Publications (42)159.37 Total impact
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ABSTRACT: We developed recently the slowly relaxing local structure (SRLS) approach for studying restricted motions in proteins by NMR. The spatial restrictions have been described by potentials comprising the traditional L = 2, K = 0, 2 spherical harmonics. However, the latter are associated with apolar ordering whereas proteinanchored probes experience polar ordering, described by oddL spherical harmonics. Here we extend the SRLS potential to include the L = 1, K = 0, 1 spherical harmonics and analyze (15)N(1)H relaxation from the third immunoglobulingbinding domain of streptococcal protein G (GB3) with the polar L = 1 potential (coefficients c10 and c11) or the apolar L = 2 potential (coefficients c20 and c22). Strong potentials, with〈c10〉~ 60 for L = 1 and〈c20〉~ 20 for L = 2 (in units of kBT), are detected. In the αhelix of GB3 the coefficients of the rhombic terms are c11 ~ c22 ~ 0; in the preceding (following) chain segment they are 〈c11〉~ 6 for L = 1 and〈c22〉~ 14 for L = 2 (〈c11〉~ 3 for L = 1 and〈c22〉~ 7 for L = 2). The local diffusion rate, D2, lies in the 5×10(9)1×10(11) s(1) range; it is generally larger for L = 1. The main ordering axis deviates moderately from the NH bond. Corresponding L = 1 and L = 2 potentials and probability density functions are illustrated for residues A26 of the αhelix, Y3 of the β1strand, and L12 of the β1/β2 loop; they differ considerably. Polar/orientational ordering is shown to be associated with GB3 binding to its cognate Fab fragment. The polarity of the local ordering is clearly an important factor. 
Article: Structural Dynamics of the Potassium Channel Blocker ShK: SRLS Analysis of (15)N Relaxation
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ABSTRACT: The 35residue ShK peptide binds with high affinity to voltagegated potassium channels. The dynamics of the binding surface was studied recently with (15)N relaxation dispersion (μsms) and (15)N spin relaxation (psns) of the backbone amide bonds. Relaxation dispersion revealed μs conformationalexchangemediated exposure of the functionally important Y23 side chain on the peptide surface. The spin relaxation parameters acquired at 14.1 and 16.45 T were subjected to modelfree (MF) analysis, which yielded a squared generalized order parameter, S(2), of approximately 0.85 for virtually all of the NH bonds. Only a "rigid backbone" evaluation could be inferred. We ascribe this limited information to the simplicity of MF in the context of challenging data (see below). To improve the analysis we apply the slowly relaxing local structure (SRLS) approach, which is a generalization of MF. SRLS describes NH bond dynamics in ShK in terms of a local potential, u, ranging from 10 to 18.5 kBT, and a local diffusion rate, D2, ranging from 4.2×10(8) to 2.4×10(10) s(1). This analysis shows that u is outstandingly strong for Y23 and relatively weak for K22, while D2 is slow for Y23 and fast for K22. These observations are relevant functionally because of the key role of the K22Y23 dyad in ShK binding to potassium channels. The disulfidebond network exhibits a mediumstrength potential and an alternating wavelike D2 pattern. This is indicative of moderate structural restraints and motional plasticity, in support of, although not directly correlated with, the μs bindingrelated conformational exchange process detected previously. Thus, new information on functionally important residues in ShK and its overall conformational stability emerged from the SRLS analysis, as compared with the previous MFbased estimate of backbone dynamics as backbone rigidity.  [Show abstract] [Hide abstract]
ABSTRACT: Deuterium line shape analysis from mobile CD and CCD3 groups has emerged as a particularly useful tool for studying dynamics in the solid state. The theoretical models devised so far consist typically of sets of independent dynamic modes. Each such mode is simple and usually casespecific. In this scenario, model improvement entails adding yet another mode (thereby changing the overall model), comparison of different cases is difficult, and ambiguity is unavoidable. We recently developed the microscopic order macroscopic disorder (MOMD) approach as a singlemode alternative. In MOMD, the local spatial restrictions are expressed by an anisotropic potential, the local motion by a diffusion tensor, and the local molecular geometry by relative (magnetic and modelrelated) tensor orientations, all of adjustable symmetry. This approach provides a consistent method of analysis, thus resolving the issues above. In this study, we apply MOMD to PSadsorbed LKα14 peptide and dimethylammonium tetraphenylborate (CCD3 and NCD3 dynamics, respectively), as well as HhaI methyltransferase target DNA and phase III of benzene6hexanoate (CD dynamics). The success with fitting these four disparate cases, as well as the two cases in the previous report, demonstrates the generality of this MOMDbased approach. In this study, CD and CCD3 are both found to execute axial diffusion (rates R⊥ and R∥) in the presence of a rhombic potential given by the L = 2 spherical harmonics (coefficients c20 and c22). R⊥ (R∥) is in the 102103 (104105) s1 range, and c20 and c22 are on the order of 23 kBT. Specific parameter values are determined for each mobile site. The diffusion and quadrupolar tensors are tilted at either 120° (consistent with transgauche isomerization) or nearly 110.5° (consistent with methyl exchange). Future prospects include extension of the MOMD formalism to include MAS, and application to 15N and 13C nuclei. 
Article: Protein Dynamics in the Solid State from 2 H NMR Line Shape Analysis: A Consistent Perspective
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ABSTRACT: Deuterium lineshape analysis of CD3 groups emerged as a particularly useful tool for studying μs  ms protein motions in the solidstate. The models devised so far consist of several independently conceived simple jumptype motions. They are comprised of physical quantities encoded in their simplest form; improvements are only possible by adding yet another simple motion, thereby changing the model. The various treatments developed are casespecific; hence comparison amongst the different systems is not possible. Here we develop a new methodology for (2)H NMR lineshape analysis free of these limitations. It is based on the microscopicordermacroscopicdisorder (MOMD) approach. In MOMD motions are described by diffusion tensors, spatial restrictions by potentials/ordering tensors, and geometric features by relative tensor orientations. Jumptype motions are recovered in the limit of large orientational potentials. Modelimprovement is accomplished by monitoring the magnitude, symmetry and orientation of the various tensors. The generality of MOMD makes possible comparison amongst different scenarios. CD3 lineshapes from the Chicken Villin Headpiece Subdomain, and the Streptomyces Subtilisin Inhibitor, are used as experimental examples. All of these spectra are reproduced by using rhombic local potentials constrained for simplicity to be given by the L = 2 spherical harmonics, and axial diffusion tensors. Potential strength and rhombicity are found to be ca. 2  3 [kBT]. The diffusion tensor is tilted at 120(o) from the CCD3 axis. The perpendicular (parallel) correlation times for local motion are 0.1  1.0 ms (3.3  30 μs). Activation energies in the 1.1  8.0 kcal/mol range are estimated. Future prospects include extension to the (2)H relaxation limit, application to the (15)N and (13)C NMR nuclei, and accounting for collective motions and anisotropic media.  [Show abstract] [Hide abstract]
ABSTRACT: NMR relaxation is a powerful method for elucidating structural dynamics. Standard stochastic dynamic models generate time correlation functions (TCFs) that feature physically welldefined parameters. We developed such a model, called the slowly relaxing local structure (SRLS) approach, for proteins. SRLS is a twobody (protein and probe) coupledrotator 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 multiexponential, in accordance with the degree of generality of the various tensors. The traditional modelfree (MF) method is based on a different conceptualization. According to it a modedecoupling biexponential (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.  [Show abstract] [Hide abstract]
ABSTRACT: We developed in recent years the twobody coupledrotator 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 spinbearing probe, e.g., the 15N1H 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 bestfit 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 jfraction, which represents the relative contribution of eigenmode, i, to a given value of the SDF function at a specific frequency, ω, is defined. jfraction profiles of the dominant eigenmodes are derived for 0 ≤ ω ≤ 1012 rad/s. They reveal which patterns of motion actuate power dissipation at given ωvalues, 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 globaldiffusiontype or conediffusiontype, and a nearly bare renormalizedlocaldiffusion 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 15N1H relaxation from the βsheet residue K19 and the αhelix residue A34 of the third immunoglobulinbinding 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 conediffusionrelated and mixed renormalizedlocaldiffusionrelated motions. At small ωvalues, A34 is more effective than K19 in dissipating power. In general, it executes faster conediffusiontype, and slower renormalizedlocaldiffusiontype and localprobefluctuationtype motions. K19 experiences faster NH fluctuations than A34. Eigenmode clustering, experienced by K19 to a larger extent, is observed in the fastprobefluctuation regime. New information on the effect of the structural context on NH bond dynamics has been obtained. The patterns of motion that dissipate NMRrelaxationrelated power illuminate protein dynamics from a new perspective. They constitute yet another qualifier of NH bond dynamics. This study sets the stage for developing ways for enhancing the contribution of desired pathways for power dissipation at selected angular velocities.  [Show abstract] [Hide abstract]
ABSTRACT: We developed in recent years the twobody (protein and probe) coupledrotator 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 (proteinrelated) diffusion tensor, D1, the local (proberelated) 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 datafitting techniques. In this study, we describe structural dynamics in terms of the eigenmodes comprising the SRLS time correlation functions (TCFs) generated by using the bestfit 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 bestfit parameters, the eigenmodes represent patterns of motion of the probeprotein 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 multiexponentiality 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 multiexponentiality 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 modecoupling 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 anticorrelated∕retrograde rotations of the global (D1) and local (D2) motional modes. The eigenmode paradigm is applied to NH bond dynamics in the βsheet residue K19, and the αhelix residue A34, of the third immunoglobulinbinding domain of streptococcal protein G. The largest contribution to the SRLS TCFs is made by mixed anticorrelated D1 and D2 eigenmodes. The next largest contribution is made by D1dominated 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 bestfit SRLS parameters and modemixing. It may be concluded that eigenmode analysis is complementary and supplementary to datafittingbased analysis.  [Show abstract] [Hide abstract]
ABSTRACT: We applied over a decade ago the twobody coupledrotator 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 (spinbearing moiety, typically the (15)N(1)H bond). So far we applied SRLS to (15)NH relaxation from seven different proteins within the scope of the commonly used datafitting paradigm. Here, we solve the SRLS Smoluchowski equation using typical bestfit 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 Ci1 (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. Modecoupling becomes important when the ratio between the global and local motional rates falls below 0.01. The traditional method of analysis  modelfree (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 wobbleinacone 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 TCFbased comparison between mesoscopic SRLS and atomistic molecular dynamics.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate psns dynamics of the RhoGTPase Binding Domain (RBD) of plexinB1, which plays a key role in plexinmediated cell signaling. Backbone (15)N relaxation data of the dimeric RBD are analyzed with the modelfree (MF) method, and with the slowly relaxing local structure/molecular dynamics (SRLSMD) 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 SRLSMD 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 plexinB1 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 αhelices and the βstrands of the dimer (the βstrands of the monomer) experience strong and highly asymmetric local ordering centered approximately at the C(α)C(α) axes (NH bonds). NH fluctuations occur on the ps timescale. An allosteric pathway for GTPase binding, providing new insights into plexin function, is delineated. 
Article: SRLS Analysis of 15N Spin Relaxation from E. coil Ribonuclease HI: The Tensorial Perspective
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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 modecoupling slowly relaxing local structure (SRLS) approach. In accordance with standard theoretical treatments of restricted motions, SRLS approaches NH 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(i1)αC(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 3125 (208344) ps for the secondary structure elements (loops) and is on average 125 ps for the Cterminal segment. The main local diffusion axis deviates from the NH bond by less than 2° (10°) for the secondary structure elements (loops). An effective datafitting 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.  [Show abstract] [Hide abstract]
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 nitroxidelabeled 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 modelfree (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 Nterminal (Cterminal) 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 Nterminal domain, the Cterminal 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 Cterminal domains, and by 2.5° for the linker. The tensorialperspectivebased and modecouplingbased SRLS picture provides new insights into the structural dynamics of bacteriophage T4 lysozyme.  [Show abstract] [Hide abstract]
ABSTRACT: Residual dipolar couplings (RDCs) in proteins arise from independent external mediumrelated and internal proteinrelated ordering of the spinbearing 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 mfRDC 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 mfRDC 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 mfRDC 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 αhelix 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 mfRDC. 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.  [Show abstract] [Hide abstract]
ABSTRACT: 15NH relaxation parameters from the first (GB1) and third (GB3) immunoglobulinbinding domains of streptococcal protein G were analyzed previously with the traditional modelfree (MF) method. These proteins comprise an αhelix and a fourstranded βsheet. An extensive study of GB1 (GB3) used combined threefield (fivefield) data acquired in the 278323 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 modecoupling. 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(i1)(α)  C(i)(α), and the average axial (rhombic) order parameter is 0.457 ± 0.017 (1.156 ± 0.015) for the αhelix and 0.484 ± 0.002 (1.10 ± 0.04) for the rest of the polypeptide chain. The NH bonds within (outside of) the αhelix reorient locally with an average correlation time, (τ), of 310 (130) ps, as compared to 3.33 ns for the global tumbling. Several NH bonds in the loops β1/β2, β2/αhelix, and αhelix/β3 have (τ) of 380, 320, and 750 ps, respectively. The distinctive experimental data of the αhelix 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 βstrands, 24.7 ± 3.9 kJ/mol for the αhelix (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. 
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ABSTRACT: An integrated computational methodology for interpreting NMR spin relaxation in proteins has been developed. It combines a twobody coupledrotator stochastic model with a hydrodynamicsbased 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 NH bonds in the Rho GTPase binding (RBD) domain of plexinB1, 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 αhelices and βsheets 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 αhelices the zaxis of the local ordering frame is parallel to the C(α)C(α) axis. For βsheets the zaxes of the S and D₂ tensors are parallel to the NH 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 12. 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.  [Show abstract] [Hide abstract]
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 modelfree (MF) method, which does not account for modecoupling 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 modecoupling 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 00.316 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 (1027) 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.  [Show abstract] [Hide abstract]
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 NH 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 (5.25.8) × 10⁶ 1/s in the temperature range investigated. The principal axis of S is (nearly) parallel to the C(i1)(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 NH bond; when the two axes are parallel, β(O) = 101.3°. For "rigid" NH bonds located in secondary structure elements the bestfit parameters are S(0)(2) = 0.880.95 (corresponding to local potentials of 8.619.9 k(B)T), R()(L) = 10⁹10¹⁰ 1/s, β(D) = 101.3° ± 2.0°, and β(O) = 101.3° ± 4°. For flexible NH bonds located in loops the bestfit values are S(0)(2) = 0.750.80 (corresponding to local potentials of 4.55.5 k(B)T), R()(L) = (1.06.3) × 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). 
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ABSTRACT: There is no abstract available for this article. 
Article: Structural dynamics of biomacromolecules by NMR: The slowly relaxing local structure approach
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ABSTRACT: The review of Progress in Nuclear Magnetic Resonance Spectroscopy demonstrated the application of the slowly relaxing local structure (SRLS) approach in structural dynamics of biomacromolecules by NMR. SRLS was demonstrated to be a stochastic twobody coupledrotator diffusive approach, having the potential to be generalized to three or more bodies that were coupled, along with the inclusion of inertial effects in these motions. The review offered the concepts that emphasized SRLS as an alternative to the modelfree pointofview approach, while describing and demonstrating the way SRLS was to be implemented in a practical manner. application of SRLS and modelfree (MF) to a large number of data sets revealed that MF was frequently a forcefitting to the experimental data and that SRLS and MF analyses were quantitative in nature.
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885  Citations  
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Institutions

19992016

Bar Ilan University
 • Faculty of Life Sciences
 • Department of Chemistry
Gan, Tel Aviv, Israel


2004

University of Pittsburgh
 Department of Medicine
Pittsburgh, Pennsylvania, United States


2002

Cornell University
Итак, New York, United States
