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.     

Simulating electron spin resonance spectra of nitroxide spin labels from molecular dynamics and stochastic trajectories

Simulating electron spin resonance spectra of nitroxide spin labels from motional models is necessary for the quantitative analysis of experimental spectra. We present a framework for modeling the spin label dynamics by using trajectories such as those from molecular dynamics (MD) simulations combined with stochastic treatment of the global protein tumbling. This is achieved in the time domain after two efficient numerical integrators are developed: One for the quantal dynamics of the spins and the other for the classical rotational diffusion. For the quantal dynamics, we propagate the relevant part of the spin density matrix in Hilbert space. For the diffusional tumbling, we work with quaternions, which enables the treatment of anisotropic diffusion in a potential expanded as a sum of spherical harmonics. Time-averaging arguments are invoked to bridge the gap between the smaller time step of the MD trajectories and the larger time steps appropriate for the rotational diffusion and/or quantal spin dynamics.     

Hyperfine structure of the electron paramagnetic resonance spectra of metal ketyls

Summary It was shown, by analyzing HFS in the EPR spectra of various metal ketyls, that the stabiliry of free radicals of the given type is determined by different factors. In aromatic metal ketyls the stabilizing factor is the considerable delocalization of the unpafred electron. In aliphatic metal ketyls the unpaired electron is mainly localized on the carbonyl carbon, and steric factors are more important than delocalization. In mixed ketyls of the type of trimethylacetophenone and benzoylferrocene K-ketyls, both factors act to a commensurable degree.Translated from Zhurnal Strukturnoi Khimii, Vol. 3, No. 5, pp. 536–540, September–October, 1962     

Electron paramagnetic resonance for everybody--MICROspec-X--a new class of electron paramagnetic resonance spectrometer

The electron paramagnetic resonance spectroscopy is the only method for detecting free radicals. Free radicals have an increased importance in our daily life. A small transportable EPR spectrometer is presented for the popularisation of the EPR method. The technical construction and some applications are illustrated which show the usability of the spectrometer.     

Signatures of the fast dynamics in glassy polystyrene: first evidence by high-field electron paramagnetic resonance of molecular guests

The reorientation of one small paramagnetic molecule (spin probe) in glassy polystyrene (PS) is studied by high-field electron paramagnetic resonance spectroscopy at two different Larmor frequencies (190 and 285 GHz). Two different regimes separated by a crossover region are evidenced. Below 180 K the rotational times are nearly temperature independent with no apparent distribution. In the temperature range of 180-220 K a large increase of the rotational mobility is observed with the widening of the distribution of correlation times which exhibits two components: (i) a deltalike, temperature-independent component representing the fraction of spin probes w which persist in the low-temperature dynamics; (ii) a strongly temperature-dependent component, to be described by a power distribution, representing the fraction of spin probes 1-w undergoing activated motion over an exponential distribution of barrier heights g(E). Above 180 K a steep decrease of w is evidenced. The shape and the width of g(E) do not differ from the reported ones for PS within the errors. For the first time the large increase of the rotational mobility of the spin probe at 180 K is ascribed to the onset of the fast dynamics detected by neutron scattering at T(f)=175+/-25 K.     

Computational modeling of isotropic electron paramagnetic resonance spectra of doublet state main group radicals

The combined use of theoretical and mathematical methods in the analysis of electron paramagnetic resonance data has greatly increased the ability to interpret even the most complex spectra reported for doublet state inorganic main group radicals. This personal account summarizes the theoretical basis of such an approach and provides an in-depth discussion of some recent illustrative examples of the utilization of this methodology in practical applications. The emphasis is on displaying the enormous potential embodied within the approach.     

Origin of additional satellites in electron paramagnetic resonance spectra of rare earth ion pairs

Electron Paramagnetic Resonance (EPR) spectrum of pairs of two identical rare earth ions is considered in the case where the two ions feel slightly different crystal fields giving different g factors. When the differences Δg between the g factors give a Zeeman difference term ΔgβB₀ of the order of magnitude of the interaction between the two ions, the pair spectrum is composed of four lines instead of two: the usual doublet structure, and two additional satellites around the main central transitions. It is shown that for rare earth ions, the shape of the EPR pair spectrum is very sensitive to small g factor differences. This situation is illustrated by the case of neodymium pairs in the SrAl₁₂O₁₉ host.     

Filling factor in a pulsed electron paramagnetic resonance experiment

A definition and mathematical treatment to calculate the filling factor in a pulsed electron paramagnetic resonance (EPR) experiment are presented. The differences between filling factors in traditional, continuous wave (CW)-EPR experiments (eta), and in pulsed-EPR experiments (eta(p)), are discussed. We present some examples to demonstrate how eta(p) depends upon the particular pulse sequence and sample characteristics.     

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.     

Hyperfine artifacts in electron paramagnetic resonance imaging

Low-molecular weight nitroxide labels (nitroxides) are commonly used as probes in electron paramagnetic resonance (EPR) spectroscopy. The nitroxides exhibit multiple lines in their EPR spectrum due to hyperfine coupling of the unpaired electron with the nitrogen nucleus. In EPR imaging, these hyperfine lines cause either hyperfine-based limitations in the maximum obtainable image resolution or hyperfine-based artifacts in the reconstructed image. In this article we discuss the effect of hyperfine artifacts on the quality of the image and report the application of a numerical method based on forward-subtraction principles for removing hyperfine artifacts in the measured projections. We demonstrate using computer simulations and imaging phantoms that marked enhancement in image quality and resolution can be obtained by removing the hyperfine-imposed limit on the gradient magnitude and performing post-acquisition corrections for removing hyperfine artifacts in the image.