Eva Meirovitch

Electron‐spin relaxation and ordering in smectic and supercooled nematic liquid crystals

We report on careful line shape studies of slow motional and orientation dependent ESR spectra of a deuterated liquid‐crystal‐like spin probe dissolved in a benzilidene‐derivative (40,6) and in cyanobiphenyl derivative (S2 and 5CB) liquid crystals. The simulation of the ESR spectra is based on the Lanczos algorithm recently applied by Moro and Freed in a general and efficient formulation of slow motional and ordering effects on ESR line shapes. With 40,6 which exhibits monolayer smectic phases, we find that the main change in the spin relaxation upon passing from the nematic to the smectic A phase consists of changes occuring in ordering attributable to packing forces on functional groups. Such ordering effects appear to be further enhanced in the SB phase with consequent alterations in dynamics. With S2, which exhibits an interpenetrating bilayer smectic A phase, we find unusual ESR spectra in that phase which may be simulated on the basis of a model of cooperative distortions static on the ESR time scal...

Structural dynamics of bio-macromolecules by NMR: The slowly relaxing local structure approach

0079-6565/

General Theoretical/Computational Tool for Interpreting NMR Spin Relaxation in Proteins

see front matter 2010 Elsevier B.V. A doi:10.1016/j.pnmrs.2010.03.002 Abbreviations: AK, adenylate kinase; AKeco, adeny anisotropy; 3D GAF, 3-dimensional Gaussian axial fluc resonance; FPK, Fokker–Planck–Kramers; GB3, the B headpiece subdomain protein; iRED, isotropic reorien free; MOMD, microscopic order macroscopic disorde Overhauser enhancement; PCA, principal component a L; RDC, residual dipolar coupling; RNA, ribonucleic ac * Corresponding author. Tel.: +972 3 5318049; fax ** Corresponding author. *** Corresponding author. E-mail addresses: eva@nmrsgi5.ls.biu.ac.il (E. Meirov 2010 Elsevier B.V. All rights reserved.

Slow motional NMR lineshapes for very anisotropic diffusion: I = 1 nuclei☆

We developed in recent years the slowly relaxing local structure (SRLS) approach for analyzing NMR spin relaxation in proteins. SRLS is a two-body coupled rotator model which accounts rigorously for mode-coupling between the global motion of the protein and the local motion of the spin-bearing probe and allows for general properties of the second rank tensors involved. We showed that a general tool of data analysis requires both capabilities. Several important functionalities were missing in our previous implementations of SRLS in data fitting schemes, and in some important cases, the calculations were tedious. Here we present a general implementation which allows for asymmetric local and global diffusion tensors, distinct local ordering and local diffusion frames, and features a rhombic local potential which includes Wigner matrix element terms of ranks 2 and 4. A recently developed hydrodynamics-based approach for calculating global diffusion tensors has been incorporated into the data-fitting scheme. The computational efficiency of the latter has been increased significantly through object-oriented programming within the scope of the C++ programming language, and code parallelization. A convenient graphical user interface is provided. Currently autocorrelated (15)N spin relaxation data can be analyzed effectively. Adaptation to any autocorrelated and cross-correlated relaxation analysis is straightforward. New physical insight is gleaned on largely preserved local structure in solution, even in chain segments which experience slow local motion. Prospects associated with improved dynamic models, and new applications made possible by the current implementation of SRLS, are delineated.

Integrated Computational Approach to the Analysis of NMR Relaxation in Proteins: Application to ps−ns Main Chain 15N−1H and Global Dynamics of the Rho GTPase Binding Domain of Plexin-B1

Abstract A general method to analyze NMR show motional lineshapes is extended to I = 1 nuclei and illustrated on 2 H NMR lineshapes of a clathrate hydrate of tetrahydrofuran (THF- d 8 ). It is shown that “ring puckering” could be the dominant mode of motion for the enclathrated THF- d 8 molecule, whereas several other models are inconsistent with experiment.

An integrated approach to NMR spin relaxation in flexible biomolecules: Application to β-D-glucopyranosyl-(1 →6)-α-D-mannopyranosyl-OMe

An integrated computational methodology for interpreting NMR spin relaxation in proteins has been developed. It combines a two-body coupled-rotator stochastic model with a hydrodynamics-based approach for protein diffusion, together with molecular dynamics based calculations for the evaluation of the coupling potential of mean force. The method is applied to ¹⁵N relaxation of N-H bonds in the Rho GTPase binding (RBD) domain of plexin-B1, which exhibits intricate internal mobility. Bond vector dynamics are characterized by a rhombic local ordering tensor, S, with principal values S₀² and S₂², and an axial local diffusion tensor, D₂, with principal values D(2,||) and D(2,⊥). For α-helices and β-sheets we find that S₀² ~ -0.5 (strong local ordering), -1.2 < S₂² < -0.8 (large S tensor anisotropy), D(2,⊥) ~ D₁ = 1.93 × 10⁷ s⁻¹ (D₁ is the global diffusion rate), and log(D(2,||)/D₁) ~ 4. For α-helices the z-axis of the local ordering frame is parallel to the C(α)-C(α) axis. For β-sheets the z-axes of the S and D₂ tensors are parallel to the N-H bond. For loops and terminal chain segments the local ordering is generally weaker and more isotropic. On average, D(2,⊥) ~ D₁ also, but log(D(2,||)/D₁) is on the order of 1-2. The tensor orientations are diversified. This study sets forth an integrated computational approach for treating NMR relaxation in proteins by combining stochastic modeling and molecular dynamics. The approach developed provides new insights by its application to a protein that experiences complex dynamics.

Efficiency of monte carlo minimization procedures and their use in analysis of NMR data obtained from flexible peptides

The description of the reorientational dynamics of flexible molecules is a challenging task, in particular when the rates of internal and global motions are comparable. The commonly used simple mode-decoupling models are based on the assumption of statistical independence between these motions. This assumption is not valid when the time scale separation between their rates is small, a situation that was found to arise in oligosaccharides in the context of certain internal motions. To make possible the interpretation of NMR spin relaxation data from such molecules, we developed a comprehensive approach generally applicable to flexible rotators with one internal degree of freedom. This approach integrates a stochastic description of coupled global tumbling and internal torsional motion, quantum chemical calculations of the local potential and the local geometry at the site of the restricted torsion, and hydrodynamics-based calculations of the diffusive properties. The method is applied to the disaccharide beta-D-Glcp-(1-->6)-alpha-D-[6-(13)C]-Manp-OMe dissolved in a DMSO-d(6)/D(2)O cryosolvent. The experimental NMR relaxation parameters, associated with the (13)CH(2) probe residing at the glycosidic linkage, include (13)C T(1) and T(2) and (13)C-{(1)H} nuclear Overhauser enhancement (NOE) as well as longitudinal and transverse dipole-dipole cross-correlated relaxation rates, acquired in the temperature range of 253-293 K. These data are predicted successfully by the new theory with only the H-C-H angle allowed to vary. Previous attempts to fit these data using mode-decoupling models failed.

SRLS analysis of 15N spin relaxation from E. coli ribonuclease HI: the tensorial perspective.

The Monte Carlo minimization (MCM) method of Li and Scheraga is an efficient tool for generating low energy minimized structures of peptides, in particular the global energy minimum (GEM). In a recent article we proposed an enhancement to MCM, called the free energy Monte Carlo minimization (FMCM) procedure. With FMCM the conformational search is carried out with respect to the harmonic free energy, which approximates the free energy of the potential energy wells around the energy minimized structures (these wells are called localized microstates). In this work we apply both methods to the pentapeptide Leu‐enkephalin described by the potential energy function ECEPP, and study their efficiency in identifying the GEM structure as well as the global harmonic free energy (GFM) structure. We also investigate the efficiency of these methods to generate localized microstates, which pertain to different energy and harmonic free energy intervals above the GEM and GFM, respectively. Such microstates constitute an important ingredient of our statistical mechanical methodology for analyzing nuclear magnetic resonance data of flexible peptides. Aspects of this methodology related to the stability properties of the localized microstates are examined.

Analysis of 15N-1H NMR relaxation in proteins by a combined experimental and molecular dynamics simulation approach: picosecond-nanosecond dynamics of the Rho GTPase binding domain of plexin-B1 in the dimeric state indicates allosteric pathways.

15N–H relaxation parameters from ribonuclease HI (RNase H), acquired in previous work at magnetic fields of 14.1 and 18.8 T, and at 300 K, are analyzed with the mode-coupling slowly relaxing local structure (SRLS) approach. In accordance with standard theoretical treatments of restricted motions, SRLS approaches N-H bond dynamics from a tensorial perspective. As shown previously, a physically adequate description of this phenomenon has to account for the asymmetry of the local spatial restrictions. So far, we used rhombic local ordering tensors; this is straightforward but computationally demanding. Here, we propose substantiating the asymmetry of the local spatial restrictions in terms of tilted axial local ordering (S) and local diffusion (D2) tensors. Although less straightforward, this description provides physically sound structural and dynamic information and is efficient computationally. We find that the local order parameter, S(0)2, is on average 0.89 (0.84, and may be as small as 0.6) for the secondary structure elements (loops). The main local ordering axis deviates from the C(i-1)α-C(i)α axis by less than 6°. At 300 K, D(2,perpendicular) is virtually the same as the global diffusion rate, D1 = 1.8 × 10(7) s(-1). The correlation time 1/6D(2,parallel) ranges from 3-125 (208-344) ps for the secondary structure elements (loops) and is on average 125 ps for the C-terminal segment. The main local diffusion axis deviates from the N-H bond by less than 2° (10°) for the secondary structure elements (loops). An effective data-fitting protocol, which leads in most cases to unambiguous results with limited uncertainty, has been devised. A physically sound and computationally effective methodology for analyzing 15N relaxation in proteins, that provides a new picture of N–H bond structural dynamics in proteins, has been set forth.

Domain mobility in proteins from NMR/SRLS.

We investigate picosecond–nanosecond dynamics of the Rho-GTPase Binding Domain (RBD) of plexin-B1, which plays a key role in plexin-mediated cell signaling. Backbone 15N relaxation data of the dimeric RBD are analyzed with the model-free (MF) method, and with the slowly relaxing local structure/molecular dynamics (SRLS-MD) approach. Independent analysis of the MD trajectories, based on the MF paradigm, is also carried out. MF is a widely popular and simple method, SRLS is a general approach, and SRLS-MD is an integrated approach we developed recently. Corresponding parameters from the RBD dimer, a previously studied RBD monomer mutant, and the previously studied complex of the latter with the GTPase Rac1, are compared. The L2, L3, and L4 loops of the plexin-B1 RBD are involved in interactions with other plexin domains, GTPase binding, and RBD dimerization, respectively. Peptide groups in the loops of both the monomeric and dimeric RBD are found to experience weak and moderately asymmetric local ordering centered approximately at the C(i–1)(α)–C(i)(α) axes, and nanosecond backbone motion. Peptide groups in the α-helices and the β-strands of the dimer (the β-strands of the monomer) experience strong and highly asymmetric local ordering centered approximately at the C(i–1)(α)–C(i)(α) axes (N–H bonds). N–H fluctuations occur on the picosecond time scale. An allosteric pathway for GTPase binding, providing new insights into plexin function, is delineated.