Yury E. Shapiro

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

0079-6565/

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

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.

Domain mobility in proteins from NMR/SRLS.

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.

Slowly relaxing local structure (SRLS) analysis of 15N-H relaxation from the prototypical small proteins GB1 and GB3.

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 = -3.3 ( = 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, approximately = 16 (c(2)(2) = 0); and the slow local motional correlation time lies at the low end of the nanosecond time scale.

Evidence for Domain Motion in Proteins Affecting Global Diffusion Properties: a Nuclear Magnetic Resonance Study

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.

NMR spectroscopy on domain dynamics in biomacromolecules.

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.

Energy and Geometry of Cooperative Hydrogen Bonds in p-Substituted Calix[n]- and Thiacalix[n]arenes: A Quantum-Chemical Approach

Domain dynamics in biomacromolecules is currently an area of intense research because of its importance for understanding the huge quantity of available data relating the structure and function of proteins and nucleic acids. Control of structural flexibility is essential for the proper functioning of the biomacromolecules. Biophysical discoveries as well as computational algorithms and databases have reshaped our understanding of the often spectacular domain dynamics. At the residue level, such flexibility occurs due to local relaxation of peptide bond angles whose cumulative effect results in large changes in the secondary, tertiary or quaternary structures. The flexibility, or its absence, most often depends on the nature of interdomain linkages. Both the flexible and relatively rigid linkers are found in many multidomain biomacromolecules. Large-scale structural heterogeneity of multidomain biomacromolecules and their complexes is now seen as the norm rather than the exception. Absence of such motion, as in the so-called molecular rulers, also has desirable functional effects in architecture of biomacromolecules. The contemporary methods of NMR spectroscopy are capable to provide the detailed information on domain motions in biomacromolecules in the wide range of timescales related to the timescales of their functioning. We review here the current point of view on the nature of domain motions based on these last achievements in the field of NMR spectroscopy. Experimental and theoretical aspects of the collective intra- and interdomain motions are considered.

The eigenmode perspective of NMR spin relaxation in proteins

(Thia)calix[n]arenes have been widely applied as molecular platforms and host molecules in supramolecular chemistry due to their high level of preorganization and well-detectable conformational preferences. Here we report on quantum-chemical calculations allowing the conformational analysis of p-substituted calix[4]-, calix[6]-, thiacalix[4]-, and thiacalix[6]arenes. To this effect, ab initio and density functional theory (DFT) calculations with the aid of RHF/3-21G, B3LYP/6-31G, B3LYP/6-31G(d,p), and B3LYP/6-311G(d,p) have been applied. The obtained structural data and the estimated energies of the intramolecular hydrogen bonds give clear evidence of the presence of cooperative effects of the hydrogen bonding. Multiple correlations between the pairs of Hammett constants of substituents and the calculated values of hydrogen bond energies in the corresponding p-substituted (thia)calix[n]arenes have been found. These energies can be considered as descriptors of a chemical reactivity of the p-substituted derivatives of (thia)calix[n]arenes. For example, the reaction of nucleophilic substitution, involving p-substituted calix[6]arenes in the presence of weak bases and in aprotic solvents or in the gas phase, under orbital control conditions should proceed through the diastereomeric transition states. Here, the achiral p-substituted calix[6]arene derivative mainly forms as an intermediate product of the reaction with a substrate without asymmetric centers.

NMR spin relaxation in proteins: The patterns of motion that dissipate power to the bath

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.

Structure and dynamics of hydrogels and organogels: An NMR spectroscopy approach

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 rep...