Eva Meirovitch

Bar Ilan University, Gan, Tel Aviv, Israel

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Publications (46)125.49 Total impact

  • Yury E. Shapiro, Eva Meirovitch
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    ABSTRACT: We developed in recent years the two-body coupled-rotator slowly relaxing local structure (SRLS) approach for the analysis of NMR relaxation in proteins. The two bodies/rotators are the protein (diffusion tensor D1) and the spin-bearing probe, e.g., the 15N-1H bond (diffusion tensor, D2), coupled by a local potential (u). A Smoluchowski equation is solved to yield the generic time correlation functions (TCFs), which are sums of weighted exponentials (eigenmodes). By Fourier transformation one obtains the generic spectral density functions (SDFs) which underlie the experimental relaxation parameters. The typical paradigm is to characterize structural dynamics in terms of the best-fit values of D1, D2, and u. Additional approaches we pursued employ the SRLS TCFs, SDFs, or eigenmodes as descriptors. In this study we develop yet another perspective. We consider the SDF as function of the angular velocity associated with the fluctuating fields underlying NMR relaxation. A parameter called j-fraction, which represents the relative contribution of eigenmode, i, to a given value of the SDF function at a specific frequency, ω, is defined. j-fraction profiles of the dominant eigenmodes are derived for 0 ≤ ω ≤ 1012 rad/s. They reveal which patterns of motion actuate power dissipation at given ω-values, what are their rates, and what is their relative contribution. Simulations are carried out to determine the effect of timescale separation, D1/D2, axial potential strength, and local diffusion axiality. For D1/D2 ≤ 0.01 and strong local potential of 15 kBT, power is dissipated by global diffusion, renormalized (by the strong potential) local diffusion, and probe diffusion on the surface of a cone (to be called cone diffusion). For D1/D2 = 0.1, power is dissipated by mixed eigenmodes largely of a global-diffusion-type or cone-diffusion-type, and a nearly bare renormalized-local-diffusion eigenmode. For D1/D2 > 0.1, most eigenmodes are of a mixed type. The analysis is affected substantially by reducing the potential strength from 15 to 5 kBT, and/or allowing for axial D2 with D2,∥/D2,⊥ = 10. The scheme developed is applied to 15N-1H relaxation from the β-sheet residue K19 and the α-helix residue A34 of the third immunoglobulin-binding domain of streptococcal protein G. Previous studies revealed rhombic local potentials with different rhombicity around C_{i - 1}^α {- C}_i^α , and different timescale separation (0.047 for K19 and 0.102 for A34). Here, we find that K19 and A34 dissipate power to the bath through global diffusion, mixed cone-diffusion-related and mixed renormalized-local-diffusion-related motions. At small ω-values, A34 is more effective than K19 in dissipating power. In general, it executes faster cone-diffusion-type, and slower renormalized-local-diffusion-type and local-probe-fluctuation-type motions. K19 experiences faster N-H fluctuations than A34. Eigenmode clustering, experienced by K19 to a larger extent, is observed in the fast-probe-fluctuation regime. New information on the effect of the structural context on N-H bond dynamics has been obtained. The patterns of motion that dissipate NMR-relaxation-related power illuminate protein dynamics from a new perspective. They constitute yet another qualifier of N-H bond dynamics. This study sets the stage for developing ways for enhancing the contribution of desired pathways for power dissipation at selected angular velocities.
    03/2014; 140(15).
  • Eva Meirovitch
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    ABSTRACT: NMR relaxation is a powerful method for elucidating structural dynamics. Standard stochastic dynamic models generate time correlation functions (TCFs) that feature physically well-defined parameters. We developed such a model, called the slowly relaxing local structure (SRLS) approach, for proteins. SRLS is a two-body (protein and probe) coupled-rotator approach. Given that the protein (featuring diffusion tensor, D1) restricts the probe (featuring diffusion tensor, D2), the two “bodies” are inherently coupled dynamically. This is substantiated by a local potential, u, associated with a local ordering tensor, S. SRLS allows for general tensorial properties of D1, D2, S and the magnetic NMR tensors, and a general form of u. The TCFs are multi-exponential, in accordance with the degree of generality of the various tensors. The traditional model-free (MF) method is based on a different conceptualization. According to it a mode-decoupling bi-exponential (one term for each rotator) TCF captures adequately the detectable features of structural dynamics. Hence, stochastic approaches are unnecessary. Here, we show that this (amply proven) oversimplification leads to physically vague constructs/composites as descriptors of structural dynamics. We illustrate misleading results obtained with MF when mode coupling, or S tensor asymmetry, dominate the analysis. Finally, we delineate the substantial advantage in using SRLS TCF as quantity to be compared with its atomistic molecular dynamicsbased counterpart.
    Israel Journal of Chemistry (Online) 01/2014; · 2.56 Impact Factor
  • Yury E Shapiro, Eva Meirovitch
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    ABSTRACT: We developed in recent years the two-body (protein and probe) coupled-rotator slowly relaxing local structure (SRLS) approach for elucidating protein dynamics from NMR spin relaxation. So far we used as descriptors the set of physical parameters that enter the SRLS model. They include the global (protein-related) diffusion tensor, D1, the local (probe-related) diffusion tensor, D2, and the local coupling∕ordering potential, u. As common in analyzes based on mesoscopic dynamic models, these parameters have been determined with data-fitting techniques. In this study, we describe structural dynamics in terms of the eigenmodes comprising the SRLS time correlation functions (TCFs) generated by using the best-fit parameters as input to the Smoluchowski equation. An eigenmode is a weighted exponential with decay constant given by an eigenvalue of the Smoluchowski operator, and weighting factor determined by the corresponding eigenvector. Obviously, both quantities depend on the SRLS parameters as determined by the SRLS model. Unlike the set of best-fit parameters, the eigenmodes represent patterns of motion of the probe-protein system. The following new information is obtained for the typical probe, the (15)N-(1)H bond. Two eigenmodes, associated with the protein and the probe, dominate when the time scale separation is large (i.e., D2 ≫ D1), the tensorial properties are simple, and the local potential is either very strong or very weak. When the potential exceeds these limits while the remaining conditions are preserved, new eigenmodes arise. The multi-exponentiality of the TCFs is associated in this case with the restricted nature of the local motion. When the time scale separation is no longer large, the rotational degrees of freedom of the protein and the probe become statistically dependent (coupled dynamically). The multi-exponentiality of the TCFs is associated in this case with the restricted nature of both the local and the global motion. The effects of local diffusion axiality, potential strength, and extent of mode-coupling on the eigenmode setup are investigated. We detect largely global motional or largely local motional eigenmodes. In addition, we detect mixed eigenmodes associated with correlated∕prograde or anti-correlated∕retrograde rotations of the global (D1) and local (D2) motional modes. The eigenmode paradigm is applied to N-H bond dynamics in the β-sheet residue K19, and the α-helix residue A34, of the third immunoglobulin-binding domain of streptococcal protein G. The largest contribution to the SRLS TCFs is made by mixed anti-correlated D1 and D2 eigenmodes. The next largest contribution is made by D1-dominated eigenmodes. Eigenmodes dominated by the local motion contribute appreciably to A34 and marginally to K19. Correlated D1 and D2 eigenmodes contribute exclusively to K19 and do not contribute above 1% to A34. The differences between K19 and A34 are delineated and rationalized in terms of the best-fit SRLS parameters and mode-mixing. It may be concluded that eigenmode analysis is complementary and supplementary to data-fitting-based analysis.
    The Journal of Chemical Physics 12/2013; 139(22):225104. · 3.12 Impact Factor
  • Yury E Shapiro, Eva Meirovitch
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    ABSTRACT: We applied over a decade ago the two-body coupled-rotator slowly relaxing local structure (SRLS) approach to NMR relaxation in proteins. One rotator is the globally moving protein and the other rotator is the locally moving probe (spin-bearing moiety, typically the (15)N-(1)H bond). So far we applied SRLS to (15)N-H relaxation from seven different proteins within the scope of the commonly used data-fitting paradigm. Here, we solve the SRLS Smoluchowski equation using typical best-fit parameters as input, to obtain the corresponding generic time correlation functions (TCFs). The following new information is obtained. For actual rhombic local ordering and main ordering axis pointing along Ci-1 (α)-Ci (α), the measurable TCF is dominated by the (K,K') = (-2,2), (2,2), and (0,2) components (K is the order of the rank 2 local ordering tensor), determined largely by the local motion. Global diffusion axiality affects the analysis significantly when the ratio between the parallel and perpendicular components exceeds approximately 1.5. Local diffusion axiality has a large and intricate effect on the analysis. Mode-coupling becomes important when the ratio between the global and local motional rates falls below 0.01. The traditional method of analysis - model-free (MF) - represents a simple limit of SRLS. The conditions under which the MF and SRLS TCFs are the same are specified. The validity ranges of wobble-in-a-cone and rotation on the surface of a cone as local motions are determined. The evolution of the intricate Smoluchowski operator from the simple diffusion operator for a sphere reorienting in isotropic medium is delineated. This highlights the fact that SRLS is an extension of the established stochastic theories for treating restricted motions. This study lays the groundwork for TCF-based comparison between mesoscopic SRLS and atomistic molecular dynamics.
    The Journal of Chemical Physics 08/2013; 139(8):084107. · 3.12 Impact Factor
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    ABSTRACT: We investigate ps-ns dynamics of the Rho-GTPase Binding Domain (RBD) of plexin-B1, which plays a key role in plexin-mediated cell signaling. Backbone (15)N 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 L(2), L(3) and L(4) 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(α)-C(α) axes, and ns 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(α)-C(α) axes (N-H bonds). N-H fluctuations occur on the ps time-scale. An allosteric pathway for GTPase binding, providing new insights into plexin function, is delineated.
    The Journal of Physical Chemistry B 12/2012; · 3.61 Impact Factor
  • Eva Meirovitch
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    ABSTRACT: Bacteriophage T4L lysozyme (T4L) comprises two domains connected by a helical linker. Several methods detected ns domain motion associated with the binding of the peptidoglycan substrate. An ESR study of nitroxide-labeled T4L, based on the slowly relaxing local structure (SRLS) approach, detected ns local motion involving the nitroxide and the helix housing it. (15)N−H spin relaxation data from T4L acquired at magnetic fields of 11.7 and 18.8 T, and 298 K, were analyzed previously with the model-free (MF) method. The results did not detect domain motion. SRLS is the generalization of MF. Here, we apply it to the same data analyzed previously with MF. The restricted local N−H motion is described in terms of tilted axial local ordering (S) and local diffusion (D(2)) tensors; dynamical coupling to the global tumbling is accounted for. We find that D(2,⊥) is 1.62 × 10(7) (1.56 × 10(7)) s(−1) for the N-terminal (C-terminal) domain. This dynamic mode represents domain motion. For the linker D(2,⊥) is the same as the rate of global tumbling, given by (1.46 ± 0.04) × 10(7) s(−1). D(2,∥) is 1.3 × 10(9), 1.8 × 10(9) and 5.3 × 10(9) s(−1) for the N-terminal domain, the C-terminal domain, and the linker, respectively. This dynamic mode represents N−H bond vector fluctuations. The principal axis of D(2) is virtually parallel to the N−H bond. The order parameter, S(0)(2), is 0.910 ± 0.046 for most N−H bonds. The principal axis of S is tilted from the C(i−1)(α) −C(i)(α) axis by −2° to 6° for the N-, and C-terminal domains, and by 2.5° for the linker. The tensorial-perspective-based and mode-coupling-based SRLS picture provides new insights into the structural dynamics of bacteriophage T4 lysozyme.
    The Journal of Physical Chemistry B 05/2012; 116(21):6118-27. · 3.61 Impact Factor
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    ABSTRACT: 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 (Φ′), 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. Φ′ 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 Φ′ 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 B 04/2012; 116(21):6106-17. · 3.61 Impact Factor
  • Yury E Shapiro, Eva Meirovitch
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    ABSTRACT: 15N-H relaxation parameters from the first (GB1) and third (GB3) immunoglobulin-binding domains of streptococcal protein G were analyzed previously with the traditional model-free (MF) method. These proteins comprise an α-helix and a four-stranded β-sheet. An extensive study of GB1 (GB3) used combined three-field (five-field) data acquired in the 278-323 K range (at 297 K). For successful analysis of the GB3 data, it was necessary to allow for variations in the 15N chemical shift anisotropy (CSA) tensor and virtually eliminate the local motion. In the case of GB1, the spectral density was parametrized. Here, we analyze these data with the slowly relaxing local structure (SRLS) approach, which is the generalization of MF in allowing for general tensorial properties, and accounting for mode-coupling. A standard (featuring constant magnetic tensors) SRLS fitting scheme is used. This analysis accounts for the important asymmetry of the local spatial restrictions; it provides physical order parameters, local diffusion rates, related activation energies, and key features of local geometry. Using data from GB3 we show that the main local ordering axis is C(i-1)(α) - C(i)(α), and the average axial (rhombic) order parameter is -0.457 ± 0.017 (1.156 ± 0.015) for the α-helix and -0.484 ± 0.002 (1.10 ± 0.04) for the rest of the polypeptide chain. The N-H bonds within (outside of) the α-helix reorient locally with an average correlation time, (τ), of 310 (130) ps, as compared to 3.33 ns for the global tumbling. Several N-H bonds in the loops β1/β2, β2/α-helix, and α-helix/β3 have (τ) of 380, 320, and 750 ps, respectively. The distinctive experimental data of the α-helix are due to relatively weak and substantially rhombic local ordering and slow local motion. For GB1, we derive activation energies from local diffusion rates. They are 43.3 ± 7.1 kJ/mol for the β-strands, 24.7 ± 3.9 kJ/mol for the α-helix (and approximately for the loop β3/β4), and 18.9 ± 1.8 kJ/mol for the other loops. The physical SRLS description provides new insights into the backbone dynamics of GB1 and GB3 in particular, and proteins in general.
    The Journal of Physical Chemistry B 03/2012; 116(13):4056-68. · 3.61 Impact Factor
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    ABSTRACT: 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.
    The Journal of Physical Chemistry B 11/2011; 116(2):886-94. · 3.61 Impact Factor
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    ABSTRACT: The slowly relaxing local structure (SRLS) approach, developed for NMR spin relaxation analysis in proteins, is applied herein to amide ¹⁵N relaxation in deoxy and carbonmonoxy hemoglobin. Experimental data including ¹⁵N T₁, T₂ and ¹⁵N-{¹H} NOE, acquired at 11.7 and 14.1 T, and 29 and 34 °C, are analyzed. The restricted local motion of the N-H bond is described in terms of the principal value (S(0)(2)) and orientation (β(D)) of an axial local ordering tensor, S, and the principal values (R(||)(L) and R(⊥)(L)) and orientation (β(O)) of an axial local diffusion tensor, R(L). The parameters c₀² (the potential coefficient in terms of which S(0)(2) is defined), R(||)(L), β(D), and β(O) are determined by data fitting; R(⊥)(L) is set equal to the global motional rate, R(C), found previously to be (5.2-5.8) × 10⁶ 1/s in the temperature range investigated. The principal axis of S is (nearly) parallel to the C(i-1)(α)-C(i)(α) axis; when the two axes are parallel, β(D) = -101.3° (in the frame used). The principal axis of R(L) is (nearly) parallel to the N-H bond; when the two axes are parallel, β(O) = -101.3°. For "rigid" N-H bonds located in secondary structure elements the best-fit parameters are S(0)(2) = 0.88-0.95 (corresponding to local potentials of 8.6-19.9 k(B)T), R(||)(L) = 10⁹-10¹⁰ 1/s, β(D) = -101.3° ± 2.0°, and β(O) = -101.3° ± 4°. For flexible N-H bonds located in loops the best-fit values are S(0)(2) = 0.75-0.80 (corresponding to local potentials of 4.5-5.5 k(B)T), R(||)(L) = (1.0-6.3) × 10⁸ 1/s, β(D) = -101.3° ± 4.0°, and β(O) = -101.3° ± 10°. These results are important in view of their physical clarity, inherent potential for further interpretation, consistency, and new qualitative insights provided (vide infra).
    The Journal of Physical Chemistry B 01/2011; 115(1):143-57. · 3.61 Impact Factor
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    ABSTRACT: We developed the slowly relaxing local structure (SRLS) approach for analyzing NMR spin relaxation in proteins. SRLS accounts for dynamical coupling between the tumbling of the protein and the local motion of the probe and for general tensorial properties. It is the generalization of the traditional model-free (MF) method, which does not account for mode-coupling and treats only simple tensorial properties. SRLS is applied herein to ²H relaxation of ¹³CDH₂ groups in the complex of Ca(2+)-calmodulin with the peptide smMLCKp. Literature data comprising ²H T₁ and T₂ acquired at 14.1 and 17.6 T, and 288, 295, 308, and 320 K, are used. We find that mode-coupling is a small effect for methyl dynamics. On the other hand, general tensorial properties are important. In particular, it is important to allow for the asymmetry of the local spatial restrictions, which can be represented in SRLS by a rhombic local ordering tensor with components S(0)(2) and S(2)(2). The principal axes frame of this tensor is obviously different from the axial frames of the magnetic tensors. Here, we find that -0.2 ≤ S(0)(2) ≤ 0.5 and -0.4 ≤ S(2)(2) ≤ 0. MF features a single "generalized" order parameter, S, confined to the 0-0.316 range; the local geometry is inherently simple. The parameter S is inaccurate, having absorbed unaccounted for effects, notably S(2)(2) ≠ 0. We find that the methionine methyls (the other methyl types) reorient with rates of 8.6 × 10⁹ to 21.4 × 10⁹ (0.67 × 10⁹ to 6.5 × 10⁹) 1/s. The corresponding activation energies are 10 (10-27) kJ/mol. By contrast, MF yields inaccurate effective local motional correlation times, τ(e), with nonphysical temperature dependence. Thus, the problematic S- and τ(e)-based MF picture of methyl dynamics has been replaced with an insightful physical picture based on a local ordering tensor related to structural features, and a local diffusion tensor that yields accurate activation energies.
    The Journal of Physical Chemistry B 01/2011; 115(2):354-65. · 3.61 Impact Factor
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    ABSTRACT: 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.
    The Journal of Physical Chemistry B 01/2011; 115(2):376-88. · 3.61 Impact Factor
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    Eva Meirovitch, Antonino Polimeno, Jack H Freed
    The Journal of Chemical Physics 05/2010; 132(20):207101. · 3.12 Impact Factor
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    Progress in Nuclear Magnetic Resonance Spectroscopy 05/2010; 56(4):360-405. · 6.02 Impact Factor
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    Progress in Nuclear Magnetic Resonance Spectroscopy - PROG NUCL MAGN RESON SPECTROS. 01/2010; 57(3):343-343.
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    ABSTRACT: 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.
    The Journal of Chemical Physics 12/2009; 131(23):234501. · 3.12 Impact Factor
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    ABSTRACT: 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.
    The Journal of Physical Chemistry B 09/2009; 113(41):13613-25. · 3.61 Impact Factor
  • Yury E Shapiro, Edith Kahana, Eva Meirovitch
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    ABSTRACT: Enhanced internal mobility in proteins is typically functional. Domain motion in enzymes, necessarily related to catalysis, is a prototype in this context. Experimental (15)N spin relaxation data from E. coli adenylate kinase report qualitatively on nanosecond motion experienced by the domains AMPbd and LID. Previous quantitative analysis based on the mode-coupling slowly relaxing local structure approach confirmed nanosecond mobility but yielded unduly small local ordering and local geometry not interpretable directly in terms of the local protein structure. Here, we show that these features ensue from having assumed axial local ordering and highly axial local diffusion. After eliminating these simplified second-rank tensor properties, a physically sound picture, with the local motion interpretable as domain motion, is obtained. Rhombic local ordering, with components given by = 0.471, = -0.952 and = 0.481, and main ordering axis, Y(M), lying along C(alpha)(i-1) - C(alpha)(i), has been determined. The associated rhombic potential is given by axial (rhombic) coefficients of <c(2)(0)> = -3.3 (<c(2)(2)> = 17.8). The average correlation time for domain motion is 10.4 (6.4) ns at 288 (302) K; the corresponding correlation time for global motion is 20.6 (14.9) ns. The rates for domain motion exhibit noteworthy Arrhenius-type temperature-dependence, yielding activation energies of 63.8 +/- 7.0 (53.0 +/- 9.1) kJ/mol for the AMPbd (LID) domain. The traditional model-free analysis ignores mode-coupling and simplifies tensor properties. Within its scope, the AKeco backbone emerges as largely rigid, approximately = 0.94; the main ordering axis, Z(M), lies along N-H, <c(2)(0)> approximately = 16 (c(2)(2) = 0); and the slow local motional correlation time lies at the low end of the nanosecond time scale.
    The Journal of Physical Chemistry B 09/2009; 113(35):12050-60. · 3.61 Impact Factor
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    ABSTRACT: Nuclear magnetic resonance (NMR) is a powerful tool for elucidating protein dynamics because of the possibility to interpret nuclear spin relaxation properties in terms of microdynamic parameters. Magnetic relaxation times T1, T2, and NOE depend on dipolar and quadrupolar interactions, on chemical shift anisotropy and cross-correlation effects. Within the framework of given motional model, it is possible to express the NMR relaxation times as functions of spectral densities (Abragam, The Principles of Nuclear Magnetism; Oxford University Press: Clarendon, London, 1961), obtaining the connection between macroscopic observables and microscopic properties. In this context, recently Meirovitch et al. (Shapiro et al., Biochemistry 2002, 41, 6271, Meirovitch et al., J Phys Chem B 2006, 110, 20615, Meirovitch et al., J Phys Chem B 2007, 111, 12865) applied the dynamical model introduced by Polimeno and Freed (Polimeno and Freed, Adv Chem Phys 1993, 83, 89, Polimeno and Freed, J Phys Chem 1995, 99, 10995), known as the slowly relaxing local structure (SRLS) model, to the study of NMR data.The program C++OPPS (http://www.chimica.unipd.it/licc/), developed in our laboratory, implements the SRLS model in an user-friendly way with a graphical user interface (GUI), introduced to simplify the work to users who do not feel at ease with the complex mathematics of the model and the difficulties of command line based programs. The program is an evolution of the old FORTRAN 77 implementation COPPS (COupled Protein Probe Smoluchowski) and presents a number of new features: the presence of an easy to use GUI written in JAVA; high calculation performance thanks to features of C++ language, employment of BLAS (basic linear algebra subprograms) library (Blackford et al., Trans Math Soft 2002, 28, 135) in handling matrix-vector operations and parallelization of the code under the MPI (message passing interface) paradigm (Gropp et al., Parallel Comput 1996, 22, 789, Gropp and Lusk, User's Guide for mpich, a Portable Implementation of MPI Mathematics and Computer Science Division; Argonne National Laboratory, 1996); possibility to predict the diffusion tensor of the protein via a hydrodynamic approach (Barone et al., J Comp Chem, in press). A cluster version of C++OPPS was also developed, which can be easily accessed by users via the web. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010
    International Journal of Quantum Chemistry 08/2009; 110(2):387 - 405. · 1.17 Impact Factor
  • Yury E Shapiro, Eva Meirovitch
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    ABSTRACT: The rotational diffusion of proteins is an important hydrodynamic property. Compact protein structures were found previously to exhibit hydration layer viscosity, etaloc, higher than the viscosity of bulk water, eta. This implies an apparent activation energy for rotational diffusion higher than the activation energy of water viscosity, Eeta=15.4+/-0.3 kJ/mol. In this study we examine etaloc of internally mobile proteins using 15N spin relaxation methods. We also examine the activation enthalpy, DeltaH#, and activation entropy, DeltaS#, for rotational diffusion. Of particular relevance are internally mobile ligand-free forms and compact ligand-bound forms of multidomain proteins. Adenylate kinase (AKeco) and Ca2+-calmodulin (Ca2+-CaM) are typical examples. For AKeco (Ca2+-CaM) we find that DeltaH# is 14.5+/-0.5 (15.7+/-0.4) kJ/mol. For the complex of AKeco with the inhibitor AP5A (the complex of Ca2+-CaM with the peptide smMLCKp), we find that DeltaH# is 18.1+/-0.7 (18.2+/-0.5) kJ/mol. The internally mobile outer surface protein A has DeltaH#=12.6+/-0.8 kJ/mol, and the compact protein Staphylococcal nuclease has DeltaH#=18.8+/-0.6 kJ/mol. For the internally mobile and compact proteins studied, <|DeltaS(|> equals 62+/-7 J/(mol K) and 44+/-5 J/(mol K), respectively. The fact is that etaloc>eta (DeltaH#>Eeta) for compact proteins was ascribed previously to electrostatic interactions between surface sites and water rigidifying the hydration layer. We find herein that obliteration of these interactions by domain motion leads to etaloc approximately eta, DeltaH# approximately Eeta, and large activation entropy for internally mobile protein structures.
    The Journal of Physical Chemistry B 05/2009; 113(19):7003-11. · 3.61 Impact Factor