Parametrization, molecular dynamics simulation, and calculation of electron spin resonance spectra of a nitroxide spin label on a polyalanine alpha-helix

The nitroxide spin label 1-oxyl-2,2,5,5-tetramethylpyrroline-3-methyl-methanethiosulfonate (MTSSL), commonly used in site-directed spin labeling of proteins, is studied with molecular dynamics (MD) simulations. After developing force field parameters for the nitroxide moiety and the spin label linker, we simulate MTSSL attached to a polyalanine alpha-helix in explicit solvent to elucidate the factors affecting its conformational dynamics. Electron spin resonance spectra at 9 and 250 GHz are simulated in the time domain using the MD trajectories and including global rotational diffusion appropriate for the tumbling of T4 Lysozyme in solution. Analysis of the MD simulations reveals the presence of significant hydrophobic interactions of the spin label with the alanine side chains.     

Simulating electron spin resonance spectra of macromolecules labeled with two dipolar-coupled nitroxide spin labels from trajectories

An efficient method for simulating continuous-wave electron spin resonance spectra (ESR) of molecules labeled with two dipolar-coupled nitroxides from trajectories of the molecular motion is presented. Two approximate treatments of the dipolar spin evolution, resulting in significantly shorter simulation times, are examined in order to determine their range of applicability. The approach is illustrated in the context of a double-helical B-DNA. ESR spectra for DNA undergoing anisotropic global diffusion and internal stretching dynamics are calculated for three different labeling geometries with the spin labels bracketing, respectively, three, two and one base pairs. While multifrequency spectra of all three labeling schemes are very sensitive to DNA tumbling, the last one is found to be most informative about the local DNA dynamics.     

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

A general approach for the prediction of EPR spectra directly and completely from single dynamical trajectories generated from Molecular Dynamics (MD) simulations is described. The approach is applicable to an arbitrary system of electron and nuclear spins described by a general form of the spin-Hamiltonian for the entire motional range. It is shown that for a reliable simulation of motional EPR spectra only a single truncated dynamical trajectory generated until the point when correlation functions of rotational dynamics are completely relaxed is required. The simulation algorithm is based on a combination of the propagation of the spin density matrix in the Liouville space for this initial time interval and the use of well defined parameters calculated entirely from the dynamical trajectory for prediction of the evolution of the spin density matrix at longer times. A new approach is illustrated with the application to a nitroxide spin label MTSL attached to the protein sperm whale myoglobin. It is shown that simulation of the EPR spectrum, which is in excellent agreement with experiment, can be achieved from a single MD trajectory. Calculations reveal the complex nature of the dynamics of a spin label which is a superposition of the fast librational motions within dihedral states, of slow rotameric dynamics among different conformational states of the nitroxide tether and of the slow rotational diffusion of the protein itself. The significance of the slow rotameric dynamics of the nitroxide tether on the overall shape of the EPR spectrum is analysed and discussed.     

Calculating slow-motional electron paramagnetic resonance spectra from molecular dynamics using a diffusion operator approach

A number of groups have utilized molecular dynamics (MD) to calculate slow-motional electron paramagnetic resonance (EPR) spectra of spin labels attached to biomolecules. Nearly all such calculations have been based on some variant of the trajectory method introduced by Robinson, Slutsky and Auteri (J. Chem. Phys. 1992,96, 2609-2616). Here we present an alternative approach that is specifically adapted to the diffusion operator-based stochastic Liouville equation (SLE) formalism that is also widely used to calculate slow-motional EPR line shapes. Specifically, the method utilizes MD trajectories to derive diffusion parameters such as the rotational diffusion tensor, diffusion tilt angles, and expansion coefficients of the orienting potential, which are then used as direct inputs to the SLE line shape program. This approach leads to a considerable improvement in computational efficiency over trajectory-based methods, particularly for high frequency, high field EPR. It also provides a basis for deconvoluting the effects of local spin label motion and overall motion of the labeled molecule or domain: once the local motion has been characterized by this approach, the label diffusion parameters may be used in conjunction with line shape analysis at lower EPR frequencies to characterize global motions. The method is validated by comparison of the MD predicted line shapes to experimental high frequency (250 GHz) EPR spectra.     

Using Markov models to simulate electron spin resonance spectra from molecular dynamics trajectories

Simulating electron spin resonance (ESR) spectra directly from molecular dynamics simulations of a spin-labeled protein necessitates a large number (hundreds or thousands) of relatively long (hundreds of nanoseconds) trajectories. To meet this challenge, we explore the possibility of constructing accurate stochastic models of the spin label dynamics from atomistic trajectories. A systematic, two-step procedure, based on the probabilistic framework of hidden Markov models, is developed to build a discrete-time Markov chain process that faithfully captures the internal spin label dynamics on time scales longer than about 150 ps. The constructed Markov model is used both to gain insight into the long-lived conformations of the spin label and to generate the stochastic trajectories required for the simulation of ESR spectra. The methodology is illustrated with an application to the case of a spin-labeled poly alanine alpha helix in explicit solvent.     

Evaluating rotational diffusion from protein MD simulations

It is now feasible to carry out molecular dynamics simulations of proteins in water that are long compared to the overall tumbling of the molecule. Here, we examine rotational diffusion in four small, globular proteins (ubiquitin, binase, lysozyme, and fragment B3 of protein G) with the TIP3P, TIP4P/EW, and SPC/E water models, in simulations that are 6 to 60 times as long as the mean rotational tumbling time. We describe a method for extracting diffusion tensors from such simulations and compare the results to experimental values extracted from NMR relaxation measurements. The simulation results accurately follow a diffusion equation, even for spherical harmonic correlation functions with l as large as 8. However, the best-fit tensors are significantly different from experiment, especially for the commonly used TIP3P water model. Simulations that are 20 to 100 times longer than the rotational tumbling times are needed for good statistics. A number of residues exhibit internal motions on the nanosecond time scale, but in all cases examined here, a product of internal and overall time-correlation functions matches the total time-correlation function well.     

Atomistic computer simulation and experimental study on the dynamics of the n-cyanobiphenyls mesogenic series

Several dynamic properties of the 4-n-alkyl-4'-cyanobiphenyls series ( nCB) with n=5, 6, 7, 8 have been studied by atomistic molecular dynamics (MD) simulations in the NVE ensemble adopting an ab initio derived force field (J. Phys. Chem. B 2007, 111, 2130). For each homologue, at least two state points, in the nematic and in the isotropic phase, as determined from lengthy equilibration runs performed in the previous work, have been considered. More than 10 ns have been produced at each state point, allowing us to calculate single-molecule properties as the translational and rotational diffusion coefficients along the series. An oscillating behavior of the diffusion coefficients, similar to the observed odd-even effect in static properties, has been predicted by MD. A good agreement with the results of purposely carried out (1)H NMR measurements is achieved, provided the MD values are increased by a factor that accounts for density overestimation. Spinning and tumbling rotational motions, monitored by calculating the rotational diffusion coefficients for all homologues in both phases, agree well with experimental data, at least for 5CB where NMR measures are reported. Collective properties, such as the isotropic shear viscosity and the rotational viscosity coefficient, have been computed for all homologues, and the MD values agree well with the experimental data reported in the literature. Finally, the origin of the odd-even effect, found for all the computed dynamic properties, is addressed.     

Effect of molecular vibrations on the MD/QC‐simulated absorption spectra

Effect of molecular vibrations on the absorption spectra simulated via a sequential approach combining molecular dynamics (MD) with quantum‐chemical calculations has been investigated. Simulated spectra have been obtained from the time‐dependent density functional theory results averaged over series of molecular geometries retrieved from Born–Oppenheimer MD trajectories. Distributions of bond lengths have been analyzed and related to the features of calculated spectra. For NVE simulations of small systems, absorption spectra exhibit bimodal bandshape as a result of classical treatment of vibrations. For NVE trajectories of larger systems or simulations in the NVT ensemble calculated absorption bands are symmetric, however, they may not agree with the results of Franck–Condon analysis. These results are practical manifestations of effects predicted theoretically from general principles. Consequences for the modeling of absorption spectra have been discussed. © 2013 Wiley Periodicals, Inc.     

General framework for studying the dynamics of folded and nonfolded proteins by NMR relaxation spectroscopy and MD simulation

A general framework is presented for the interpretation of NMR relaxation data of proteins. The method, termed isotropic reorientational eigenmode dynamics (iRED), relies on a principal component analysis of the isotropically averaged covariance matrix of the lattice functions of the spin interactions responsible for spin relaxation. The covariance matrix, which is evaluated using a molecular dynamics (MD) simulation, is diagonalized yielding reorientational eigenmodes and amplitudes that reveal detailed information about correlated protein dynamics. The eigenvalue distribution allows one to quantitatively assess whether overall and internal motions are statistically separable. To each eigenmode belongs a correlation time that can be adjusted to optimally reproduce experimental relaxation parameters. A key feature of the method is that it does not require separability of overall tumbling and internal motions, which makes it applicable to a wide range of systems, such as folded, partially folded, and unfolded biomolecular systems and other macromolecules in solution. The approach was applied to NMR relaxation data of ubiquitin collected at multiple magnetic fields in the native form and in the partially folded A-state using MD trajectories with lengths of 6 and 70 ns. The relaxation data of native ubiquitin are well reproduced after adjustment of the correlation times of the 10 largest eigenmodes. For this state, a high degree of separability between internal and overall motions is present as is reflected in large amplitude and collectivity gaps between internal and overall reorientational modes. In contrast, no such separability exists for the A-state. Residual overall tumbling motion involving the N-terminal beta-sheet and the central helix is observed for two of the largest modes only. By adjusting the correlation times of the 10 largest modes, a high degree of consistency between the experimental relaxation data and the iRED model is reached for this highly flexible biomolecule.     

Microphase separation in poly(acrylonitrile–butadiene–styrene) (ABS) studied with paramagnetic spin probes. II. Simulation of electron spin resonance spectra

We recently presented electron spin resonance spectra of poly(acrylonitrile–butadiene–styrene) (ABS) doped with 10‐doxylnonadecane (10DND) and 5‐doxyldecane (5DD) as spin probes. The spectra were measured in three types of ABS that differed in their butadiene contents and methods of preparation. Results for the ABS polymers were evaluated by comparison with similar studies on the homopolymers polybutadiene (PB) and polystyrene (PS) and the copolymers poly(styrene‐co‐acrylonitrile) (SAN) and poly(styrene‐co‐butadiene) (SB). Only one spectral component was detected for 10DND in PB, PS, SAN, and SB. In contrast, two spectral components differing in their dynamic properties were detected in the ABS samples and were assigned to spin probes located in butadiene‐rich domains (the fast component) and SAN‐rich domains (the slow component). The presence of two spectral components was taken as an indication of microphase separation. In this study, we present details on the dynamics and microphase separation by simulating spectra of 10DND in ABS, PB, PS, and SAN. The simulations are based on a dynamic model defined by the components of the rotational diffusion tensor and the diffusion tilt angle between the symmetry axis of the rotational diffusion tensor and the direction of the nitrogen 2p_z atomic orbital. The jump diffusion model led to good agreement with experimental spectra. In this model, the spin probe has a fixed orientation for a given time and then jumps instantaneously to a new orientation. The temperature variation of the rotational correlation time in PB and PS consisted of two dynamic regimes, with different activation energies. The transition temperature at which the change in dynamics occurs (T_tr) is 380 K for PS and 205 K for PB, essentially the same as the corresponding glass‐transition temperatures measured by differential scanning calorimetry. We suggest that T_tr is a better indicator of the glass transition than the temperature at which the total spectral width is 50 G, especially for large probes. The simulation program allowed the determination of the relative intensities of the fast and slow spectral components as a function of temperature; this information was used to clarify the redistribution of the probe above the glass transition of the SAN‐rich component in ABS systems. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 424–433, 2002; DOI 10.1002/polb.10110     

Dynamic coupling of a small rigid probe to viscous ortho-terphenyl

We have measured the dielectric relaxation of 2,2,6,6-tetramethyl-piperidine-1-oxyl (TEMPO) as a rotational probe in supercooled ortho-terphenyl (OTP). Due to the significant dipole moment of TEMPO compared with OTP, its contribution to the loss spectra can be identified already at moderate concentrations. For time scales ranging from 10 μs to 1 s, it is found that the tumbling mode of TEMPO is a true replica of the structural relaxation of OTP regarding average time constant, relaxation time dispersion, and the temperature dependence. While the present dielectric results are consistent with a decoupling of a spinning mode (about the nitroxyl dipole axis) of TEMPO from viscosity, they do not agree with the strong decoupling of the tumbling mode derived from electron spin resonance experiments.     

Ab initio modeling of CW-ESR spectra of the double spin labeled peptide Fmoc-(Aib-Aib-TOAC)2-Aib-OMe in acetonitrile

In this work we address the interpretation, via an ab initio integrated computational approach, of the CW-ESR spectra of the double spin labeled, 310-helical, peptide Fmoc-(Aib-Aib-TOAC)2-Aib-OMe dissolved in acetonitrile. Our approach is based on the determination of geometric and local magnetic parameters of the heptapeptide by quantum mechanical density functional calculations taking into account solvent and, when needed, vibrational averaging contributions. The system is then described by a stochastic Liouville equation for the two electron spins interacting with each other and with two 14N nuclear spins, in the presence of diffusive rotational dynamics. Parametrization of the diffusion rotational tensor is provided by a hydrodynamic model. CW-ESR spectra are simulated with minimal resorting to fitting procedures, proving that the combination of sensitive ESR spectroscopy and sophisticated modeling can be highly helpful in providing 3D structural and dynamic information on molecular systems.     

On the interpretation of continuous wave electron spin resonance spectra of tempo-palmitate in 5-cyanobiphenyl

Electron spin resonance (ESR) measurements are highly informative on the dynamic behavior of molecules, which is of fundamental importance to understand their stability, biological functions and activities, and catalytic action. The wealth of dynamic information which can be extracted from a continuous wave electron spin resonance (cw-ESR) spectrum can be inferred by a basic theoretical approach defined within the stochastic Liouville equation formalism, i.e., the direct inclusion of motional dynamics in the form of stochastic (Fokker-Planck/diffusive) operators in the super Hamiltonian H governing the time evolution of the system. Modeling requires the characterization of magnetic parameters (e.g., hyperfine and Zeeman tensors) and the calculation of ESR observables in terms of spectral densities. The magnetic observables can be pursued by the employment of density functional theory which is apt, provided that hybrid functionals are employed, for the accurate computation of structural properties of molecular systems. Recently, an ab initio integrated computational approach to the in silico interpretation of cw-ESR spectra of multilabeled systems in isotropic fluids has been discussed. In this work we present the extension to the case of nematic liquid crystalline environments by performing simulations of the ESR spectra of the prototypical nitroxide probe 4-(hexadecanoyloxy)-2,2,6,6-tetramethylpiperidine-1-oxy in isotropic and nematic phases of 5-cyanobiphenyl. We first discuss the basic ingredients of the integrated approach, i.e., (1) determination of geometric and local magnetic parameters by quantum-mechanical calculations, taking into account the solvent and, when needed, the vibrational averaging contributions; (2) numerical solution of a stochastic Liouville equation in the presence of diffusive rotational dynamics, based on (3) parameterization of diffusion rotational tensor provided by a hydrodynamic model. Next we present simulated spectra with minimal resorting to fitting procedures, proving that the combination of sensitive ESR spectroscopy and sophisticated modeling can be highly helpful in providing three-dimensional structural and dynamic information on molecular systems in anisotropic environments.     

Rotational dynamics in supercooled water from nuclear spin relaxation and molecular simulations

Structural dynamics in liquid water slow down dramatically in the supercooled regime. To shed further light on the origin of this super-Arrhenius temperature dependence, we report high-precision (17)O and (2)H NMR relaxation data for H(2)O and D(2)O, respectively, down to 37 K below the equilibrium freezing point. With the aid of molecular dynamics (MD) simulations, we provide a detailed analysis of the rotational motions probed by the NMR experiments. The NMR-derived rotational correlation time τ(R) is the integral of a time correlation function (TCF) that, after a subpicosecond librational decay, can be described as a sum of two exponentials. Using a coarse-graining algorithm to map the MD trajectory on a continuous-time random walk (CTRW) in angular space, we show that the slowest TCF component can be attributed to large-angle molecular jumps. The mean jump angle is ～48° at all temperatures and the waiting time distribution is non-exponential, implying dynamical heterogeneity. We have previously used an analogous CTRW model to analyze quasielastic neutron scattering data from supercooled water. Although the translational and rotational waiting times are of similar magnitude, most translational jumps are not synchronized with a rotational jump of the same molecule. The rotational waiting time has a stronger temperature dependence than the translation one, consistent with the strong increase of the experimentally derived product τ(R)?D(T) at low temperatures. The present CTRW jump model is related to, but differs in essential ways from the extended jump model proposed by Laage and co-workers. Our analysis traces the super-Arrhenius temperature dependence of τ(R) to the rotational waiting time. We present arguments against interpreting this temperature dependence in terms of mode-coupling theory or in terms of mixture models of water structure.     

Hydrophilic domain structure in polymer exchange membranes: Simulations of NMR spin diffusion experiments to address ability for model discrimination

We detail the development of a flexible simulation program (NMR_DIFFSIM) that solves the nuclear magnetic resonance (NMR) spin diffusion equation for arbitrary polymer architectures. The program was used to explore the proton (¹H) NMR spin diffusion behavior predicted for a range of geometrical models describing polymer exchange membranes. These results were also directly compared with the NMR spin diffusion behavior predicted for more complex domain structures obtained from molecular dynamics (MD) simulations. The numerical implementation and capabilities of NMR_DIFFSIM were demonstrated by evaluating the experimental NMR spin diffusion behavior for the hydrophilic domain structure in sulfonated Diels‐Alder Poly(Phenylene) (SDAPP) polymer membranes. The impact of morphology variations as a function of sulfonation and hydration level on the resulting NMR spin diffusion behavior were determined. These simulations allowed us to critically address the ability of NMR spin diffusion to discriminate between different structural models, and to highlight the extremely high fidelity experimental data required to accomplish this. A direct comparison of experimental double‐quantum‐filtered ¹H NMR spin diffusion in SDAPP membranes to the spin diffusion behavior predicted for MD‐proposed morphologies revealed excellent agreement, providing experimental support for the MD structures at low to moderate hydration levels. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 62–78     

Rotational and spin viscosities of water: Application to nanofluidics

In this paper we evaluate the rotational viscosity and the two spin viscosities for liquid water using equilibrium molecular dynamics. Water is modeled via the flexible SPC/Fw model where the Coulomb interactions are calculated via the Wolf method which enables the long simulation times required. We find that the rotational viscosity is independent of the temperature in the range from 284 to 319 K. The two spin viscosities, on the other hand, decrease with increasing temperature and are found to be two orders of magnitude larger than that estimated by Bonthuis et al. [Phys. Rev. Lett. 103, 144503 (2009)] We apply the results from molecular dynamics simulations to the extended Navier-Stokes equations that include the coupling between intrinsic angular momentum and linear momentum. For a flow driven by an external field the coupling will reduce the flow rate significantly for nanoscale geometries. The coupling also enables conversion of rotational electrical energy into fluid linear momentum and we find that in order to obtain measurable flow rates the electrical field strength must be in the order of 0.1?MV?m(-1) and rotate with a frequency of more than 100 MHz.     

Characteristic behavior of short-term dynamics in reorientation for Gay-Berne particles near the nematic-isotropic phase transition temperature

A specific transition behavior was found in the tumbling motion near the nematic-isotropic phase boundary using molecular dynamics simulations of the Gay-Berne mesogenic model under isobaric conditions at a reduced pressure P* of 2.0. The relaxation time for the motion obtained from the second-rank orientational time correlation function and the rotational diffusion coefficient showed a clear jump at the nematic-isotropic phase transition temperature. Regardless of the temperature dependence of the relaxation time, the change in the rotational diffusion coefficient evaluated from the orientational order parameters and the relaxation time agreed qualitatively with that of real mesogens. The rotational viscosity coefficients gamma(1) and gamma(2) were obtained from the simulation data for the relaxation time for the short-term dynamics and for the rotational diffusion coefficients. gamma(1) was proportional to (2), where is the second-rank orientational parameter. Furthermore, the rotational behavior of the model was compared with that of the Debye approximation in the isotropic phase.     

N2,O2水溶液光谱的分子动力学模拟

用分子动力学模拟方法研究了N2和O2水溶液的光谱性质．给出了能描述分子内部运动的溶质－溶剂相互作用势．对溶质和溶剂原子的速度自相关函数（VACF）作了计算．讨论了所得VACF的性质并计算了其谱密度．溶质分子振动谱出现的红移，与液态N2，O2的Raman实验结果相吻合．模拟得出的转动谱表明了溶剂分子对溶质转动运动的阻滞，模拟结果也表明VACF计算对溶液和液体光谱的研究十分有效．     

On the pressure dependence of the muon spin polarization in mixtures of noble gases

In muon spin rotation (μSR) experiments, where spin-polarized positive muons are stopped in condensed matter, three magnetically distinguishable chemical environments can be observed. That is, the Larmor frequencies associated with diamagnetic environments and two types of paramagnetic environments (muonium and radicals) can be resolved. The chemical identities of the latter two are distinct since their Larmor frequencies are distinct, whereas the chemical identities of the possible diamagnetic species are not determined by the Larmor frequency since chemical shifts can not be resolved in μSR experiments. However, two different diamagnetic species have been observed in experiments performed on mixtures of noble gases. Their distinction arises through different thermal rate constants that lead to “fast” and “slow” relaxing components of the diamagnetic signal. The pressure dependencies of the amplitudes associated with these components are related to the stopping dynamics of muons in noble gas targets. A set of coupled rate equations for muon spin dynamics, based upon quantal Boltzmann equations, have been developed to describe this process in single component gases. This theory is now extended to mixtures. In particular, the dynamics of the muon spin is generated by the muonium hyperfine interaction and by time dependent rate constants for the various chemical species that are assumed to be present, namely, muonium and three diamagnetic species. Radicals have not yet been observed in low pressure gases. The coupled quantal rate equations are solved for two models of the stopping dynamics wherein the rates are taken as square box functions of time.