1,721,007 research outputs found
A many-body stochastic approach to rotational motions in liquids - A reassessment of the Hubbard-Einstein relation
No full textA multidimensional Fokker-Planck-Kramers equation for rotational relaxation of small solutes in complex liquids is developed wherein collective solvent effects are explicitly represented by rotating torques and stochastic fields. A simplified version of the model is applied to interpret the breakdown of the Hubbard-Einstein relation at high viscosities
SLOW MOTIONAL ESR IN COMPLEX FLUIDS - THE SLOWLY RELAXING LOCAL-STRUCTURE MODEL OF SOLVENT CAGE EFFECTS
No full textA detailed formulation is presented for the analysis of slow motional ESR in terms of the reorientation of the probe molecule within a dynamic solvent cage. This formulation is appropriate for isotropic and ordered fluids. The solvent cage is modeled in terms of a set of collective variables that represent the instantaneous solvent structure around the probe and that reorient on a slower time scale than the probe. This ''slowly relaxing local structure'' model is incorporated into an augmented stochastic Liouville equation that is solved by efficient computational means which enables nonlinear least squares fitting to experimental spectra. This formulation is applied to some recent slow motional ESR spectra obtained at 250 GHz. Such high-frequency ESR spectra have been shown to be particularly sensitive to the microscopic details of the molecular reorientational process. Significant improvements are found in fitting the ESR spectra for the cases studied, viz., perdeuterated 2,2,6,6-tetramethyl-4-piperidone (PDT) in toluene and 3-doxylcholestane (CSL) in o-terphenyl (OTP), a glass-forming liquid, when compared to a model of simple Brownian reorientation. In both cases the cage is found to relax at least 1 order of magnitude slower than the probe itself, and it provides a potential for probe reorientation on the order of 2-7 k(B)T. The cage potential for the PDT case is characterized by minima at more than one orientational angle, allowing for jump-type reorientations between such minima superimposed on substantial local motions suggestive of earlier simulations based on a simple jump model. For CSL in OTP, weak negative ordering is found, consistent with an oblate-shaped local structure provided by the OTP solvent molecules. These examples illustrate the potential of utilizing high-frequency slow motional ESR to discern details of solvent interactions associated with molecular reorientations in fluids
A many-body stochastic approach to rotational motions in liquids
No full textAn analysis is performed on several stochastic models for rotational relaxation of rigid molecules in complex liquids
ESR studies of 0−2 adsorbed on Ti supported surfaces: Analysis of motional dynamics
No full textTemperature‐dependent ESR spectra of O−2 adsorbed on Ti ions supported on porous Vycor glass were observed over the range 4.2 to 400 °K. These spectra were obtained under normal high vacuum conditions as well as under UHV conditions (P⩽10−9 Torr) and are very well resolved. It was observed that the line position of the g tensor component that is perpendicular to the internuclear axis of O−2 remained constant with temperature, whereas the other two components of the g tensor shift in position with temperature, and are accompanied by drastic line shape changes. This observation indicates that the molecular motion of O−2 on the surface is highly anisotropic, consisting essentially of planar rotation about the axis perpendicular to the internuclear axis of O−2 and parallel to the normal to the surface. Furthermore, the observation of nonequivalent 17O hfs of O−2 suggests that the internuclear axis of O−2 might be tilted slightly from the surface and/or one oxygen is closer to the Ti4+. The ESR line shapes were simulated for the different possible models: Brownian diffusion, jump diffusion (from weak jump to strong jump), approximate free diffusion, and discrete jump. It was found that the theoretical spectra calculated using the model of weak jump rotational diffusion best fit the observed spectra in the temperature range below 57.4 °K. However, in the temperature range above 57.4 °K, although the Brownian diffusion model seems the best among the models used, none of the present models used could successfully reproduce the observed line shapes. The rotational correlation time τR∥ was found to range between 10−5 sec (below 14.5 °K) and 10−9 sec (263 °K). The values of τR∥ depend strongly on the model used in the lower temperature range, but were essentially independent of model above 100 °K. The activation energy for rotational diffusion was estimated to be 0.5 kcal/mole above 100 °K. The line shape below 15 °K is independent of temperature, although the O−2 spectrum appears to exhibit residual motional effects. This observation suggests that coherent quantum mechanical motion is predominant below 15 °K. This matter is discussed in some detail, and the appropriate theory to investigate quantum effects on the motional dynamics is outlined including possible isotope effects on the motion. Spectral observation of possible interaction between C2H4 and O−2 on the surface is presented. Also discussed are the techniques for preparing samples with strong well‐resolved signals and for removing the other types of O−2 signals, which do not show significant temperature‐dependent spectral change
Protein dynamics from NMR: The slowly relaxing local structure analysis compared with model-free analysis
No full text15N−1H spin relaxation is a powerful method for deriving information on protein dynamics. The traditional method of data analysis is model-free (MF), where the global and local N−H motions are independent and the local geometry is simplified. The common MF analysis consists of fitting single-field data. The results are typically field-dependent, and multifield data cannot be fit with standard fitting schemes. Cases where known functional dynamics has not been detected by MF were identified by us and others. Recently we applied to spin relaxation in proteins the slowly relaxing local structure (SRLS) approach, which accounts rigorously for mode mixing and general features of local geometry. SRLS was shown to yield MF in appropriate asymptotic limits. We found that the experimental spectral density corresponds quite well to the SRLS spectral density. The MF formulas are often used outside of their validity ranges, allowing small data sets to be force-fitted with good statistics but inaccurate best-fit parameters. This paper focuses on the mechanism of force-fitting and its implications. It is shown that MF analysis force-fits the experimental data because mode mixing, the rhombic symmetry of the local ordering and general features of local geometry are not accounted for. Combined multifield multitemperature data analyzed with the MF approach may lead to the detection of incorrect phenomena, and conformational entropy derived from MF order parameters may be highly inaccurate. On the other hand, fitting to more appropriate models can yield consistent physically insightful information. This requires that the complexity of the theoretical spectral densities matches the integrity of the experimental data. As shown herein, the SRLS spectral densities comply with this requirement
An improved picture of methyl dynamics in proteins from slowly relaxing local structure analysis of H-2 spin relaxation
No full textProtein dynamics is intimately related to biological function. Core dynamics is usually studied with 2H spin relaxation of the 13CDH2 group, analyzed traditionally with the model-free (MF) approach. We showed recently that MF is oversimplified in several respects. This includes the assumption that the local motion of the dynamic probe and the global motion of the protein are decoupled, the local geometry is simple, and the local ordering is axially symmetric. Because of these simplifications MF has yielded a puzzling picture where the methyl rotation axis is moving rapidly with amplitudes ranging from nearly complete disorder to nearly complete order in tightly packed protein cores. Our conclusions emerged from applying to methyl dynamics in proteins the slowly relaxing local structure (SRLS) approach of Polimeno and Freed (Polimeno, A.; Freed, J. H. J. Phys. Chem. 1995, 99, 10995−11006.), which can be considered the generalization of MF, with all the simplifications mentioned above removed. The SRLS picture derived here for the B1 immunoglobulin binding domain of peptostreptococcal protein L, studied over the temperature range of 15−45 °C, is fundamentally different from the MF picture. Thus, methyl dynamics is characterized structurally by rhombic local potentials with varying symmetries and dynamically by tenfold slower rates of local motion. On average, potential rhombicity decreases, mode-coupling increases, and the rate of local motion increases with increasing temperature. The average activation energy for local motion is 2.0 ± 0.2 kcal/mol. Mode-coupling affects the analysis even at 15 °C. The accuracy of the results is improved by including in the experimental data set relaxation rates associated with rank 2 coherences
Rotational-dynamics of axially-symmetrical solutes in isotropic liquids .1. A collective cage description from molecular-dynamics simulations
No full textAn operational definition of collective cage variables previously introduced for liquid argon is extended, via a molecular dynamics study, to the rotational properties of axially symmetric molecules. Quantitative measures of the static and dynamic cage properties are extracted for liquid Cl2 near the triple point. The collective cage variables are well described by the potential acting on an arbitrary molecule (i.e. solute) for a fixed configuration of the other molecules (i.e. solvent). A dynamic separability of the solute orientation relative to the cage potential and of the relative solute displacement is justified in part by the faster relaxation found for the latter. Large and persistent orientational cage potentials (∼15–20 kBT) lead to substantial alignment of the solute in the cage with an average local order parameter of 0.87. The reorientational correlation times for the cage are consistent with axially symmetric Brownian motion. The reorientational correlation times for the solute are nearly equal to the equivalent ones of the cage, consistent with the strong coupling of solute within its cage which leads to a collective reorientation of solute and cage (e.g. τcage(2)=1.4 ps, and τsolute(2)=1.2 ps). Solute librations within the cage are much faster (τ libr(2)=0.12 ps) and are comparable to the relaxation of the relative solute displacements (τr=0.15 ps). The solute angular momentum exhibits the fastest correlation time (τ J=0.06 ps). While the orientational cage potential shows rapidly and slowly relaxing components (τωf=0.14 ps and τωs=2.87 ps, respectively), its dominant portion shows a very long persistence
Comment on "The physical basis of model-free analysis of NMR relaxation data from proteins and complex fluids" [J. Chem. Phys. 131, 224507 (2009)]
No full textStructural dynamics of bio-macromolecules by NMR: The slowly relaxing local structure approach
No full textProtein dynamics by NMR has been reviewed extensively in recent years. These surveys show decisively that information on structure should be complemented by information on motion both to properly characterize the protein, and to understand its function. The time scale accessible by NMR extends from picoseconds to days, with different methods accessing different parts of this time axis. Here we focus on heteronuclear NMR spin relaxation used to study ps to ns protein dynamics. The slow limit of this time regime is determined by the global tumbling of the protein, with the rates for internal motion of the probe being typically faster.
Based on experience gained over nearly a decade we came to the conclusion that the traditional method of NMR spin relaxation analysis in proteins and nucleic acids, called “model-free” (MF), does not extract adequately and fully the information inherent in the experimental data largely because it is oversimplified. We have developed an approach that overcomes many of the MF deficiencies. This method, called the slowly relaxing local structure (SRLS) may be regarded as a generalization of MF. SRLS predates the MF approach, and even provided derivations of the exact equivalents of the MF equations .
The issues brought up above will be addressed in detail in this review. It will be shown that analogous, but physically distinct, SRLS and MF analyses often yield substantially different results, indicating that the oversimplifications inherent in MF have unfavorable practical implications. Within a broader perspective, we illustrate the disadvantages of applying parameterization instead of setting forth models, using mathematical instead of physical parameter definitions, and not abiding by the assumptions underlying the various equations used. We offer the concepts that underlie SRLS as an alternative to the model-free point-of-view, and we describe and illustrate how SRLS can be implemented in a practical fashion. We also indicate how improvements to the current SRLS approach can be introduced
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