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Papers by Eva Meirovitch

The Journal of Physical Chemistry, Dec 1, 1982

ESR spectra of deoxycholic acid channel type inclusion compounds doped with 2,2,5,5-tetramethyl-3... more ESR spectra of deoxycholic acid channel type inclusion compounds doped with 2,2,5,5-tetramethyl-3-carbamidopyrrolinyl-1-oxy1 (Tempyo) and 2,2,6,6-tetramethylpiperidinyl-l-oxyl-4-ol (Tanol) free radicals were recorded as a function of temperature, radical concentration, and photochemically triggering UV irradiation. At room temperature the spin probes are immobile and isotropically dispersed within the channels. Onset of isotropic molecular reorientation is observed upon increasing the temperature to 50-70 "C and nearly complete motional averaging is achieved between 120 and 140 "C with activation energies of the order of 6-8 kcal/mol. For 5-30% molar enrichment of the guest with the paramagnetic dopant, second-order rate constants for bimolecular encounters of 1.65 X lov M-' s-l at 130 "C and a related activation energy of 5 kcal/mol are measured from concentrdtion-dependent spin exchange effects on the ESR line shape. Clustering is observed for radical concentrations relative to the guest of the order of 0.2 M. With acetophenone as guest we find that, following the photochemical reaction between host and guest, the rate for rotational reorientation and the rate constant for bimolecular encounters are slowed down considerably.

Israel Journal of Chemistry, Jan 23, 2014

Journal of Physical Chemistry B, Aug 24, 2018

We have developed the microscopic-order-macroscopic-disorder (MOMD) approach for studying interna... more We have developed the microscopic-order-macroscopic-disorder (MOMD) approach for studying internal mobility in polycrystalline proteins with 2 H lineshape analysis. The motion itself is expressed by a diffusion tensor, R, the local spatial restraints by a potential, u, and the "local geometry" by the relative orientation of the model-related and NMR-related tensors. Here, we apply MOMD to phenyl-ring dynamics in several Aβ 40-amyloid-fibrils, and the villin headpiece subdomain (HP36). Because the available data are limited in extent and sensitivity, we adjust u and R in the relevant parameter ranges, fixing the "local geometry" in accordance with standard stereochemistry. This yields a physically well-defined and consistent picture of phenyl-ring dynamics enabling comparison between different systems. In the temperature-range of 278-308 K, u has strength of (1.7-1.8) kT and rhombicity of (2.4-2.6) kT, and R has components of 5.0×10 2 ≤ R ⊥ ≤ 2.0×10 3 s −1 and 6.3×10 5 ≤ R || ≤ 2.0×10 6 s −1. At 278 K fibril hydration increases the axiality of both u and R; HP36 hydration has a similar effect at 295 K, reducing R ⊥ considerably. The D23N mutation slows down the motion of the probe; Aβ 40 polymorphism affects both this motion and the related local potential. The present study identifies the impact of various factors on phenyl-ring mobility in amyloid fibrils and globular proteins; the difference between the two protein forms is considerable. The distinctive impact of hydration on phenyl-ring motion and previously-studied methyl-group motion is also examined. The 2 H lineshapes considered here were analyzed previously with various multi-simple-mode (MSM) models, where several simple motional modes are combined. The MOMD and MSM interpretations differ in essence.

Solid State Nuclear Magnetic Resonance, Feb 1, 2018

We report on a new approach to the analysis of dynamic NMR lineshapes from polycrystalline (i.e.,... more We report on a new approach to the analysis of dynamic NMR lineshapes from polycrystalline (i.e., macroscopically disordered) samples in the presence of Magic Angle Spinning (MAS). This is an application of the Stochastic Liouville Equation developed by Freed and co-workers for treating restricted (i.e., microscopically ordered) motions. The 2 H nucleus in an internally-mobile C-CD 3 moiety serves as a prototype probe. The acronym is 2 H/MOMD/MAS, where MOMD stands for "microscopic-order-macroscopic-disorder." The key elements describing internal motions-their type, the local spatial restrictions, and related features of local geometry-are treated in MOMD generally, within their rigorous three-dimensional tensorial requirements. Based on this representation a single physically well-defined model of local motion has the capability of reproducing experimental spectra. There exist other methods for analyzing dynamic 2 H/MAS spectra which advocate simple motional modes. Yet, to reproduce satisfactorily the experimental lineshapes, one has either to use unusual parameter values, or combine several simple motional modes. The multi-simple-mode reasoning assumes independence of the constituent modes, features ambiguity as different simple modes may be used, renders inter-system comparison difficult as the overall models differ, and makes possible model-improvement only by adding yet another simple mode, i.e., changing the overall model. 2 H/MOMD/MAS is free of such limitations and inherently provides a clear physical interpretation. These features are illustrated. The advantage of 2 H/MOMD/MAS in dealing with sensitive but hardly investigated slow-motional lineshapes is demonstrated by applying it to actual experimental data. The results differ from those obtained previously with a two-site exchange scheme that yielded unusual parameters.

Journal of Physical Chemistry B, Feb 5, 2022

We have developed the stochastic microscopic-order-macroscopic-disorder (MOMD) approach for eluci... more We have developed the stochastic microscopic-order-macroscopic-disorder (MOMD) approach for elucidating dynamic structures in the solid-state from 2H NMR lineshapes. In MOMD, the probe experiences an effective/collective motional mode. The latter is described by a potential, u, which represents the local spatial-restrictions, a local-motional diffusion tensor, R, and key features of local geometry. Previously we applied MOMD to the well-structured core domain of the 3-fold-symmetric twisted polymorph of the Aβ40-amyloid fibril. Here, we apply it to the N-terminal domain of this fibril. We find that the dynamic structures of the two domains are largely similar but differ in the magnitude and complexity of the key physical parameters. This interpretation differs from previous multisimple-mode (MSM) interpretations of the same experimental data. MSM used for the two domains different combinations of simple motional modes taken to be independent. For the core domain, MOMD and MSM disagree on the character of the dynamic structure. For the N-terminal domain, they even disagree on whether this chain segment is structurally ordered (MOMD finds that it is), and whether it undergoes a phase transition at 260 K where bulklike water located in the fibril matrix freezes (MOMD finds that it does not). These are major differences associated with an important system. While the MOMD description is a physically sound one, there are drawbacks in the MSM descriptions. The results obtained in this study promote our understanding of the dynamic structure of protein aggregates. Thus, they contribute to the effort to pharmacologically control neurodegenerative disorders believed to be caused by such aggregates.

The Journal of Physical Chemistry, Jun 1, 1984

We report on a line-shape study of angular-dependent ESR spectra from uniform samples of spin-pro... more We report on a line-shape study of angular-dependent ESR spectra from uniform samples of spin-probe-doped supercooled phase V. Experiments were performed at-50 OC, a temperature at which the liquid-crystalline director stops reorienting along the magnetic field of the ESR spectrometer, smectic-type layering sets in, and the paramagnetic dopants are immobile. Typical ESR spectra, generated by different functional forms of the spatial distribution of molecular orientations, are associated with distinct sites for locating additives, the main distinguishing qualifiers being the nature of the dynamic mode experienced by the probe at higher temperatures and the extent of solute-solvent interactive coupling. This study highlights the potential use of anisotropic rigid-limit ESR spectra to determine the spatial molecular distribution. It may have direct implications on the phenomenon of monotropic formation of liquid-crystalline mesophases.

The Journal of Physical Chemistry, May 1, 1985

Journal of Physical Chemistry B, May 17, 2012

Residual dipolar couplings (RDCs) in proteins arise from independent external medium-related and ... more Residual dipolar couplings (RDCs) in proteins arise from independent external medium-related and internal protein-related ordering of the spin-bearing probe. Griesinger et al. developed a method for treating RDCs in proteins. The global ordering is given in the standard manner by a rank 2 tensor specified in a known molecular frame, MF. The local ordering is described by the spherical harmonic ensemble averages, ⟨Y 2m (θ, φ)⟩, m = 0, ±1, ±2, also given in MF. From these quantities, a method we call mf-RDC derives the squared generalized order parameter (S rdc 2), the amplitude (direction) of the anisotropic disorder, η (Φ̅ ′), and an approximation, (N−H) eff , to the average probe orientation, i.e., to the local director. (N−H) eff is determined through a frame transformation where ⟨Y 20 ⟩ is maximized. Φ̅ ′ is associated with a subsequent frame transformation where ⟨Y 22 + Y 2−2 ⟩ is maximized. The mf-RDC method was applied previously to N−H and C−C methyl sites in ubiquitin. In this study, we convert the respective ⟨Y 2m (θ, φ)⟩'s into a Saupe tensor, which is diagonalized. This is the standard procedure. It yields the eigenvalues, S xx , S yy , and S zz , and the Principal Axis System (PAS) of the rank 2 local ordering tensor, S l. S rdc 2 , η, and Φ̅ ′ can be recast as S xx , S yy , and S zz. The mf-RDC frame transformations are not the same as the conventional Wigner rotation. The standard tensorial analysis provides new information. The contribution of local ordering rhombicity to S rdc 2 is evaluated. For the α-helix of ubiquitin, the main local ordering axis is assigned as C i−1 α − C i α ; for the methyl sites, it is associated with the C−C methyl axis, as in mf-RDC. Ordering strength correlates with methyl type. The strength (rhombicity) of S l associated with picosecond−nanosecond local motions is reduced moderately (substantially) by nanosecond−millisecond local motions. A scheme for analyzing experimental RDCs based on the standard tensorial perspective, which allows for arbitrary orientation of the local director in the protein and of the PAS of S l in the probe, is formulated.

Journal of Physical Chemistry B, Jan 5, 2012

Physical review, 1977

We have investigated elastic deformations by external magnetic fields in flat samples of smectic-... more We have investigated elastic deformations by external magnetic fields in flat samples of smectic-C with fixed boundary conditions. In the calculations the internal parameters {tilt angle, density, interlayer distance) are assumed to be fixed, distortions of the smectic layers are neglected, and only reorientations of the director about the normal to the smectic layers are allowed. The problem is solved exactly assuming a one-dimensional variation of the order parameter. Stability conditions and explicit expressions for the orientation of the director as a function of position are derived for general orientations of the magnetic field. Solutions of the variational problem can be classified according to the maximum deviation angle, 4, of the director. In general there are several separated allowed regions of 4. When Freedericksz transitions occur, they are usually discontinuous first-order transitions. The properties of the solutions are discussed and some special examples are considered in detail. Transitions are investigated both as a function of the magnitude and of the orientation of the magnetic field. Expressions for the free energy are also derived.

Journal of Computational Chemistry, Jan 30, 1997

... Efficiency of monte carlo minimization procedures and their use in analysis of NMR data obtai... more ... Efficiency of monte carlo minimization procedures and their use in analysis of NMR data obtained from flexible peptides. Hagai Meirovitch,; Eva Meirovitch. Article first published online: 7 DEC 1998. ... Res. Inst. (DOE). Grant Number: DE-FC05-35ER250000; Doe. ...

Biopolymers, 1996

Under certain experimental conditions peptide solutions can generate sufficient NMR data for stru... more Under certain experimental conditions peptide solutions can generate sufficient NMR data for structure determination. Yet, unlike proteins, peptides typically prevail as ensembles of interconverting structures, and therefore, the experimental variables (which are intensities of cross peaks in nuclear Overhauser enhancement spectroscopy (NOESY) spectra, or NOEs) are average quantities. The process of structure elucidation is complex, and many related questions are still open to debate. We have developed a new theoretical methodology for treating ensembles of interconverting conformations which is based on purely thermodynamic grounds. The peptide is described by a potential energy function, and its conformational space is viewed as a collection of microstates, which are local conformational regions around energy minima. The overall methodology enables one to identify the thermodynamically most stable microstates, determine their populations, calculate the individual microstate NOEs, and obtain the overall NOEs as averages over the individual contributions, weighted by the microstate populations. In this paper we develop for the first time theoretical methods for calculating the relative contribution of microstates to the partition function, as their minimum energy is increased above the global energy minimum (GEM). This is necessary for determining which microstates should be considered in detail in the next stage of the analysis. The new methods presented herein are applied to the pentapeptide Leu-enkephalin (H-Tyr-Gly-Gly-Phe-Leu-OH) described by the potential energy function ECEPP, with calculations carried out at 280 K. We find that the microstates contained within relatively small ranges of 2 to 3 kcal/mol above the GEM (or above the lowest harmonic free energy) constitute 0.59 to 0.75 of the partition function. This should be compared with energy ranges up to 15 kcaymol set arbitrarily in previous studies. A detailed comparison of theoretical predictions with experimental data, obtained from a cryoprotective Leu-enkephalin solution at 280 K, will be carried out in the next paper of this series.

The Journal of Physical Chemistry, 2012

Residual dipolar couplings (RDCs) in proteins arise from independent external medium-related and ... more Residual dipolar couplings (RDCs) in proteins arise from independent external medium-related and internal protein-related ordering of the spin-bearing probe. Griesinger et al. developed a method for treating RDCs in proteins. The global ordering is given in the standard manner by a rank 2 tensor specified in a known molecular frame, MF. The local ordering is described by the spherical harmonic ensemble averages, ⟨Y 2m (θ, φ)⟩, m = 0, ±1, ±2, also given in MF. From these quantities, a method we call mf-RDC derives the squared generalized order parameter (S rdc 2), the amplitude (direction) of the anisotropic disorder, η (Φ̅ ′), and an approximation, (N−H) eff , to the average probe orientation, i.e., to the local director. (N−H) eff is determined through a frame transformation where ⟨Y 20 ⟩ is maximized. Φ̅ ′ is associated with a subsequent frame transformation where ⟨Y 22 + Y 2−2 ⟩ is maximized. The mf-RDC method was applied previously to N−H and C−C methyl sites in ubiquitin. In this study, we convert the respective ⟨Y 2m (θ, φ)⟩'s into a Saupe tensor, which is diagonalized. This is the standard procedure. It yields the eigenvalues, S xx , S yy , and S zz , and the Principal Axis System (PAS) of the rank 2 local ordering tensor, S l. S rdc 2 , η, and Φ̅ ′ can be recast as S xx , S yy , and S zz. The mf-RDC frame transformations are not the same as the conventional Wigner rotation. The standard tensorial analysis provides new information. The contribution of local ordering rhombicity to S rdc 2 is evaluated. For the α-helix of ubiquitin, the main local ordering axis is assigned as C i−1 α − C i α ; for the methyl sites, it is associated with the C−C methyl axis, as in mf-RDC. Ordering strength correlates with methyl type. The strength (rhombicity) of S l associated with picosecond−nanosecond local motions is reduced moderately (substantially) by nanosecond−millisecond local motions. A scheme for analyzing experimental RDCs based on the standard tensorial perspective, which allows for arbitrary orientation of the local director in the protein and of the PAS of S l in the probe, is formulated.

The Journal of Physical Chemistry, 2012

Chemischer Informationsdienst, Oct 9, 1984

The Journal of Physical Chemistry, Oct 1, 1982

We report on temperature-and angular-dependent ESR spectra of two types of nitroxide-labeled fatt... more We report on temperature-and angular-dependent ESR spectra of two types of nitroxide-labeled fatty acid chains, the commonly used but sterically bulky doxyl nitroxides and the recently prepared "minimum steric perturbation" azethoxyl nitroxides, dissolved in various liquid crystalline phases. The main spectral feature examined was the effective hyperfine splitting of the nitroxide radical, which in almost all cases was found to exceed the isotropic value of this parameter. The interpretation of this result in terms of deviations from an extended-chain conformation is shown to be unique with the azethoxyls and ambiguous with the doxyls, as it is based on the inherent geometric molecular feature 8, the tilt angle of the free-electron a orbital relative to the main chain axis. In the various mesophases studied, 0 was found to range from 30' to 50°, as compared to 60° for an extended chain. Use of azethoxyl probes, rather than doxyl probes, in addressing questions related to the conformation of flexible chains in locally ordered media is thus suggested, for with the azethoxyl probes valuable information is available before detailed line-shape analysis.

The Journal of Physical Chemistry, Sep 1, 1984

The Journal of Physical Chemistry, Sep 1, 1984

We report on a careful line-shape study of ESR spectra from the smectic Ad phase of S2 doped with... more We report on a careful line-shape study of ESR spectra from the smectic Ad phase of S2 doped with the common doxyl and the "minimum-perturbation" azethoxyl nitroxides, with the NO group attached at the midchain region. The primary goal of this investigation is to address unresolved questions related to chain conformation, dynamics, and local ordering in anisotropic solvents, as reflected in the spin relaxation of the above-mentioned paramagnetic hydrocarbons. We find that the NO groups of both doxyl and azethoxyl nitroxides experience similar, relatively low, and only slightly temperature-dependent local ordering. On the other hand, both motional and conformational properties of the two types of spin probes are at variance. Thus, the azethoxyl nitroxides reorient at average rates of roughly 2.0 X lo7 s-' at the lower end of the smectic Ad phase, which are about twice higher than the reorientational rates of the doxyl analogues at similar temperatures. Azethoxyl nitroxides reorient basically as individual particles whereas with doxyl nitroxides, we detect substantial dynamic coupling to collective modes of the liquid-crystalline solvent. The doxyl chains were found to be fully extended whereas the azethoxyl chains bent. We discuss the unique value of slow-motional ESR in complementing information obtained previously with both NMR and ESR in the motional-narrowing regime.

The Journal of Physical Chemistry, Jun 1, 1984

ESR spectra of five nitroxide spin probes dissolved in the discotic mesophase of hexakis(hexy1oxy... more ESR spectra of five nitroxide spin probes dissolved in the discotic mesophase of hexakis(hexy1oxy)triphenylene (THE6) were measured as function of temperature in the mesophase region. The different spin probes exhibit a variety of line shapes and temperature dependencies. The results could be explained in terms of the existence of two solvation sites for the probe molecules. These sites are assumed to correspond to (I) probe molecules intercalated within the columnar structures of the discotic mesophase and (11) probe molecules dissolved in the aliphatic region between the columns. In one case (CSL) the experimental results actually exhibited distinct spectra due to two solvation sites. The other spin probes gave simpler spectra but their temperature dependence was unusual and could in general be interpreted in terms of fast dynamic equilibrium between the two solvation sites.

The Journal of Physical Chemistry, Jun 1, 1994

A simple and efficient method for searching the conformational space of macromolecules is present... more A simple and efficient method for searching the conformational space of macromolecules is presented. With this method an initial set of relatively low-energy structures is generated, and their energies are further minimized with a procedure that enables escaping from local energy minima. Illustrative calculations are described for Met-and Leu-enkephalin.

The Journal of Physical Chemistry, Dec 1, 1982

ESR spectra of deoxycholic acid channel type inclusion compounds doped with 2,2,5,5-tetramethyl-3... more ESR spectra of deoxycholic acid channel type inclusion compounds doped with 2,2,5,5-tetramethyl-3-carbamidopyrrolinyl-1-oxy1 (Tempyo) and 2,2,6,6-tetramethylpiperidinyl-l-oxyl-4-ol (Tanol) free radicals were recorded as a function of temperature, radical concentration, and photochemically triggering UV irradiation. At room temperature the spin probes are immobile and isotropically dispersed within the channels. Onset of isotropic molecular reorientation is observed upon increasing the temperature to 50-70 "C and nearly complete motional averaging is achieved between 120 and 140 "C with activation energies of the order of 6-8 kcal/mol. For 5-30% molar enrichment of the guest with the paramagnetic dopant, second-order rate constants for bimolecular encounters of 1.65 X lov M-' s-l at 130 "C and a related activation energy of 5 kcal/mol are measured from concentrdtion-dependent spin exchange effects on the ESR line shape. Clustering is observed for radical concentrations relative to the guest of the order of 0.2 M. With acetophenone as guest we find that, following the photochemical reaction between host and guest, the rate for rotational reorientation and the rate constant for bimolecular encounters are slowed down considerably.

Israel Journal of Chemistry, Jan 23, 2014

Journal of Physical Chemistry B, Aug 24, 2018

We have developed the microscopic-order-macroscopic-disorder (MOMD) approach for studying interna... more We have developed the microscopic-order-macroscopic-disorder (MOMD) approach for studying internal mobility in polycrystalline proteins with 2 H lineshape analysis. The motion itself is expressed by a diffusion tensor, R, the local spatial restraints by a potential, u, and the "local geometry" by the relative orientation of the model-related and NMR-related tensors. Here, we apply MOMD to phenyl-ring dynamics in several Aβ 40-amyloid-fibrils, and the villin headpiece subdomain (HP36). Because the available data are limited in extent and sensitivity, we adjust u and R in the relevant parameter ranges, fixing the "local geometry" in accordance with standard stereochemistry. This yields a physically well-defined and consistent picture of phenyl-ring dynamics enabling comparison between different systems. In the temperature-range of 278-308 K, u has strength of (1.7-1.8) kT and rhombicity of (2.4-2.6) kT, and R has components of 5.0×10 2 ≤ R ⊥ ≤ 2.0×10 3 s −1 and 6.3×10 5 ≤ R || ≤ 2.0×10 6 s −1. At 278 K fibril hydration increases the axiality of both u and R; HP36 hydration has a similar effect at 295 K, reducing R ⊥ considerably. The D23N mutation slows down the motion of the probe; Aβ 40 polymorphism affects both this motion and the related local potential. The present study identifies the impact of various factors on phenyl-ring mobility in amyloid fibrils and globular proteins; the difference between the two protein forms is considerable. The distinctive impact of hydration on phenyl-ring motion and previously-studied methyl-group motion is also examined. The 2 H lineshapes considered here were analyzed previously with various multi-simple-mode (MSM) models, where several simple motional modes are combined. The MOMD and MSM interpretations differ in essence.

Solid State Nuclear Magnetic Resonance, Feb 1, 2018

We report on a new approach to the analysis of dynamic NMR lineshapes from polycrystalline (i.e.,... more We report on a new approach to the analysis of dynamic NMR lineshapes from polycrystalline (i.e., macroscopically disordered) samples in the presence of Magic Angle Spinning (MAS). This is an application of the Stochastic Liouville Equation developed by Freed and co-workers for treating restricted (i.e., microscopically ordered) motions. The 2 H nucleus in an internally-mobile C-CD 3 moiety serves as a prototype probe. The acronym is 2 H/MOMD/MAS, where MOMD stands for "microscopic-order-macroscopic-disorder." The key elements describing internal motions-their type, the local spatial restrictions, and related features of local geometry-are treated in MOMD generally, within their rigorous three-dimensional tensorial requirements. Based on this representation a single physically well-defined model of local motion has the capability of reproducing experimental spectra. There exist other methods for analyzing dynamic 2 H/MAS spectra which advocate simple motional modes. Yet, to reproduce satisfactorily the experimental lineshapes, one has either to use unusual parameter values, or combine several simple motional modes. The multi-simple-mode reasoning assumes independence of the constituent modes, features ambiguity as different simple modes may be used, renders inter-system comparison difficult as the overall models differ, and makes possible model-improvement only by adding yet another simple mode, i.e., changing the overall model. 2 H/MOMD/MAS is free of such limitations and inherently provides a clear physical interpretation. These features are illustrated. The advantage of 2 H/MOMD/MAS in dealing with sensitive but hardly investigated slow-motional lineshapes is demonstrated by applying it to actual experimental data. The results differ from those obtained previously with a two-site exchange scheme that yielded unusual parameters.

Journal of Physical Chemistry B, Feb 5, 2022

We have developed the stochastic microscopic-order-macroscopic-disorder (MOMD) approach for eluci... more We have developed the stochastic microscopic-order-macroscopic-disorder (MOMD) approach for elucidating dynamic structures in the solid-state from 2H NMR lineshapes. In MOMD, the probe experiences an effective/collective motional mode. The latter is described by a potential, u, which represents the local spatial-restrictions, a local-motional diffusion tensor, R, and key features of local geometry. Previously we applied MOMD to the well-structured core domain of the 3-fold-symmetric twisted polymorph of the Aβ40-amyloid fibril. Here, we apply it to the N-terminal domain of this fibril. We find that the dynamic structures of the two domains are largely similar but differ in the magnitude and complexity of the key physical parameters. This interpretation differs from previous multisimple-mode (MSM) interpretations of the same experimental data. MSM used for the two domains different combinations of simple motional modes taken to be independent. For the core domain, MOMD and MSM disagree on the character of the dynamic structure. For the N-terminal domain, they even disagree on whether this chain segment is structurally ordered (MOMD finds that it is), and whether it undergoes a phase transition at 260 K where bulklike water located in the fibril matrix freezes (MOMD finds that it does not). These are major differences associated with an important system. While the MOMD description is a physically sound one, there are drawbacks in the MSM descriptions. The results obtained in this study promote our understanding of the dynamic structure of protein aggregates. Thus, they contribute to the effort to pharmacologically control neurodegenerative disorders believed to be caused by such aggregates.

The Journal of Physical Chemistry, Jun 1, 1984

We report on a line-shape study of angular-dependent ESR spectra from uniform samples of spin-pro... more We report on a line-shape study of angular-dependent ESR spectra from uniform samples of spin-probe-doped supercooled phase V. Experiments were performed at-50 OC, a temperature at which the liquid-crystalline director stops reorienting along the magnetic field of the ESR spectrometer, smectic-type layering sets in, and the paramagnetic dopants are immobile. Typical ESR spectra, generated by different functional forms of the spatial distribution of molecular orientations, are associated with distinct sites for locating additives, the main distinguishing qualifiers being the nature of the dynamic mode experienced by the probe at higher temperatures and the extent of solute-solvent interactive coupling. This study highlights the potential use of anisotropic rigid-limit ESR spectra to determine the spatial molecular distribution. It may have direct implications on the phenomenon of monotropic formation of liquid-crystalline mesophases.

The Journal of Physical Chemistry, May 1, 1985

Journal of Physical Chemistry B, May 17, 2012

Residual dipolar couplings (RDCs) in proteins arise from independent external medium-related and ... more Residual dipolar couplings (RDCs) in proteins arise from independent external medium-related and internal protein-related ordering of the spin-bearing probe. Griesinger et al. developed a method for treating RDCs in proteins. The global ordering is given in the standard manner by a rank 2 tensor specified in a known molecular frame, MF. The local ordering is described by the spherical harmonic ensemble averages, ⟨Y 2m (θ, φ)⟩, m = 0, ±1, ±2, also given in MF. From these quantities, a method we call mf-RDC derives the squared generalized order parameter (S rdc 2), the amplitude (direction) of the anisotropic disorder, η (Φ̅ ′), and an approximation, (N−H) eff , to the average probe orientation, i.e., to the local director. (N−H) eff is determined through a frame transformation where ⟨Y 20 ⟩ is maximized. Φ̅ ′ is associated with a subsequent frame transformation where ⟨Y 22 + Y 2−2 ⟩ is maximized. The mf-RDC method was applied previously to N−H and C−C methyl sites in ubiquitin. In this study, we convert the respective ⟨Y 2m (θ, φ)⟩'s into a Saupe tensor, which is diagonalized. This is the standard procedure. It yields the eigenvalues, S xx , S yy , and S zz , and the Principal Axis System (PAS) of the rank 2 local ordering tensor, S l. S rdc 2 , η, and Φ̅ ′ can be recast as S xx , S yy , and S zz. The mf-RDC frame transformations are not the same as the conventional Wigner rotation. The standard tensorial analysis provides new information. The contribution of local ordering rhombicity to S rdc 2 is evaluated. For the α-helix of ubiquitin, the main local ordering axis is assigned as C i−1 α − C i α ; for the methyl sites, it is associated with the C−C methyl axis, as in mf-RDC. Ordering strength correlates with methyl type. The strength (rhombicity) of S l associated with picosecond−nanosecond local motions is reduced moderately (substantially) by nanosecond−millisecond local motions. A scheme for analyzing experimental RDCs based on the standard tensorial perspective, which allows for arbitrary orientation of the local director in the protein and of the PAS of S l in the probe, is formulated.

Journal of Physical Chemistry B, Jan 5, 2012

Physical review, 1977

We have investigated elastic deformations by external magnetic fields in flat samples of smectic-... more We have investigated elastic deformations by external magnetic fields in flat samples of smectic-C with fixed boundary conditions. In the calculations the internal parameters {tilt angle, density, interlayer distance) are assumed to be fixed, distortions of the smectic layers are neglected, and only reorientations of the director about the normal to the smectic layers are allowed. The problem is solved exactly assuming a one-dimensional variation of the order parameter. Stability conditions and explicit expressions for the orientation of the director as a function of position are derived for general orientations of the magnetic field. Solutions of the variational problem can be classified according to the maximum deviation angle, 4, of the director. In general there are several separated allowed regions of 4. When Freedericksz transitions occur, they are usually discontinuous first-order transitions. The properties of the solutions are discussed and some special examples are considered in detail. Transitions are investigated both as a function of the magnitude and of the orientation of the magnetic field. Expressions for the free energy are also derived.

Journal of Computational Chemistry, Jan 30, 1997

... Efficiency of monte carlo minimization procedures and their use in analysis of NMR data obtai... more ... Efficiency of monte carlo minimization procedures and their use in analysis of NMR data obtained from flexible peptides. Hagai Meirovitch,; Eva Meirovitch. Article first published online: 7 DEC 1998. ... Res. Inst. (DOE). Grant Number: DE-FC05-35ER250000; Doe. ...

Biopolymers, 1996

Under certain experimental conditions peptide solutions can generate sufficient NMR data for stru... more Under certain experimental conditions peptide solutions can generate sufficient NMR data for structure determination. Yet, unlike proteins, peptides typically prevail as ensembles of interconverting structures, and therefore, the experimental variables (which are intensities of cross peaks in nuclear Overhauser enhancement spectroscopy (NOESY) spectra, or NOEs) are average quantities. The process of structure elucidation is complex, and many related questions are still open to debate. We have developed a new theoretical methodology for treating ensembles of interconverting conformations which is based on purely thermodynamic grounds. The peptide is described by a potential energy function, and its conformational space is viewed as a collection of microstates, which are local conformational regions around energy minima. The overall methodology enables one to identify the thermodynamically most stable microstates, determine their populations, calculate the individual microstate NOEs, and obtain the overall NOEs as averages over the individual contributions, weighted by the microstate populations. In this paper we develop for the first time theoretical methods for calculating the relative contribution of microstates to the partition function, as their minimum energy is increased above the global energy minimum (GEM). This is necessary for determining which microstates should be considered in detail in the next stage of the analysis. The new methods presented herein are applied to the pentapeptide Leu-enkephalin (H-Tyr-Gly-Gly-Phe-Leu-OH) described by the potential energy function ECEPP, with calculations carried out at 280 K. We find that the microstates contained within relatively small ranges of 2 to 3 kcal/mol above the GEM (or above the lowest harmonic free energy) constitute 0.59 to 0.75 of the partition function. This should be compared with energy ranges up to 15 kcaymol set arbitrarily in previous studies. A detailed comparison of theoretical predictions with experimental data, obtained from a cryoprotective Leu-enkephalin solution at 280 K, will be carried out in the next paper of this series.

The Journal of Physical Chemistry, 2012

Residual dipolar couplings (RDCs) in proteins arise from independent external medium-related and ... more Residual dipolar couplings (RDCs) in proteins arise from independent external medium-related and internal protein-related ordering of the spin-bearing probe. Griesinger et al. developed a method for treating RDCs in proteins. The global ordering is given in the standard manner by a rank 2 tensor specified in a known molecular frame, MF. The local ordering is described by the spherical harmonic ensemble averages, ⟨Y 2m (θ, φ)⟩, m = 0, ±1, ±2, also given in MF. From these quantities, a method we call mf-RDC derives the squared generalized order parameter (S rdc 2), the amplitude (direction) of the anisotropic disorder, η (Φ̅ ′), and an approximation, (N−H) eff , to the average probe orientation, i.e., to the local director. (N−H) eff is determined through a frame transformation where ⟨Y 20 ⟩ is maximized. Φ̅ ′ is associated with a subsequent frame transformation where ⟨Y 22 + Y 2−2 ⟩ is maximized. The mf-RDC method was applied previously to N−H and C−C methyl sites in ubiquitin. In this study, we convert the respective ⟨Y 2m (θ, φ)⟩'s into a Saupe tensor, which is diagonalized. This is the standard procedure. It yields the eigenvalues, S xx , S yy , and S zz , and the Principal Axis System (PAS) of the rank 2 local ordering tensor, S l. S rdc 2 , η, and Φ̅ ′ can be recast as S xx , S yy , and S zz. The mf-RDC frame transformations are not the same as the conventional Wigner rotation. The standard tensorial analysis provides new information. The contribution of local ordering rhombicity to S rdc 2 is evaluated. For the α-helix of ubiquitin, the main local ordering axis is assigned as C i−1 α − C i α ; for the methyl sites, it is associated with the C−C methyl axis, as in mf-RDC. Ordering strength correlates with methyl type. The strength (rhombicity) of S l associated with picosecond−nanosecond local motions is reduced moderately (substantially) by nanosecond−millisecond local motions. A scheme for analyzing experimental RDCs based on the standard tensorial perspective, which allows for arbitrary orientation of the local director in the protein and of the PAS of S l in the probe, is formulated.

The Journal of Physical Chemistry, 2012

Chemischer Informationsdienst, Oct 9, 1984

The Journal of Physical Chemistry, Oct 1, 1982

We report on temperature-and angular-dependent ESR spectra of two types of nitroxide-labeled fatt... more We report on temperature-and angular-dependent ESR spectra of two types of nitroxide-labeled fatty acid chains, the commonly used but sterically bulky doxyl nitroxides and the recently prepared "minimum steric perturbation" azethoxyl nitroxides, dissolved in various liquid crystalline phases. The main spectral feature examined was the effective hyperfine splitting of the nitroxide radical, which in almost all cases was found to exceed the isotropic value of this parameter. The interpretation of this result in terms of deviations from an extended-chain conformation is shown to be unique with the azethoxyls and ambiguous with the doxyls, as it is based on the inherent geometric molecular feature 8, the tilt angle of the free-electron a orbital relative to the main chain axis. In the various mesophases studied, 0 was found to range from 30' to 50°, as compared to 60° for an extended chain. Use of azethoxyl probes, rather than doxyl probes, in addressing questions related to the conformation of flexible chains in locally ordered media is thus suggested, for with the azethoxyl probes valuable information is available before detailed line-shape analysis.

The Journal of Physical Chemistry, Sep 1, 1984

The Journal of Physical Chemistry, Sep 1, 1984

We report on a careful line-shape study of ESR spectra from the smectic Ad phase of S2 doped with... more We report on a careful line-shape study of ESR spectra from the smectic Ad phase of S2 doped with the common doxyl and the "minimum-perturbation" azethoxyl nitroxides, with the NO group attached at the midchain region. The primary goal of this investigation is to address unresolved questions related to chain conformation, dynamics, and local ordering in anisotropic solvents, as reflected in the spin relaxation of the above-mentioned paramagnetic hydrocarbons. We find that the NO groups of both doxyl and azethoxyl nitroxides experience similar, relatively low, and only slightly temperature-dependent local ordering. On the other hand, both motional and conformational properties of the two types of spin probes are at variance. Thus, the azethoxyl nitroxides reorient at average rates of roughly 2.0 X lo7 s-' at the lower end of the smectic Ad phase, which are about twice higher than the reorientational rates of the doxyl analogues at similar temperatures. Azethoxyl nitroxides reorient basically as individual particles whereas with doxyl nitroxides, we detect substantial dynamic coupling to collective modes of the liquid-crystalline solvent. The doxyl chains were found to be fully extended whereas the azethoxyl chains bent. We discuss the unique value of slow-motional ESR in complementing information obtained previously with both NMR and ESR in the motional-narrowing regime.

The Journal of Physical Chemistry, Jun 1, 1984

ESR spectra of five nitroxide spin probes dissolved in the discotic mesophase of hexakis(hexy1oxy... more ESR spectra of five nitroxide spin probes dissolved in the discotic mesophase of hexakis(hexy1oxy)triphenylene (THE6) were measured as function of temperature in the mesophase region. The different spin probes exhibit a variety of line shapes and temperature dependencies. The results could be explained in terms of the existence of two solvation sites for the probe molecules. These sites are assumed to correspond to (I) probe molecules intercalated within the columnar structures of the discotic mesophase and (11) probe molecules dissolved in the aliphatic region between the columns. In one case (CSL) the experimental results actually exhibited distinct spectra due to two solvation sites. The other spin probes gave simpler spectra but their temperature dependence was unusual and could in general be interpreted in terms of fast dynamic equilibrium between the two solvation sites.

The Journal of Physical Chemistry, Jun 1, 1994

A simple and efficient method for searching the conformational space of macromolecules is present... more A simple and efficient method for searching the conformational space of macromolecules is presented. With this method an initial set of relatively low-energy structures is generated, and their energies are further minimized with a procedure that enables escaping from local energy minima. Illustrative calculations are described for Met-and Leu-enkephalin.