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  • 1. Belorizky, Elie
    et al.
    Fries, Pascal H
    Helm, Lothar
    Kowalewski, Jozef
    Kruk, Danuta
    Sharp, Robert R
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Chemistry.
    Comparison of different methods for calculating the paramagnetic relaxation enhancement of nuclear spins as a function of the magnetic field2008In: The Journal of Chemical Physics, Vol. 128, no 5, p. 17-Article in journal (Refereed)
    Abstract [en]

    The enhancement of the spin-lattice relaxation rate for nuclear spins in a ligand bound to a paramagnetic metal ion [known as the paramagnetic relaxation enhancement (PRE)] arises primarily through the dipole-dipole (DD) interaction between the nuclear spins and the electron spins. In solution, the DD interaction is modulated mostly by reorientation of the nuclear spin-electron spin axis and by electron spin relaxation. Calculations of the PRE are in general complicated, mainly because the electron spin interacts so strongly with the other degrees of freedom that its relaxation cannot be described by second-order perturbation theory or the Redfield theory. Three approaches to resolve this problem exist in the literature: The so-called slow-motion theory, originating from Swedish groups [Benetis et al., Mol. Phys. 48, 329 (1983); Kowalewski et al., Adv. Inorg. Chem. 57, (2005); Larsson et al., J. Chem. Phys. 101, 1116 (1994); T. Nilsson et al., J. Magn. Reson. 154, 269 (2002)] and two different methods based on simulations of the dynamics of electron spin in time domain, developed in Grenoble [Fries and Belorizky, J. Chem. Phys. 126, 204503 (2007); Rast et al., ibid. 115, 7554 (2001)] and Ann Arbor [Abernathy and Sharp, J. Chem. Phys. 106, 9032 (1997); Schaefle and Sharp, ibid. 121, 5387 (2004); Schaefle and Sharp, J. Magn. Reson. 176, 160 (2005)], respectively. In this paper, we report a numerical comparison of the three methods for a large variety of parameter sets, meant to correspond to large and small complexes of gadolinium(III) and of nickel(II). It is found that the agreement between the Swedish and the Grenoble approaches is very good for practically all parameter sets, while the predictions of the Ann Arbor model are similar in a number of the calculations but deviate significantly in others, reflecting in part differences in the treatment of electron spin relaxation. The origins of the discrepancies are discussed briefly.

  • 2. Bergenstråhle-Wohlert, Malin
    et al.
    Berglund, Lars A
    Brady, John W
    Larsson, P Tomas
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Wohlert, Jakob
    Concentration enrichment of urea at cellulose surfaces: results from molecular dynamics simulations and NMR spectroscopy2012In: Cellulose (London), ISSN 0969-0239, E-ISSN 1572-882X, Vol. 19, no 1, p. 1-12Article in journal (Refereed)
    Abstract [en]

    A combined solid-state NMR and Molecular Dynamics simulation study of cellulose in urea aqueous solution and in pure water was conducted. It was found that the local concentration of urea is significantly enhanced at the cellulose/solution interface. There, urea molecules interact directly with the cellulose through both hydrogen bonds and favorable dispersion interactions, which seem to be the driving force behind the aggregation. The CP/MAS 13C spectra was affected by the presence of urea at high concentrations, most notably the signal at 83.4 ppm, which has previously been assigned to C4 atoms in cellulose chains located at surfaces parallel to the (110) crystallographic plane of the cellulose Iβ crystal. Also dynamic properties of the cellulose surfaces, probed by spin-lattice relaxation time 13CT 1 measurements of C4 atoms, are affected by the addition of urea. Molecular Dynamics simulations reproduce the trends of the T 1measurements and lends new support to the assignment of signals from individual surfaces. That urea in solution is interacting directly with cellulose may have implications on our understanding of the mechanisms behind cellulose dissolution in alkali/urea aqueous solutions.

  • 3.
    Edman, Peter
    et al.
    Umeå University, Faculty of Science and Technology, Chemistry.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Chemistry.
    Johansson, Lennart B-Å
    Umeå University, Faculty of Science and Technology, Chemistry.
    On determining intramolecular distances from donor–donor energy migration (DDEM) within bifluorophoric macromolecules2000In: PHYSICAL CHEMISTRY CHEMICAL PHYSICS, Vol. 2, p. 1789-94Article in journal (Refereed)
    Abstract [en]

    Recently a model based on donor–donor energy migration (DDEM) was developed for examining structure–function properties of biomacromolecules such as proteins (J. Chem. Soc., Faraday Trans., 1996, 92, 1563). Unlike the extended Förster theory (EFT; J. Chem. Phys., 1996, 105, 10896) the DDEM model is straightforward to apply in the analyses of fluorescence depolarisation experiments, as obtained by the time-correlated single photon counting (TCSPC) technique. In order to test the validity of the DDEM model, the EFT was used to create synthetic depolarisation data. These mimic true TCSPC experiments and cover a wide range of physical conditions, which are difficult to arrange for in real experiments with model systems. In particular, the relative rate of DDEM () and the rotation correlation time () of the donor molecules was examined. The DDEM rates obtained from the analyses were compared to the true rates. From these results the relative error of the intramolecular distances were calculated. For values 1<12<25, the DDEM model is slightly overestimating the distances. Typically, the distances determined with the DDEM model are overestimated by 5–10%.

  • 4. Gustafsson, Håkan
    et al.
    Ahrén, Maria
    Söderlind, Fredrik
    Córdoba Gallego, José M
    Käll, Per-Olov
    Nordblad, Per
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Uvdal, Kajsa
    Engström, Maria
    Magnetic and Electron Spin Relaxation Properties of (GdxY1−x)2O3 (0 ≤ x ≤ 1) Nanoparticles Synthesized by the Combustion Method. Increased Electron Spin Relaxation Times with Increasing Yttrium Content2011In: The Journal of Physical Chemistry C, ISSN 1932-7447, E-ISSN 1932-7455, Vol. 115, no 13, p. 5469-5477Article in journal (Refereed)
    Abstract [en]

    The performance of a magnetic resonance imaging contrast agent (CA) depends on several factors, including the relaxation times of the unpaired electrons in the CA. The electron spin relaxation time may be a key factor for the performance of new CAs, such as nanosized Gd2O3 particles. The aim of this work is, therefore, to study changes in the magnetic susceptibility and the electron spin relaxation time of paramagnetic Gd2O3 nanoparticles diluted with increasing amounts of diamagnetic Y2O3. Nanoparticles of (GdxY1−x)2O3 (0 ≤ x ≤ 1) were prepared by the combustion method and thoroughly characterized (by X-ray diffraction, transmission electron microscopy, thermogravimetry coupled with mass spectroscopy, photoelectron spectroscopy, Fourier transform infrared spectroscopy, and magnetic susceptibility measurements). Changes in the electron spin relaxation time were estimated by observations of the signal line width in electron paramagnetic resonance spectroscopy, and it was found that the line width was dependent on the concentration of yttrium, indicating that diamagnetic Y2O3 may increase the electron spin relaxation time of Gd2O3 nanoparticles.

  • 5.
    Han, Guangye
    et al.
    Umeå University, Faculty of Science and Technology, Department of Chemistry. Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, USA .
    Huang, Yang
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Koua, Faisal Hammad Mekky
    Graduate School of Natural Science and Technology, Department of Biology, Faculty of Science, Okayama University, Tsushima, Japan .
    Shen, Jian-Ren
    Graduate School of Natural Science and Technology, Department of Biology, Faculty of Science, Okayama University, Tsushima, Japan.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Messinger, Johannes
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Hydration of the oxygen-evolving complex of photosystem II probed in the dark-stable S1 state using proton NMR dispersion profiles2014In: Physical Chemistry, Chemical Physics - PCCP, ISSN 1463-9076, E-ISSN 1463-9084, no 16, p. 11924-11935Article in journal (Refereed)
    Abstract [en]

    The hydration of the oxygen-evolving complex (OEC) was characterized in the dark stable S1 state of photosystem II using water R1(ω) NMR dispersion (NMRD) profiles. The R1(ω) NMRD profiles were recorded over a frequency range from 0.01 MHz to 40 MHz for both intact and Mn-depleted photosystem II core complexes from Thermosynechococcus vulcanus (T. vulcanus). The intact-minus-(Mn)-depleted difference NMRD profiles show a characteristic dispersion from approximately 0.03 MHz to 1 MHz, which is interpreted on the basis of the Solomon-Bloembergen-Morgan (SBM) and the slow motion theories as being due to a paramagnetic enhanced relaxation (PRE) of water protons. Both theories are qualitatively consistent with the ST = 1, g = 4.9 paramagnetic state previously described for the S1 state of the OEC; however, an alternative explanation involving the loss of a separate class of long-lived internal waters due to the Mn-depletion procedure can presently not be ruled out. Using a point-dipole approximation the PRE-NMRD effect can be described as being caused by 1-2 water molecules that are located about 10 Å away from the spin center of the Mn4CaO5 cluster in the OEC. The application of the SBM theory to the dispersion observed for PSII in the S1 state is questionable, because the parameters extracted do not fulfil the presupposed perturbation criterion. In contrast, the slow motion theory gives a consistent picture indicating that the water molecules are in fast chemical exchange with the bulk (τw < 1 μs). The modulation of the zero-field splitting (ZFS) interaction suggests a (restricted) reorientation/structural equilibrium of the Mn4CaO5 cluster with a characteristic time constant of τZFS = 0.6-0.9 μs.

  • 6.
    Huang, Yang
    et al.
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Nam, Kwangho
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    The water R1(ω) NMRD profiles of a hydrated protein from molecular dynamics simulation2013In: Physical Chemistry, Chemical Physics - PCCP, ISSN 1463-9076, E-ISSN 1463-9084, Vol. 15, no 33, p. 14089-14097Article in journal (Refereed)
    Abstract [en]

     The hydration of a protein, peroxiredoxin 5, is obtained from a molecular dynamics simulation and compared with the picture of hydration which is obtained by analysing the water proton R1 NMRD profiles using a generally accepted relaxation model [K. Venu, V.P. Denisov and B. Halle, J. Am. Chem. Soc. 119,3122(1997)]. The discrepancy between the hydration pictures derived from the water R1 0)-NMRD profiles and MD is relevant in a discussion of the factors behind the stretched NMRD profile, the distribution of orientationalorder parameters and residence times of buried water used in the NMRD model.

  • 7. Håkansson, P
    et al.
    Persson, L
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Chemistry.
    Itô diffusions on hypersurfaces with application to the Schwarz-P surface and nuclear magnetic resonance theory2002In: The Journal of Chemical Physics, Vol. 117, no 19, p. 8634-43Article in journal (Refereed)
    Abstract [en]

    This work presents a new Brownian dynamics simulation method of translational diffusion on curved surfaces. This new method introduce any implicit defined surface into the stochastic differential equation describing Brownian motion on that surface. The surface curvature will thus enter the force term (A) in the stochastic differential equation dXt = A(Xt)dt + B(Xt)dWt describing an Itô process. We apply the method calculating time correlation functions relevant in nuclear magnetic resonance (NMR) relaxation and translational diffusion studies of cubic phases of lyotropic systems. In particularly we study some bicontinuous cubic liquid crystalline phases which can be described as triply periodic minimal surfaces. The curvature dependent spin relaxation of the Schwarz-P minimal surface is calculated. A comparison of relaxation is made with the more complex topology of the Neovius surface which is another minimal surface in the same space group, and with parallel displacement of the minimal surface which thus results in a nonminimal surface. The curvature dependent relaxation effects are determined by calculating the translational diffusion modulated time-correlation function which determine the relaxation rates of a quadrupole nuclei residing in the water–lipid interface. The results demonstrates that spin relaxation data can provide quantitative information about micro-structure of biocontinuous cubic phases and that it is sensitive to the topology of the surface and to parallel displacement of the model surface. Consequently, spin relaxation may be used as a complement to x-ray diffraction in order to discriminate between different microstructures. It is concluded that fast and accurate computer simulations experiments is needed to be able to interpret NMR relaxation experiments on curved surfaces. © 2002 American Institute of Physics.

  • 8.
    Håkansson, Pär
    et al.
    Umeå University, Faculty of Science and Technology, Chemistry.
    Isaksson, Mikael
    Umeå University, Faculty of Science and Technology, Chemistry. Umeå University, Faculty of Science and Technology, Chemistry.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Chemistry.
    Johansson, Lennart B-Å
    Umeå University, Faculty of Science and Technology, Chemistry.
    Extended Förster theory for determining intraprotein distances: 1. The K2-dynamics and fluorophore reorientation2004In: Journal of Physical Chemistry B, ISSN 1520-6106, E-ISSN 1520-5207, Vol. 108, no 44, p. 17243-17250Article in journal (Refereed)
    Abstract [en]

    A detailed analysis of the previously developed (J. Chem. Phys. 1996, 105, 10896) extended Förster theory (EFT) is presented for analyzing electronic energy migration within pairs of donors (D). Synthetic data that mimics experimental time-correlated single photon counting data were generated and re-analyzed. To cover a wide dynamic range and various orientational restrictions, the rates of reorientation, as well as the orientational configurations of the interacting D-groups were varied. In general DD distances are recovered within an error limit of 5%, while the errors in orientational configurations are usually larger. The Maier−Saupe and cone potentials were used to generate an immense variety of orientational trajectories. The results obtained exhibit no significant dependence on the choice of potential function used for generating EFT data. Present work demonstrates how to overcome the classical “κ2-problem” and the frequently applied approximation of κ2 = 2/3 in the data analyses. This study also outlines the procedure for analyzing fluorescence depolarization data obtained for proteins, which are specifically labeled with D-groups. The EFT presented here brings the analyses of DDEM data to the same level of molecular detail as in ESR- and NMR-spectroscopy.

  • 9.
    Håkansson, Pär
    et al.
    Umeå University, Faculty of Science and Technology, Chemistry.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Chemistry.
    The effect of memory in the stochastic master equation analyzed using the stochastic Liouville equation of motion: Electronic energy migration transfer between reorienting donor–donor, donor–acceptor chromophores2005In: Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, Vol. 61, no 1-2, p. 299-304Article in journal (Refereed)
    Abstract [en]

    This paper discusses the process of energy migration transfer within reorientating chromophores using the stochastic master equation (SME) and the stochastic Liouville equation (SLE) of motion. We have found that the SME over-estimates the rate of the energy migration compared to the SLE solution for a case of weakly interacting chromophores. This discrepancy between SME and SLE is caused by a memory effect occurring when fluctuations in the dipole–dipole Hamiltonian (H(t)) are on the same timescale as the intrinsic fast transverse relaxation rate characterized by (1/T2). Thus the timescale critical for energy-transfer experiments is T2≈10−13 s. An extended SME is constructed, accounting for the memory effect of the dipole–dipole Hamiltonian dynamics. The influence of memory on the interpretation of experiments is discussed.

  • 10.
    Håkansson, Pär
    et al.
    Umeå University, Faculty of Medicine, Department of Medical Biochemistry and Biophysics.
    Westlund, Per-Olof
    Umeå University, Faculty of Medicine, Department of Medical Biochemistry and Biophysics.
    Lindahl, Erik
    Edholm, Olle
    A direct simulation of EPR slow-motion spectra of spin labelled phospholipids in liquid crystalline bilayers based on a molecular dynamics simulation of the lipid dynamics2001In: Physical Chemistry, Chemical Physics - PCCP, ISSN 1463-9076, E-ISSN 1463-9084, Vol. 3, no 23, p. 5311-5319Article in journal (Refereed)
    Abstract [en]

    EPR line shapes can be calculated from the stochastic Liouville equation assuming a stochastic model for the reorientation of the spin probe. Here we use instead and for the first time a detailed molecular dynamics (MD) simulation to generate the stochastic input to the Langevin form of the Liouville equation. A 0.1 μs MD simulation at T = 50°C of a small lipid bilayer formed by 64 dipalmitoylphosphatidylcholine (DPPC) molecules at the water content of 23 water molecules per lipid was used. In addition, a 10 ns simulation of a 16 times larger system consisting of 32 DPPC molecules with a nitroxide spin moiety attached at the sixth position of the sn2 chain and 992 ordinary DPPC molecules, was used to investigate the extent of the perturbation caused by the spin probe. Order parameters, reorientational dynamics and the EPR FID curve were calculated for spin probe molecules and ordinary DPPC molecules. The timescale of the electron spin relaxation for a spin-moiety attached at the sixth carbon position of a DPPC lipid molecule is 11.9 × 107 rad s−1 and for an unperturbed DPPC molecule it is 3.5 × 107 rad s−1.

  • 11.
    Isaksson, Mikael
    et al.
    Umeå University, Faculty of Science and Technology, Chemistry.
    Norlin, Nils
    Umeå University, Faculty of Science and Technology, Chemistry.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Chemistry.
    Johansson, Lennart B-Å
    Umeå University, Faculty of Science and Technology, Chemistry.
    On the quantitative molecular analysis of electronic energy transfer within donor–acceptor pairs2007In: Physical Chemistry, Chemical Physics - PCCP, ISSN 1463-9076, E-ISSN 1463-9084, Vol. 9, p. 1941-51Article in journal (Refereed)
    Abstract [en]

    An extended Förster theory (EFT) on electronic energy transfer is presented for the quantitative analysis of time-resolved fluorescence lifetime and depolarisation experiments. The EFT, which was derived from the stochastic Liouville equation, yields microscopic information concerning the reorientation correlation times, the order parameters, as well as inter chromophoric distances. Weakly interacting donor and acceptor groups, which reorient and interact in a pair wise fashion, are considered, under isotropic and anisotropic conditions. For the analysis of experiments it is shown that not only do we need to consider the orientational distributions of the transition dipoles, but the internal reorienting molecular dynamics within the pair which is of even greater importance. The latter determines the shape as well as the rate of the observed donor fluorescence and depolarisation decays, which are most often not mono-exponential functions. It is shown that the commonly used Förster theory is a special case of the EFT. Strategies are presented for applying the EFT, which makes use of Brownian dynamics simulation.

  • 12.
    Jonsson, Sofi
    et al.
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Skyllberg, Ulf
    Department of Forest Ecology and Management, Swedish University of Agricultural Sciences, Umeå, Sweden.
    Nilsson, Mats B
    Department of Forest Ecology and Management, Swedish University of Agricultural Sciences, Umeå, Sweden.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Shchukarev, Andrey
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Lundberg, Erik
    Umeå University, Faculty of Science and Technology, Umeå Marine Sciences Centre (UMF).
    Björn, Erik
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Mercury methylation rates for geochemically relevant HgII species in sediments2012In: Environmental Science and Technology, ISSN 0013-936X, E-ISSN 1520-5851, Vol. 46, no 21, p. 11653-11659Article in journal (Refereed)
    Abstract [en]

    Monomethylmercury (MeHg) in fish from freshwater, estuarine and marine environments are a major global environmental issue. Mercury levels in biota are mainly controlled by the methylation of inorganic mercuric mercury (HgII) to MeHg in water, sediments and soils. There is, however, a knowledge gap concerning the mechanisms and rates of methylation of specific geochemical HgII species. Such information is crucial for a better understanding of variations in MeHg concentrations among ecosystems and, in particular, for predicting the outcome of currently proposed measures to mitigate mercury emissions and reduce MeHg concentrations in fish. To fill this knowledge gap we propose an experimental approach using HgII isotope tracers, with defined and geochemically important adsorbed and solid HgII forms in sediments, to study MeHg formation. We report HgII methylation rate constants, km, in estuarine sediments which span over two orders of magnitude depending on chemical form of added tracer: metacinnabar (β-201HgS(s)) < cinnabar (α-199HgS(s)) < HgII reacted with mackinawite (≡FeS-202HgII) < HgII bonded to natural organic matter (NOM-196HgII) < a typical aqueous tracer (198Hg(NO3)2(aq)). We conclude that a combination of thermodynamic and kinetic effects of HgII solid-phase dissolution and surface desorption control the HgII methylation rate in sediments and causes the large observed differences in km-values. The selection of relevant solid-phase and surface adsorbed HgII tracers will therefore be crucial to achieving biogeochemically accurate estimates of ambient HgII methylation rates.

  • 13. Kowalewski, J
    et al.
    Egorov, A
    Kruk, D
    Laaksonen, A
    Nikkhou Aski, S
    Parigi, G
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Chemistry.
    Extensive NMRD studies of Ni(II) salt solutions in water and water-glycerol mixtures2008In: Journal of Magnetic Resonance, Vol. 195, no 1, p. 103-11Article in journal (Refereed)
    Abstract [en]

    Aqueous solutions of simple nickel(II) salts are a classical test case for theories of the paramagnetic relaxation enhancement (PRE) and its dependence on the magnetic field (nuclear magnetic relaxation dispersion, NMRD), going back to late fifties. We present here new experimental data, extending the NMRD range up to 21 T (900 MHz). In addition to salt solutions in (acidified) water, we have also measured on solutions containing glycerol. The aqueous solution data do not show any significant changes compared to the earlier experiments. The interpretation, based on the general ("slow-motion") theory is also similar to the earlier work from our laboratory. The NMRD-data in mixed solvents are qualitatively different, indicating that the glycerol not only changes the solution viscosity, but may also enter the first coordination sphere of the metal ion, resulting in lower symmetry complexes, characterized by non-vanishing averaged zero-field splitting. This hypothesis is corroborated by molecular dynamics simulations. A strategy appropriate for interpreting the NMRD-data for the chemically complicated systems of this type is proposed.

  • 14. Kruk, Danuta
    et al.
    Kowalewski, Jozef
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Chemistry.
    Nuclear and electron spin relaxation in paramagnetic complexes in solution: Effects of the quantum nature of molecular vibrations2004In: The Journal of Chemical Physics, Vol. 121, no 5, p. 2215-27Article in journal (Refereed)
    Abstract [en]

    A model of the paramagnetic relaxation enhancement is developed in terms of electron-spin relaxation caused by the zero-field splitting (ZFS) fluctuating in time due to a coupling between the electron-spin variables and quantum vibrations. The ZFS interaction provides a coupling between the electron-spin variables and vibrational degrees of freedom, and is represented as a Taylor series expansion in a set of vibrational modes (normal coordinates). A two-level harmonic oscillator subsystem is assumed, and the electron-spin relaxation associated with T2V and T1V vibrational relaxation is considered. The description of vibrationally induced electron-spin dynamics is incorporated into the calculations of the paramagnetic relaxation enhancement by the Solomon–Bloembergen–Morgan approach as well as in the framework of the general slow-motion theory. The theoretical predictions are compared with the experimental paramagnetic relaxation enhancement values for the Ni(H2O) complex in aqueous solution. The parameters required by the model are obtained from quantum chemical and molecular dynamics studies. Comparison is made between the current model and its recently published classical counterpart.

  • 15. Larsson, Per Tomas
    et al.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Chemistry.
    Line shapes in CP/MAS 13C NMR spectra of cellulose I2005In: Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, Vol. 62, no 1-3, p. 539-46Article in journal (Refereed)
    Abstract [en]

    The CP/MAS 13C NMR line shape of cellulose I has been qualitatively analyzed by direct simulations using the Ornstein–Uhlenbeck stochastic process and the Kubo model. Both approaches describe a anhydroglucose C4 carbon as a oscillator with fluctuating Larmor frequency. The NMR resonance frequency is written , where the fluctuating part with zero mean was modelled as a stationary Markov diffusion process.

    The simulation results both motivates the use of multiple line shapes when fitting CP/MAS 13C NMR spectra recorded on cellulose I and gives some insights into why signals from crystalline cellulose I give rise to Lorentzian line shapes.

  • 16.
    Lindgren, Matteus
    et al.
    Umeå University, Faculty of Science and Technology, Chemistry.
    Laaksonen, Aatto
    Stockholms universitet, Avdelningen för fysikalisk kemi.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Chemistry.
    A theoretical spin relaxation and molecular dynamics simulation study of the Gd(H2O)93+ complex2009In: Physical Chemistry, Chemical Physics - PCCP, ISSN 1463-9076, E-ISSN 1463-9084, Vol. 11, p. 10368-76Article in journal (Refereed)
    Abstract [en]

    A theoretical analysis of the paramagnetically enhanced water proton spin–lattice relaxation of a hydrated Gd3+ ion is combined with Molecular Dynamics (MD) simulations. The electron–proton dipole–dipole correlation function, CDDp(), as well as the pseudo-rotation (PR) model of the transient zero-field splitting (ZFS) are evaluated with the help of the data from MD simulations. The fast local water motion in the first hydration shell, i.e. the wagging and rocking motions, is found not to change the mono exponential character of the dipole correlation function CDDp(), but is important in the time dependence of the transient ZFS interaction.The dynamics of the transient ZFS interaction is modeled as the water-induced electric field gradient tensor at the site of the metal ion. This approach follows the ideas of the pseudo-rotation model, describing the fluctuating zero-field interaction as a constant amplitude in the principal frame but reorienting according to a rotational diffusion equation of motion. The MD results indicate that the pseudo-rotation model gives a multi-exponential correlation function which oscillates at short times and is described by three exponential terms. The time scale is shorter than previously assumed but contain an intermediate time constant (1–2 ps). The electron spin resonance (ESR) spectral width at half height at frequencies of X-band, Q-band, 75 MHz, 150 MHz and 225 MHz can be reproduced at 320 K without any contributions from 4th or 6th rank ZFS interactions. Consequently, there are two mutually inconsistent dynamic models of the ZFS interaction which can describe the water proton T1-NMRD (nuclear magnetic resonance dispersion) profile and the field dependent ESR spectra of the hydrated Gd(III) complex equally well.

     

  • 17.
    Lindgren, Matteus
    et al.
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Sparrman, Tobias
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    A combined molecular dynamic simulation and Urea 14N NMR relaxation study of the Urea - lysozyme system2010In: Spectrochimica Acta Part A - Molecular and Biomolecular Spectroscopy, ISSN 1386-1425, E-ISSN 1873-3557, Vol. 75, no 3, p. 953-9Article in journal (Refereed)
    Abstract [en]

    Urea in the lysozyme solvation shell has been studied by utilizing a combination of urea , water NMR relaxation experiments and a molecular dynamics simulation of the urea–lysozyme system. Samples with lysozyme in the native fold in water as well as in 3 M urea have been studied, as well as denatured lysozyme in a 8.5 M urea solvent. The spin relaxation rates of the samples with folded protein show a clear field dependence, which is consistent with a few urea molecules having long residence times on the protein surface and preferentially located in pockets and grooves on the protein. By combining the 3 M urea NMR relaxation data and data from the MD simulation, a full parameter set of the relaxation model is found which can successfully predict the experimental relaxation rates of the 3 M urea sample. However, in the parameter fitting it is evident that the rotational dynamics of urea in the MD simulation is slightly too fast to be consistent with the NMR relaxation rates, perhaps a result of the fast dynamics of the TIP3P water model. The relaxation rates of urea in the proximity of the unfolded lysozyme lack field dependence, which can be interpreted as a loss of pockets and grooves on the denatured protein. The extracted model parameters from the 3 M sample are adjusted and tested on a simple model of the unfolded protein sample and are seen to be in agreement with the relaxation rates. It is shown that the combination of NMR relaxation and MD simulations can be used to create a microscopic picture of the solvent at the protein interface, which can be used for example in the study of chemical denaturation.

  • 18.
    Lindgren, Matteus
    et al.
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    On the stability of chymotrypsin inhibitor 2 in a 10 M urea solution: the role of interaction energies for urea-induced protein denaturation2010In: Physical Chemistry, Chemical Physics - PCCP, ISSN 1463-9076, E-ISSN 1463-9084, Vol. 12, no 32, p. 9358-9366Article in journal (Refereed)
    Abstract [en]

    Molecular dynamics simulations of chymotrypsin inhibitor 2 in both water and in 10 M urea have been compared with respect to the energies of interaction between protein and solvent. The analysis yield clear and detailed information regarding the enthalpic driving force of urea-induced protein denaturation. The protein is kept in the folded structure by applying positional restraints on the alpha-carbons, thereby creating an equilibrium system from which appropriate driving forces for denaturation can be obtained. All protein atoms are classified as belonging to the backbone, the polar side chains or to the hydrophobic side chains. The interaction energies are extracted for each class separately. The commonly proposed mechanisms of urea denaturation, i.e. that urea interacts mainly with the backbone or with the hydrophobic side chains, can then be tested. The results show that urea decreases the Lennard-Jones interaction energies between protein and solvent by a large amount. The electrostatic energies are almost unaffected by the switch of solvent. The energetically favorable interaction between CI2 and the urea solvent will function as a driving force for the protein to increase its solvent accessible surface area as compared to the folded protein in water. The magnitude of the decrease in the Lennard-Jones energies for the hydrophobic and the hydrophilic side chains and for the backbone were similar. We therefore conclude that urea interacts favorably with the whole protein surface and that all parts of the protein are important in urea-induced denaturation.

  • 19.
    Lindgren, Matteus
    et al.
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    The affect of urea on the kinetics of local unfolding processes in chymotrypsin inhibitor 22010In: Biophysical Chemistry, ISSN 0301-4622, E-ISSN 1873-4200, Vol. 151, no 1-2, p. 46-53Article in journal (Refereed)
    Abstract [en]

    The dynamics of chymotrypsin inhibitor 2 (CI2) in water, as well as in 10M urea, have been studied by Molecular Dynamics simulations. The analysis aims at investigating how local protein processes are affected by urea and how the perturbation by urea on the local level manifests itself in the kinetics of the global unfolding. The results show that the effect of urea on local processes depends upon the type of process at hand. An isolated two-residue contact on the surface of CI2 has a decreased frequency of rupture in the urea solvent. This is in contrast to the increased frequency of rupture of the hydrogen bonds in secondary structure elements in the urea solvent. It is proposed that the increase in the unfolding rates of complex protein processes is based upon the retardation of the refolding rate of small scale, isolated processes.

  • 20.
    Lindgren, Matteus
    et al.
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    The molecular mechanism of urea denaturation2012In: Advances in Chemistry Research: Volume 11 / [ed] James C. Taylor, Nova Science Publishers, Inc., 2012Chapter in book (Refereed)
    Abstract [en]

    Proteins are known to denature in high concentrations of compounds such as urea or guanidinium chloride. However, the mechanism by which urea and guanidinium chloride destabilizes proteins is not yet known, despite many decades of reasearch. Attempts have been made to understand protein denaturation on a thermodynamic level as well as on a molecular level. The long term goal in the field is to merge the results of these two types of studies into one mechanism that covers both the microscopic and the macroscopic level. In this text we firstly review thermodynamic studies as well as spectroscopic and computer simulation studies of chemical denaturation. The results of the different types of studies is then merged together in order to find a consistent view on chemical denaturation. In contrast to common belief in the field, a high degree of consensus is found between the different studies and a molecular mechanism of urea-induced protein denaturation can therefore be proposed.

  • 21.
    Norlin, Nils
    et al.
    Umeå University, Faculty of Science and Technology, Chemistry.
    Håkansson, Per
    Umeå University, Faculty of Science and Technology, Chemistry.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Chemistry.
    Johansson, Lennart B-Å
    Umeå University, Faculty of Science and Technology, Chemistry.
    Extended Förster theory for determining intraprotein distances: Part III. Partial donor–donor energy migration among reorienting fluorophores2008In: Physical Chemistry Chemical Physics, Vol. 10, p. 6962-70Article in journal (Refereed)
    Abstract [en]

    An extended Förster theory (EFT) is derived and outlined for electronic energy migration between two fluorescent molecules which are chemically identical, but photophysically non-identical. These molecules exhibit identical absorption and fluorescence spectra, while their fluorescence lifetimes differ. The latter means that the excitation probability becomes irreversible. Unlike the case of equal lifetimes, which is often referred to as, donor–donor energy migration (DDEM), the observed fluorescence relaxation is then no longer invariant to the energy migration process. To distinguish, the present case is therefore referred to as partial donor–donor energy migration (PDDEM). The EFT of PPDEM is described by a stochastic master equation (SME), which has been derived from the stochastic Liouville equation (SLE) of motion. The SME accounts for the reorienting as well as the translational motions of the interacting chromophores. Synthetic fluorescence lifetime and depolarisation data that mimics time-correlated single photon counting experiments have been generated and re-analysed. The rates of reorientation, as well as the orientational configurations of the interacting D-groups were examined. Moreover the EFT of PPDEM overcomes the classical 2-problem and the frequently applied approximation of 2 = 2/3 in the data analyses. An outline for the analyses of fluorescence lifetime and depolarisation data is also given, which might prove applicable to structural studies of D-labelled macromolecules, e.g. proteins. The EFT presented here brings the analyses of PDDEM data to the same level of molecular detail as that used in ESR- and NMR-spectroscopy.

  • 22.
    Norlin, Nils
    et al.
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Johansson, Lennart B-Å
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Fluorescence spectroscopic properties analysed within the extended Förster theory with application to Biomacromolecular systems2009In: Journal of Fluorescence, ISSN 1053-0509, E-ISSN 1573-4994, Vol. 19, no 5, p. 837-845Article in journal (Refereed)
    Abstract [en]

    The extended Förster theory (EFT) of electronic energy transport accounts for translational and rotational dynamics, which are neglected by the classical Förster theory (FT). EFT has been developed for electronic energy transfer within donor-acceptor pairs [Isaksson, et al, Phys. 16 Chem. Chem. Phys., 9, 1941(2007)] and donor-donor pairs [Johansson, et al, J. Chem. Phys., 105, 10896 (1996); Norlin, et al, Phys. Chem. Chem. Phys., 10, 6962(2008)]. For donors that exhibit different or identical non-exponential fluorescence relaxation within a donor-donor pair, the process of reverberating energy migration is reversible to a higher or lower degree. Here the impact of the EFT has been studied with respect to its influence on fluorescence quantum yields, fluorescence lifetimes as well as depolarisation experiments. The FT predicts relative fluorescence quantum yields which usually agree with the EFT within experimental accuracy, however, substantial deviations occurs in the steady-state and in particular the time-resolved depolarisation data. 

  • 23.
    Sparrman, Tobias
    et al.
    Umeå University, Faculty of Science and Technology, Chemistry.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Chemistry.
    An NMR line shape and relaxation analysis of heavy water powder spectra of the L, L and P phases in the DPPC/water system2003In: Physical Chemistry Chemical Physics, Vol. 5, p. 2114-21Article in journal (Refereed)
    Abstract [en]

    The 2H2O NMR powder line shapes and relaxation times, T1 and T2, of the liquid crystal L, the intermediate P and the gel L phases of dipalmitoylphosphatidylcholine (DPPC)/2H2O-system are analysed. The water structure and dynamics of the lipid/water interfaces of DPPC in the hydration regime, where all water molecules are associated to the interface, are described in terms of orientational order parameters and correlation times. The line shape of the ripple phase (P) is analysed assuming model parameters of the gel or liquid crystalline phase. The narrow line shape of the ripple phase is partly due to an extra average of the quadrupole interaction because of lateral diffusion along the curved surface, reducing the splitting with a factor 0.5–0.2 depending on the nature of the curved ripple surface. However, more importantly, an extra reduction of the quadrupole splitting may be due to the same reorganization of water, among bound sites with different signs of the order parameter, which also explains the increase in the quadrupole splitting with temperature observed in the liquid crystalline phase. The linewidths in 14N MAS NMR spectra clearly indicate slow dynamics of the polar headgroup in the ripple phase. The results indicate that the headgroup hydrations of the ripple and liquid crystalline phases are similar, while the acyl chains are still in their gel state in the ripple phase. The increased headgroup area introduces a stress, as confirmed by the slow headgroup dynamics, which causes the bilayer to curve in the ripple phase.

  • 24.
    Sparrman, Tobias
    et al.
    Umeå University, Faculty of Science and Technology, Chemistry.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Chemistry.
    H-2 NMR relaxation and line shape analysis of water in a lamellar liquid crystalline phase formed by dodecyldimethylamineoxide (DDAO) and (H2O)-H-22001In: JOURNAL OF PHYSICAL CHEMISTRY B, ISSN 1520-6106, Vol. 105, no 50, p. 12524-8Article in journal (Refereed)
    Abstract [en]

    Present study combines NMR relaxation and line shape analysis for heavy water in the lamellar liquid crystalline phase of DDAO/(2)-H2O, NMR spin-lattice, spin-spin relaxation times and the quadrupole splitting are measured at two temperatures and three different water contents in the hydration regime. A molecular picture of water hydration of the DDAO/(2)-H2O interface is extracted, which indicates a much more rapid water translational diffusion along the detergent interface, as compared to phospholipid interfaces. The local order and dynamics of the bound water are, however, not changing much between the two interfaces. This indicates, that local interactions of water with the headgroup are not much dependent on the actual phase or detergent system. This work also presents clear experimental evidence for a dip at the magic angle of the H-2 powder spectrum, as theoretically predicted. Raising the temperature removes this observed dip at the isotropic frequency. This corresponds to an increase in the correlation time tau (c) from 8.5 ns at 25 degreesC to 20 ns at 55 degreesC, where tau (c) is related to translational dynamics of water along the detergent/water interface. However, this counter-intuitive increase in tau (c) with temperature may be interpreted as a reorganization of water at the interface, as is further supported by increasing quadrupolar splittings with increasing temperature.

  • 25. Usova, N
    et al.
    Persson, L
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Chemistry.
    Theory of slow-motion EPR lineshapes for studies of membrane curvature2000In: PHYSICAL CHEMISTRY CHEMICAL PHYSICS, ISSN 1463-9076, Vol. 2, no 12, p. 2785-93Article in journal (Refereed)
    Abstract [en]

    The direct calculation method of slow-motion EPR spectra is presented based on the stochastic Liouville equation in the Langevin form, using the trajectories of Brownian dynamics (BD) simulations. We have developed a model of EPR slow-motion lineshapes describing a probe molecule residing in a curved bilayer system. Two dynamic processes are active: one is local reorientation motion of the lipid chain, and the second is the lateral diffusion of the spin probe along the curved lipid bilayer surface. The trajectories of two independent BD simulations are combined in order to describe the stochastic fluctuation of the electron spin-lattice Hamiltonian. The method of obtaining the Langevin equation describing lateral diffusion from the diffusion equation is discussed in detail. We solve the stochastic Liouville-von Neumann equation in the semiclassical approximation. EPR slow-motion lineshapes are obtained together with electron spin correlation functions. The synthesis of classical simulation methods and the lineshape model is illustrated by calculating a number of curvature dependent EPR lineshapes. Two curved model surfaces are considered namely the rippled z=a sin(bx) surface and the so called "Baltic Sea" z=a[sin(bx)+sin(by)].

  • 26.
    Wennerström, Håkan
    et al.
    Division of Physical Chemistry, University of Lund.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    On Stern‐Gerlach coincidence measurements and their application to Bell's theorem2013In: Physics essays, ISSN 0836-1398, Vol. 26, no 2, p. 174-180Article in journal (Refereed)
    Abstract [en]

    We analyze a coincidence Stern-Gerlach measurement often discussed in connection with the derivation and illustration of Bell's theorem. The treatment is based on our recent analysis of the original Stern-Gerlach experiment (PCCP, 14, 1677‐1684 (2012)), where it is concluded that it is necessary to include a spin relaxation process to account for the experimental observations. We consider two limiting cases of a coincidence measurement using both an analytical and a numerical description. In on limit relaxation effects are neglected. In this case the correlation between the two spins present in the initial state is conserved during the passage through the magnets. However, at exit the z coordinate along the magnetic field gradient is randomly distributed between the two extreme values. In the other limit T2 relaxation is assumed to be fast relative to the time of flight through the magnet. In this case the z coordinate takes one of two possible values as observed in the original Stern‐Gerlach experiment. Due to the presence of a relaxation process involving transfer of angular momentum between particle and magnet the initially entangled spin state changes character leading to a loss of correlation between the two spins. In the original derivations of Bell's theorem based on a coincidence Stern‐Gerlach setup one assumes both a perfect correlation between the spins and only two possible values for the z‐coordinate on exit. According to the present calculations one can satisfy either of these conditions but not both simultaneously.

  • 27.
    Wennerström, Håkan
    et al.
    Division of Physical Chemistry, Chemical Center, P.O. Box 124, University of Lund, SE 22100 Lund, Sweden.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    The Stern-Gerlach experiment and the effects of spin relaxation2012In: Physical Chemistry, Chemical Physics - PCCP, ISSN 1463-9076, E-ISSN 1463-9084, Vol. 14, p. 1677-1684Article in journal (Refereed)
    Abstract [en]

    The classical Stern-Gerlach experiment is analyzed with an emphasis on the spin dynamics. The central question asked is whether there occurs a relaxation of the spin angular momentum during the time the particle passes through the Stern-Gerlach magnet. We examine in particular the transverse relaxation, involving angular momentum exchange between the spin of the particles and the spins of the magnet. A method is presented describing relaxation effects at an individual particle level. This leads to a stochastic equation of motion for the spins. This is coupled to a classical equation of motion for the particle translation. The experimental situation is then modeled through simulations of individual trajectories using two sets of parameter choices and three different sets of initial conditions. The two main conclusions are: (A) if the coupling between the magnet and the spin is solely described by the Zeeman interaction with the average magnetic field the simulations show a clear disagreement with the experimental observation of Stern and Gerlach. (B) If one, on the other hand, also allows for a T(2) relaxation time shorter than the passage time one can obtain a practically quantitative agreement with the experimental observations. These conclusions are at variance with the standard textbook explanation of the Stern-Gerlach experiment.

  • 28.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Chemistry.
    Line shape analysis of NMR powder spectra of (H2O)-H-2 in lipid bilayer systems2000In: JOURNAL OF PHYSICAL CHEMISTRY B, Vol. 104, no 25, p. 6059-64Article in journal (Refereed)
    Abstract [en]

    A NMR line shape/spin relaxation model is developed for (H2O)-H-2 studies of structure and dynamics of the lipid-water interfaces of phosphatidylcholine bilayers. A line shape function describing the orientational dependence of (H2O)-H-2 is derived. In addition, also expressions of the observed quadrupole splitting and the spin-lattice relaxation rate are derived within the same dynamic model. The model comprises two chemically interchanging fractions of water namely, "free", and "bound". There are four molecular parameters characterizing the "bound" water of the lipid water interface, namely, (1) the fraction water molecules bound to lipid molecules, (2) the local water order parameter S-0(Pd), (3) the order parameter S-0(dD) which describes the averaged "bound" water, and an effective correlation time (4) tau(c), characterizing water translational diffusion at the interface. This model allows for analyzing quadrupole splittings, spin-lattice relaxation rates, and water powder line shapes. Thus, dynamics as well as structural information about the water molecules residing in the water lipid interface may be extracted. In the reinterpretation of (H2O)-H-2 powder spectra obtained for lamellar phases of dipalmitoylphosphatidylcholine (DPPC), the results clearly indicate that S-0(dD)(L-alpha) > S-0(dD)(L-beta') when comparing the liquid crystalline phase with 10-11 water molecules per lipid molecule and the gel phase with 3.5-4.2 water molecules per lipid molecule. Whereas the order of the perturbed water is similar in both phases, S-0(Pd)(L-alpha) approximate to S-0(Pd)(L-beta'). The lateral diffusion is characterized by a correlation time tau(c) > 60 ns but cannot be determined without measuring the spin-lattice relaxation measurements.

  • 29.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Quadrupole-enhanced proton spin relaxation for a slow reorienting spin pair: (I)-(S). A stochastic Liouville approach2009In: Molecular Physics, ISSN 0026-8976, E-ISSN 1362-3028, Vol. 107, no 20, p. 2141-8Article in journal (Refereed)
    Abstract [en]

    The field dependence of the proton (I) spin-lattice relaxation rate is calculated for a dipole-dipole coupled spin pair, (I = 1/2) - (S = 1), where the quadrupole nucleus (S) is 2H or 14N with asymmetry parameter η = 0. The observed relaxation profile shows a marked enhancement for equal proton Larmor and quadrupole spin frequencies (i.e. ωI = ωQ). This phenomenon is referred to as the quadrupole dip, and has been observed, for instance, in 14N-1H amide groups of immobilized proteins. In this work, an analysis of the observed relaxation enhancement is presented when the dipole-dipole coupling and the quadrupole interaction are modulated by the overall re-orientational motion. A characteristic low field dispersion is observed when (3/2) τRωI ≥ 1, where τR is the rotational correlation time and ωI is the proton Larmor frequency. At higher fields, the relaxation peak exhibits a Lorentzian-like line shape,  , which is centred at the quadrupole frequency. The quadrupole spin system shows a spin-lattice T1Q and a spin-spin relaxation time T2Q that become equal in the zero field limit. In the slow tumbling limit, the quadrupole spin relaxation times, T1Q, T2Q, are equal to (3/2)τR.

  • 30.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Chemistry.
    The quadrupole enhanced (1)H spin-lattice relaxation of the amide proton in slow tumbling proteins2010In: Physical Chemistry, Chemical Physics - PCCP, ISSN 1463-9076, E-ISSN 1463-9084, Vol. 12, no 13, p. 3136-40Article in journal (Refereed)
    Abstract [en]

    An analysis, based on the stochastic Liouville approach, is presented of the R(1)-NMRD or field dependent spin-lattice relaxation rate of amide protons. The proton relaxivity, displayed as R(1)-NMRD profiles, is calculated for a reorienting (1)H-(14)N spin group, where the inter spin coupling is due to spin dipole-dipole coupling or the scalar coupling. The quadrupole nucleus (14)N has an asymmetry parameter eta = 0.4 and a quadrupole interaction which is modulated by the overall reorientational motion of the protein. In the very slow reorientational regime, omega(Q)tau(R)>> 1 and tau(R)>/= 2.0 mus, both the dipole-dipole coupling and the scalar coupling yield a T(1)-NMRD profile with three marked peaks of proton spin relaxation enhancement. These peaks appear when the proton Larmor frequency, omega(I), matches the nuclear quadrupole spin transition frequencies: omega(1) = omega(Q)2eta/3, omega(2) = omega(Q)(1 -eta/3) and omega(3) = omega(Q)(1 + eta/3), and the quadrupole spin system thus acts as a relaxation sink. The relative relaxation enhancements of the peaks are different for the dipole-dipole and the scalar coupling. Considering the dipole-dipole coupling, the low frequency peak, omega(1), is small compared to the high field peaks whereas for the scalar coupling the situation is changed. For slow tumbling proteins with a correlation time of tau(R) = 400 ns, omega(2) and omega(3) are not resolved but become one relatively broad peak. At even faster reorientation, tau(R) < 60 ns, the marked peaks disappear. In this motional regime, the main effect of the cross relaxation phenomenon is a subtle perturbation of the main amide proton T(1) NMRD dispersion. The low field part of it can be approximately described by a Lorentzian function: R(DD,SC)(0.01)/(1 + (omega(I)tau(R)3/2)(2)) whereas the high field part coincides with R(DD,SC)(0.01)/(1 + (omega(I)tau(R))(2)).

  • 31.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Theoretical reason for the lack of influence of 1H–14N cross-relaxation on the water proton T 1 NMRD profile in slow tumbling proteins2012In: Molecular Physics, ISSN 0026-8976, E-ISSN 1362-3028, Vol. 110, no 18, p. 2251-2255Article in journal (Refereed)
    Abstract [en]

    For immobilized protein the water proton T 1-NMRD profile displays three enhanced relaxation peaks (QP). For slow tumbling proteins these relaxation peaks are not experimentally observed. However, the theoretically determined QP effect on the amide proton T 1-NMRD profile displays a distorted Lorentzian dispersion profile. The question arises as to whether there is also a distortion of the water-proton T 1-NMRD profile due to QP. The model of Sunde and Halle [J. Magn. Reson. 203, 257 (2010)] predicts a decreasing QP relaxation contribution and, with the aid of a model for tumbling proteins [P.-O. Westlund, Phys. Chem. Chem. Phys, 12, 3136 (2010)], it is shown that the QP effect is absent in water-proton T 1-NMRD profiles for slow tumbling proteins with τR < 1 µs, τI.

  • 32.
    Westlund, Per-Olof
    et al.
    Umeå University, Faculty of Science and Technology, Chemistry.
    Wennerstrom, H.
    Photon emission from translational energy in atomic collisions: A dynamic Casimir-Polder effect2005In: PHYSICAL REVIEW A, ISSN 1050-2947, Vol. A 71, no 062106, p. 1-5Article in journal (Refereed)
    Abstract [en]

    It is demonstrated, using a Liouville formalism, that the relative motion of two atoms can result in the emission of photons and conversely that photons can be absorbed to excite the relative translational motion. The mechanism responsible for the energy transfer between the radiation field and the translational motion of the atoms is a dynamic version of the long-range Casimir-Polder interaction between two fixed atoms. The phenomenon is analogous to the dynamic Casimir effect discussed for moving macro- (or meso)scopic objects and we term it the dynamic Casimir-Polder effect. The absorption or emission is a two-photon process and we find that the transition probability is proportional to the spectral density of a correlation function involving the relative translational motion of two atoms. An energy transfer only occurs for photons with energies smaller than or of the same magnitude as the thermal energy. The effect provides a microscopic mechanism for establishing thermal equilibrium between the radiation field and a gas. A sufficiently large volume of gas would be perceived as a black-body radiator. Applications of the dynamic Casimir-Polder effect might be found in the microscopic description of the cosmic low-temperature black-body radiation.

  • 33.
    Westlund, Per-Olof
    et al.
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Wennerström, Håkan
    Division of Physical Chemistry, Chemical Center, Lund University.
    Electron spin relaxation at low field2010In: Physical Chemistry, Chemical Physics - PCCP, ISSN 1463-9076, E-ISSN 1463-9084, Vol. 12, no 1, p. 201-206Article in journal (Refereed)
    Abstract [en]

    The low field ESR lineshape and the electron spin-lattice relaxation correlation function are calculated using the stochastic Liouville theory for an effective electron spin quantum number S = 1. When an axially symmetric permanent zero field splitting provides the dominant relaxation mechanism, and when it is much larger than the rotational diffusion constant, it is shown that both electron spin correlation functions S(0)S(t) (n = 0,1) are characterized by the same relaxation time tau(S) = (4D(R))(-1). This confirms the conjectures made by Schaefle and Sharp, J. Chem. Phys., 2004, 121, 5287 and by Fries and Belorizky, J. Chem. Phys., 2005, 123, 124510, based on numerical results using a different formalism. The stochastic Liouville approach also gives the paramagnetically enhanced nuclear spin relaxation time constants, T(1) and T(2), and the ESR lineshape function I(omega). In particular, the L-band (B(0) = 0.035 T) ESR spectrum of a low symmetry Ni(ii)-complex with a cylindrical ZFS tensor is shown to be detectable at sufficiently slowly reorientation of the complex. The analysis shows that the L-band spectrum becomes similar to the zero-field spectrum with a electron spin relaxation time tau(S) = (4D(R))(-1).

  • 34.
    Zhou, Xiangzhi
    et al.
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Caravan, Peter
    Clarkson, R B
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    On the philosophy of optimizing contrast agents: an analysis of 1H NMRD profiles and ESR lineshapes of the Gd(III)complex MS-325 + HSA2004In: Journal of magnetic resonance, ISSN 1090-7807, E-ISSN 1096-0856, Vol. 167, no 1, p. 147-160Article in journal (Refereed)
    Abstract [en]

    A generalization of the modified SBM theory is developed in closed analytical form. The theory is applied to describe the paramagnetically enhanced water proton spin–lattice relaxation rates of the aqueous-systems containing a gadolinium(S=7/2) complex(MS-325) in the presence or absence of human serum albumin (HSA). MS-325 binds to HSA: in the absence of the protein the reorientational time, τR, is short, but when HSA is added τR becomes much longer. In this way, the effect of reorientational motion, static (Δs), and transient (Δt) zero-field splitting (ZFS) interactions on both the water proton relaxivity and the Gd ESR lineshapes are investigated.

    Two dynamic models of electron spin relaxation are presented, characterized by transient and static ZFS-interactions. X-, Q-, and W-bands ESR spectra of MS-325+HSA are analyzed in order to describe the effect on the electron spin system upon binding to a macromolecule. A computer program based on this theory is developed which calculates solvent water proton T1 NMRD profiles and the corresponding X-, Q-, U-, and W-bands ESR lineshapes.

  • 35.
    Zhou, Xiangzhi
    et al.
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    1H NMRD profiles and ESR lineshapes of Gd(III) complexes: a comparison between the generalized SBM and the stochastic Liouville approach2005In: Journal of magnetic resonance, ISSN 1090-7807, E-ISSN 1096-0856, Vol. 173, no 1, p. 75-83Article in journal (Refereed)
    Abstract [en]

    A complete description of the T1-NMRD profiles and the ESR lineshape of Gd(III) complexes (S = 7/2) was presented using second-order perturbation theory (GSBM) by Zhou et al. [J. Magn. Reson. 167 (2004) 147]. This report compares the GSBM with the stochastic Liouville approach (SLA) to determine the validity of the closed analytical expressions of NMRD and the ESR lineshape functions. Both approaches give the same results at high fields while a very small divergence is observed for X- and W-band ESR lineshapes when the magnitude of the perturbation term times the correlation time approaches the limit of the perturbation regime, ΔZFSτf ≈ 0.1. There was a clear discrepancy between the theoretical GSBM X-band spectrum and the recorded ESR spectrum of the Gd(III) MS-325 + HSA complex. This is probably due to a slow-motion effect caused by a slow modulation of the ZFS interaction. The characteristic correlation time of this slow modulation is in the range of 150 ps, which therefore cannot be due to the reorientational motion of the whole MS-325 + HSA complex.

  • 36.
    Zhou, Xiangzhi
    et al.
    Umeå University, Faculty of Science and Technology, Chemistry.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Chemistry.
    The viscosity and temperature dependence of 1H T1-NMRD of the Gd(H2O)83+ complex2005In: Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, Vol. 62, no 1-3, p. 335-42Article in journal (Refereed)
    Abstract [en]

    Water proton T1-NMRD profiles of the Gd(H2O)83+ complex have been recorded at three temperatures and at four concentrations of glycerol. The analysis is performed using both the generalized Solomon–Bloembergen–Morgan (GSBM) theory [J. Magn. Reson. 167(2004), 147–160], and the stochastic Liouville approach (SLA). The GSBM approach uses a two processes dynamic model of the zero-field splitting (ZFS) correlation function whereas SLA uses a single process model. Both models reproduce the proton T1-NMRD profiles well. However, the model parameters extracted from the two analyses, yield different ESR X-band spectra which moreover do not reproduce the experimental ESR spectra. It is shown that the analyses of the proton T1-NMRD profiles recorded for a solution Gd(H2O)83+ ions are relatively insensitive to the slow modulation part of dynamic model of the ZFS interaction correlation function. The description of the electron spin system results in a very small static ZFS, while recent ESR lineshape analysis indicates that the contribution from the static ZFS is important. Analysis of proton T1-NMRD profiles of Gd(H2O)83+ complex do result in a description of the electron spin system but these microscopic parameters are uncertain unless they also are tested in a ESR-lineshape analysis.

  • 37.
    Zhou, Xiangzhi
    et al.
    Umeå University, Faculty of Science and Technology, Chemistry.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Chemistry.
    The viscosity and temperature dependence of X-band ESR lineshapes of Gd(III) aqueous complex2005In: Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, Vol. 62, no 1-3, p. 76-82Article in journal (Refereed)
    Abstract [en]

    X-band ESR spectra of Gd-aqua complex in various weight concentration of glycerol have been recorded at four temperatures. The interpretation of the ESR linewidth is preformed using both the stochastic Liouville approach (SLA) and a perturbation theory. The SLA uses a one dynamic model of the zero-field splitting whereas the perturbation approach uses a two dynamic model. Both models can reproduce the variation of the linewidth with respect to viscosity. In the SLA model, both the zero-field splitting (ZFS) interaction and the correlation time vary with the glycerol content. In the two dynamic perturbation model, only the correlation times are viscosity dependent. The two models give different NMRD profiles.

  • 38.
    Åman, Ken
    et al.
    Umeå University, Faculty of Science and Technology, Chemistry.
    Hakansson, Pär
    Umeå University, Faculty of Science and Technology, Chemistry.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Chemistry.
    A general approach to the calculation of (H2O)-H-2 NMR lineshapes in microheterogeneous systems: a distorted bicontinuous cubic phase2005In: PHYSICAL CHEMISTRY CHEMICAL PHYSICS, ISSN 1463-9076, Vol. 7, no 7, p. 1394-1401Article in journal (Refereed)
    Abstract [en]

    A new computational method is developed for calculating H-2 NMR lineshapes of H2O in microheterogeneous systems, such as lyotropic liquid crystals that exhibit curved lipid/water interfaces. The method presented is based on the stochastic Liouville equation (SLE) in its Langevin form. This means that the Liouville equation of motion is combined with Brownian dynamics simulations to describe the stochastic spin - lattice Liouvillian. The NMR relaxation is caused by translational diffusion of the heavy water molecules, along the curved (H2O)-H-2/lipid interface. The model used is a nodal surface approximation of the cubic symmetric gyroid minimal surface. This unit cell is then isotropically expanded or distorted in two dimension. The changes in (H2O)-H-2 NMR lineshapes have been calculated for the enlarged or the distorted cubic unit cell. The timescale of the residual quadrupole interaction, which determines the NMR lineshape, ranges from the Redfield regime to the slow-motional regime depending on the curvature of the interface. The distortion of the cubic phase illustrates the possibility to explore the intermediate interfaces of a phase transition, by means of (H2O)-H-2 lineshape analysis.

  • 39.
    Åman, Ken
    et al.
    Umeå University, Faculty of Science and Technology, Chemistry.
    Lindahl, Erik
    Edholm, Olle
    Håkansson, Pär
    Umeå University, Faculty of Science and Technology, Chemistry.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Chemistry.
    Structure and Dynamics of Interfacial Water in an L Phase Lipid Bilayer from Molecular Dynamics Simulations2003In: Biophysical Journal, Vol. 84, p. 102-15Article in journal (Refereed)
    Abstract [en]

    Based on molecular dynamics simulations, an analysis of structure and dynamics is performed on interfacial water at a liquid crystalline dipalmitoylphosphatidycholine/water system. Water properties relevant for understanding NMR relaxation are emphasized. The first and second rank orientational order parameters of the water O–H bonds were calculated, where the second rank order parameter is in agreement with experimental determined quadrupolar splittings. Also, two different interfacial water regions (bound water regions) are revealed with respect to different signs of the second rank order parameter. The water reorientation correlation function reveals a mixture of fast and slow decaying parts. The fast (ps) part of the correlation function is due to local anisotropic water reorientation whereas the much slower part is due to more complicated processes including lateral diffusion along the interface and chemical exchange between free and bound water molecules. The 100-ns-long molecular dynamics simulation at constant pressure (1 atm) and at a temperature of 50°C of 64 lipid molecules and 64 x 23 water molecules lack a slow water reorientation correlation component in the ns time scale. The 2H2O powder spectrum of the dipalmitoylphosphatidycholine/water system is narrow and consequently, the NMR relaxation time T2 is too short compared to experimental results.

  • 40.
    Åman, Ken
    et al.
    Umeå University, Faculty of Science and Technology, Chemistry.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Chemistry.
    Direct calculation of (H2O)-H-1 T-1 NMRD profiles and EPR lineshapes for the electron spin quantum numbers S=1, 3/2, 2, 5/2, 3, 7/2, based on the stochastic Liouville equation combined with Brownian dynamics simulation2007In: PHYSICAL CHEMISTRY CHEMICAL PHYSICS, ISSN 1463-9076, Vol. 9, no 6, p. 691-700Article in journal (Refereed)
    Abstract [en]

    Direct calculation of electron spin relaxation and EPR lineshapes, based on Brownian dynamics simulation techniques and the stochastic Liouville equation approach (SLE-L) [Mol. Phys., 2004, 102, 1085-1093], is here generalized to high spin systems with spin quantum number S = 3/2, 2, 5/2, 3 and 7/2. A direct calculation method is demonstrated for electron spin-spin and spin-lattice relaxation, S-, X- and Q-band EPR-lineshapes and paramagnetic enhanced water proton T1- NMRD profiles. The main relaxation mechanism for the electron spin system is a stochastic second rank zero field splitting (ZFS). Brownian dynamics simulation techniques are used in describing a fluctuating ZFS interaction which comprises two parts namely the permanent part which is modulated by isotropic reorientation diffusion, and the transient part which is modulated by fast local distortion, which is also modelled by the isotropic rotation diffusion model. The SLE-L approach present is applicable both in the perturbation (Redfield) regime as well as outside the perturbation regime, in the so called slow motion regime.

  • 41.
    Åman, Ken
    et al.
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Westlund, Per-Olof
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    The Electron Spin Relaxation and Paramagnetic Relaxation Enhancement: an Application of the Stochastic Liouville Equation in the Langevin Form2004In: Molecular Physics, ISSN 0026-8976, E-ISSN 1362-3028, Vol. 102, no 9-10, p. 1085-1093Article in journal (Refereed)
    Abstract [en]

    A novel theoretical approach, based on the stochastic Liouville equation (SLE) in its Langevin form, is developed to describe paramagnetic relaxation enhancement (PRE). This approach is more applicable to different dynamic models than the old slow-motion theory which was based on the SLE in the operator or Fokker-Planck form. Moreover, the SLE in the Langevin form supplies a detailed description of the electron spin relaxation in the time domain. This new approach is applied to the analysis of the T1-NMRD profile of water protons in Ni2+(H2O)6.

1 - 41 of 41
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