labelled oligonucleotides: Molecular dynamics study focusing on the EPR-silent components of base pairing

Nitroxide labels are combined with nucleic acid structures and are studied using electron paramagnetic resonance experiments (EPR). As X-ray/NMR structures are unavailable with the nitroxide labels, detailed residue level information, down to atomic resolution, about the effect of these nitroxide labels on local RNA structures is currently lacking. This information is critical to evaluate the choice of spin label. In this study, we compare and contrast the effect of TEMPO-based (N^T) and rigid spin (Ç) labels (in both 2'-O methylated and not-methylated forms) on RNA duplexes. We also investigate sequence- dependent effects of N^T label on RNA duplex along with the more complex G-quadruplex RNA. Distances measured from molecular dynamics simulations between the two spin labels are in agreement with the EPR experimental data. To understand the effect of labelled oligonucleotides on the structure, we studied the local base pair geometries and global structure in comparison with the unlabelled structures. Based on the structural analysis, we can conclude that TEMPO-based and Ç labels do not significantly perturb the base pair arrangements of the native oligonucleotide. When experimental structures for the spin labelled DNA/RNA molecules are not available, general framework offered by the current study can be used to provide information critical to the choice of spin labels to facilitate future EPR studies.

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.

A Global Minimization Toolkit for Batch-Fitting and χ2 Cluster Analysis of CW-EPR Spectra

Electron paramagnetic resonance spectroscopy (EPR) is a uniquely powerful technique for characterizing conformational dynamics at specific sites within a broad range of molecular species in water. Computational tools for fitting EPR spectra have enabled dynamics parameters to be determined quantitatively. These tools have dramatically broadened the capabilities of EPR dynamics analysis, however, their implementation can easily lead to overfitting or problems with self-consistency. As a result, dynamics parameters and associated properties become difficult to reliably determine, particularly in the slow-motion regime. Here, we present an EPR analysis strategy and the corresponding computational tool for batch-fitting EPR spectra and cluster analysis of the χ2 landscape in Linux. We call this tool CSCA (Chi-Squared Cluster Analysis). The CSCA tool allows us to determine self-consistent rotational diffusion rates and enables calculations of activation energies of diffusion from Arrhenius plots. We demonstrate CSCA using a model system designed for EPR analysis: a self-assembled nanoribbon with radical electron spin labels positioned at known distances off the surface. We anticipate that the CSCA tool will increase the reproducibility of EPR fitting for the characterization of dynamics in biomolecules and soft matter.

Modeling of spin–spin distance distributions for nitroxide labeled biomacromolecules

Combining CREST and MD simulations based on GFN-FF for the automated computation of distance distributions for nitroxide labeled (metallo-) proteins.

Electron spin echo detection of stochastic molecular librations: Non-cooperative motions on solid surface

In frozen biological media and molecular glasses only restricted motions exist; because of the weakness and disorder of intermolecular bonds these motions may have stochastic nature. Electron spin echo (ESE) spectroscopy of spin-labeled molecules allows detecting their restricted stochastic rotations (stochastic molecular librations). As in molecular disordered media motions may be highly cooperative, it would be desirable to investigate their spectroscopic manifestation also in the systems where cooperative effects would be certainly ruled out. In this work, ESE of spin-labeled molecules adsorbed on inorganic SiO₂ surface was investigated in a wide temperature range. The rate of motion-induced spin relaxation was found to become measurable above 130 K, increasing with temperature and attaining then a saturating behavior with a well-defined maximum near 250 K. For two types of molecules differing remarkably in their size and polarity (a small highly-polar nitroxide radical and a large spin-labeled peptide), quite similar results were obtained. This saturating behavior was quantitatively reproduced in simulations within a simple model of jump between two close orientations. Comparison with experiment allowed estimate that at 250 K the correlation time of the motion τ_c is of the order of several tens of nanoseconds and the angle α between two orientations is around 0.02 rad. As the found saturating behavior is a property of individual motions, for any other molecular system an excess of the spin relaxation rate above the maximum found here for adsorbed molecules may be ascribed to cooperative motions. Comparison with literature data on molecular systems of different origin has shown that effects of cooperativity indeed are present and, moreover, may be very essential.

Trajectory-Based Simulation of EPR Spectra: Models of Rotational Motion for Spin Labels on Proteins

Direct time-domain simulation of continuous-wave (CW) electron paramagnetic resonance (EPR) spectra from molecular dynamics (MD) trajectories has become increasingly popular, especially for proteins labeled with nitroxide spin labels. Due to the time-consuming nature of simulating adequately long MD trajectories, two approximate methods have been developed to reduce the MD-trajectory length required for modeling EPR spectra: hindered Brownian diffusion (HBD) and hidden Markov models (HMMs). Here, we assess the accuracy of these two approximate methods relative to direct simulations from MD trajectories for three spin-labeled protein systems (a simple helical peptide, a soluble protein, and a membrane protein) and two nitroxide spin labels with differing mobilities (R1 and 2,2,6,6-tetramethylpiperidine-1-oxyl-4-amino-4-carboxylic acid (TOAC)). We find that the HMMs generally outperform HBD. Although R1 dynamics partially resembles hindered Brownian diffusion, HMMs accommodate the multiple dynamic time scales for the transitions between rotameric states of R1 that cannot be captured accurately by a HBD model. The MD trajectories of the TOAC-labeled proteins show that its dynamics closely resembles slow multisite exchange between twist-boat and chair ring puckering states. This motion is modeled well by HMM but not by HBD. All MD-trajectory data processing, stochastic trajectory simulations, and CW EPR spectral simulations are implemented in EasySpin, a free software package for MATLAB.

Direct Prediction of EPR Spectra from Lipid Bilayers: Understanding Structure and Dynamics in Biological Membranes

Of the many biophysical techniques now being brought to bear on studies of membranes, electron paramagnetic resonance (EPR) of nitroxide spin probes was the first to provide information about both mobility and ordering in lipid membranes. Here, we report the first prediction of variable temperature EPR spectra of model lipid bilayers in the presence and absence of cholesterol from the results of large scale fully atomistic molecular dynamics (MD) simulations. Three types of structurally different spin probes were employed in order to study different parts of the bilayer. Our results demonstrate very good agreement with experiment and thus confirm the accuracy of the latest lipid force fields. The atomic resolution of the simulations allows the interpretation of the molecular motions and interactions in terms of their impact on the sensitive EPR line shapes. Direct versus indirect effects of cholesterol on the dynamics of spin probes are analysed. Given the complexity of structural organisation in lipid bilayers, the advantage of using a combined MD-EPR simulation approach is two-fold. Firstly, prediction of EPR line shapes directly from MD trajectories of actual phospholipid structures allows unambiguous interpretation of EPR spectra of biological membranes in terms of complex motions. Secondly, such an approach provides an ultimate test bed for the up-to-date MD simulation models employed in the studies of biological membranes, an area that currently attracts great attention.

All-atom molecular dynamics simulations of spin labelled double and single-strand DNA for EPR studies

Prediction of motional EPR spectra of spin labelled DNA structures from fully atomistic MD simulations.

Prediction of EPR Spectra of Lyotropic Liquid Crystals using a Combination of Molecular Dynamics Simulations and the Model-Free Approach

We report the first application of fully atomistic molecular dynamics (MD) simulations to the prediction of the motional electron paramagnetic resonance (EPR) spectra of lyotropic liquid crystals in different aggregation states doped with a paramagnetic spin probe. The purpose of this study is twofold. First, given that EPR spectra are highly sensitive to the motions and order of the spin probes doped within lyotropic aggregates, simulation of EPR line shapes from the results of MD modelling provides an ultimate test bed for the force fields currently employed to model such systems. Second, the EPR line shapes are simulated using the motional parameters extracted from MD trajectories using the Model-Free (MF) approach. Thus a combined MD-EPR methodology allowed us to test directly the validity of the application of the MF approach to systems with multi-component molecular motions. All-atom MD simulations using the General AMBER Force Field (GAFF) have been performed on sodium dodecyl sulfate (SDS) and dodecyltrimethylammonium chloride (DTAC) liquid crystals. The resulting MD trajectories were used to predict and interpret the EPR spectra of pre-micellar, micellar, rod and lamellar aggregates. The predicted EPR spectra demonstrate good agreement with most of experimental line shapes thus confirming the validity of both the force fields employed and the MF approach for the studied systems. At the same time simulation results confirm that GAFF tends to overestimate the packing and the order of the carbonyl chains of the surfactant molecules.

A combined EPR and MD simulation study of a nitroxyl spin label with restricted internal mobility sensitive to protein dynamics

EPR studies combined with fully atomistic Molecular Dynamics (MD) simulations and an MD-EPR simulation method provide evidence for intrinsic low rotameric mobility of a nitroxyl spin label, Rn, compared to the more widely employed label MTSL (R1). Both experimental and modelling results using two structurally different sites of attachment to Myoglobin show that the EPR spectra of Rn are more sensitive to the local protein environment than that of MTSL. This study reveals the potential of using the Rn spin label as a reporter of protein motions.

Determination of nitroxide spin label conformations via PELDOR and X-ray crystallography

PELDOR is used to unravel the position and orientation of MTSSL in six singly-labelled azurin mutants. A comparison with X-ray structures of the mutants shows good agreement with respect to the position and orientation of the nitroxide group.

Characterizing the conformational dynamics of metal-free PsaA using molecular dynamics simulations and electron paramagnetic resonance spectroscopy

Prokaryotic metal-ion receptor proteins, or solute-binding proteins, facilitate the acquisition of metal ions from the extracellular environment. Pneumococcal surface antigen A (PsaA) is the primary Mn(2+)-recruiting protein of the human pathogen Streptococcus pneumoniae and is essential for its in vivo colonization and virulence. The recently reported high-resolution structures of metal-free and metal-bound PsaA have provided the first insights into the mechanism of PsaA-facilitated metal binding. However, the conformational dynamics of metal-free PsaA in solution remain unknown. Here, we use continuous wave electron paramagnetic resonance (EPR) spectroscopy and molecular dynamics (MD) simulations to study the relative flexibility of the structural domains in metal-free PsaA and its distribution of conformations in solution. The results show that the crystal structure of metal-free PsaA is a good representation of the dominant conformation in solution, but the protein also samples structurally distinct conformations that are not captured by the crystal structure. Further, these results suggest that the metal binding site is both larger and more solvent exposed than indicated by the metal-free crystal structure. Collectively, this study provides atomic-resolution insight into the conformational dynamics of PsaA prior to metal binding and lays the groundwork for future EPR and MD based studies of PsaA in solution.

Visualizing transient dark states by NMR spectroscopy

Myriad biological processes proceed through states that defy characterization by conventional atomic-resolution structural biological methods. The invisibility of these 'dark' states can arise from their transient nature, low equilibrium population, large molecular weight, and/or heterogeneity. Although they are invisible, these dark states underlie a range of processes, acting as encounter complexes between proteins and as intermediates in protein folding and aggregation. New methods have made these states accessible to high-resolution analysis by nuclear magnetic resonance (NMR) spectroscopy, as long as the dark state is in dynamic equilibrium with an NMR-visible species. These methods - paramagnetic NMR, relaxation dispersion, saturation transfer, lifetime line broadening, and hydrogen exchange - allow the exploration of otherwise invisible states in exchange with a visible species over a range of timescales, each taking advantage of some unique property of the dark state to amplify its effect on a particular NMR observable. In this review, we introduce these methods and explore two specific techniques - paramagnetic relaxation enhancement and dark state exchange saturation transfer - in greater detail.

Simulation of electron paramagnetic resonance spectra of spin-labeled molecules from replica-exchange molecular dynamics

We report a general approach for the simulation of the electron paramagnetic resonance (EPR) spectra of spin labels attached to peptides and proteins directly from replica-exchange molecular dynamics (REMD) trajectories. Conventional MD trajectories are generally inadequate for the prediction of EPR line shapes since the label can become trapped in one or more of a set of rotameric states, thus preventing both conformational sampling and accurate estimates of the exchange rates between different rotamers. The advantage of using REMD is its ability to provide both efficient conformational sampling and kinetic information for spin-label dynamics. Our approach is illustrated with spin-labeled peptide. This approach to REMD-EPR simulation paves the way for the wider application of MD modeling to the simulation and interpretation of EPR spectra of spin-labeled molecules.

Conformational dynamics and distribution of nitroxide spin labels

Long-range distance measurements based on paramagnetic relaxation enhancement (PRE) in NMR, quantification of surface water dynamics near biomacromolecules by Overhauser dynamic nuclear polarization (DNP) and sensitivity enhancement by solid-state DNP all depend on introducing paramagnetic species into an otherwise diamagnetic NMR sample. The species can be introduced by site-directed spin labeling, which offers precise control for positioning the label in the sequence of a biopolymer. However, internal flexibility of the spin label gives rise to dynamic processes that potentially influence PRE and DNP behavior and leads to a spatial distribution of the electron spin even in solid samples. Internal dynamics of spin labels and their static conformational distributions have been studied mainly by electron paramagnetic resonance spectroscopy and molecular dynamics simulations, with a large body of results for the most widely applied methanethiosulfonate spin label MTSL. These results are critically discussed in a unifying picture based on rotameric states of the group that carries the spin label. Deficiencies in our current understanding of dynamics and conformations of spin labeled groups and of their influence on NMR observables are highlighted and directions for further research suggested.

Dynamical Line-Shifts in High-Field Electron Spin Resonance: Applications to Polymer Physics

High-field high-frequency Electron Paramagnetic Resonance spectroscopy (HF 2 -EPR) is a powerful tool to investigate, with ultra-high angular resolution, the rotational dynamics of complex systems like polymers, viscous fluids and glasses. Usually, information is drawn by detailed numerical analysis of the overall lineshape. Here, we present a simplified analytical model of the line shifts due to the rotational dynamics of the paramagnetic centre. The model captures the basic features of the reorientation process (time scale and size of the angular jump). It is compared with experimental results concerning the reorientation of a paramagnetic guest molecule dissolved in polystyrene. We find that, if the rotational model to describe the reorientation of the radical is consistent, the best-fit parameters yield equally acceptable best-fits of the overall spectrum by numerical simulations and dynamical line shifts by independent analytic expressions.

Direct simulation of magnetic resonance relaxation rates and line shapes from molecular trajectories

We simulate spin relaxation processes, which may be measured by either continuous wave or pulsed magnetic resonance techniques, using trajectory-based simulation methodologies. The spin-lattice relaxation rates are extracted numerically from the relaxation simulations. The rates obtained from the numerical fitting of the relaxation curves are compared to those obtained by direct simulation from the relaxation Bloch-Wangsness-Abragam-Redfield theory (BWART). We have restricted our study to anisotropic rigid-body rotational processes, and to the chemical shift anisotropy (CSA) and a single spin-spin dipolar (END) coupling mechanisms. Examples using electron paramagnetic resonance (EPR) nitroxide and nuclear magnetic resonance (NMR) deuterium quadrupolar systems are provided. The objective is to compare those rates obtained by numerical simulations with the rates obtained by BWART. There is excellent agreement between the simulated and BWART rates for a Hamiltonian describing a single spin (an electron) interacting with the bath through the chemical shift anisotropy (CSA) mechanism undergoing anisotropic rotational diffusion. In contrast, when the Hamiltonian contains both the chemical shift anisotropy (CSA) and the spin-spin dipolar (END) mechanisms, the decay rate of a single exponential fit of the simulated spin-lattice relaxation rate is up to a factor of 0.2 smaller than that predicted by BWART. When the relaxation curves are fit to a double exponential, the slow and fast rates extracted from the decay curves bound the BWART prediction. An extended BWART theory, in the literature, includes the need for multiple relaxation rates and indicates that the multiexponential decay is due to the combined effects of direct and cross-relaxation mechanisms.

Simulating the dynamics and orientations of spin-labeled side chains in a protein-DNA complex

Site-directed spin labeling, wherein a nitroxide side chain is introduced into a protein at a selected mutant site, is increasingly employed to investigate biological systems by electron spin resonance (ESR) spectroscopy. An understanding of the packing and dynamics of the spin label is needed to extract the biologically relevant information about the macromolecule from ESR measurements. In this work, molecular dynamics (MD) simulations were performed on the spin-labeled restriction endonuclease, EcoRI in complex with DNA. Mutants of this homodimeric enzyme were previously constructed, and distance measurements were performed using the double electron electron resonance experiment. These correlated distance constraints have been leveraged with MD simulations to learn about side chain packing and preferred conformers of the spin label on sites in an α-helix and a β-strand. We found three dihedral angles of the spin label side chain to be most sensitive to the secondary structure where the spin label was located. Conformers sampled by the spin label differed between secondary structures as well. C(α)-C(α) distance distributions were constructed and used to extract details about the protein backbone mobility at the two spin labeled sites. These simulation studies enhance our understanding of the behavior of spin labels in proteins and thus expand the ability of ESR spectroscopy to contribute to knowledge of protein structure and dynamics.

MtsslWizard: In Silico Spin-Labeling and Generation of Distance Distributions in PyMOL

MtsslWizard is a computer program, which operates as a plugin for the PyMOL molecular graphics system. MtsslWizard estimates distances between spin labels on proteins quickly with user-configurable options through a simple graphical interface. In default mode, the program searches for ensembles of possible MTSSL conformations that do not clash with a static model of the protein. Once conformations are assigned, distance distributions between two or more ensembles are calculated, displayed, and can be exported to other software. The program's use is evaluated in a number of challenging test cases and its strengths and weaknesses evaluated. The benefits of the program are its accuracy and simplicity. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s00723-012-0314-0) contains supplementary material, which is available to authorized users.

Implicit numerical schemes for the stochastic Liouville equation in Langevin form

We present and numerically test implicit as well as explicit numerical schemes for solving the Stochastic Liouville Equation in Langevin form. It is found that implicit schemes provide significant gain in robustness, for example, when nonsecular Hamiltonian terms cannot be ignored in electron and nuclear spin resonance. Implicit schemes open up several spectroscopic relaxation problems for direct interpretation using the Stochastic Liouville Equation. To illustrate the proposed numerical schemes, studies are presented for an electron paramagnetic resonance problem involving a coordinated copper complex and a fluorescence problem.