An improved picture of methyl dynamics in proteins from slowly relaxing local structure analysis of 2H spin relaxation

Protein dynamics is intimately related to biological function. Core dynamics is usually studied with 2H spin relaxation of the 13CDH2 group, analyzed traditionally with the model-free (MF) approach. We showed recently that MF is oversimplified in several respects. This includes the assumption that the local motion of the dynamic probe and the global motion of the protein are decoupled, the local geometry is simple, and the local ordering is axially symmetric. Because of these simplifications MF has yielded a puzzling picture where the methyl rotation axis is moving rapidly with amplitudes ranging from nearly complete disorder to nearly complete order in tightly packed protein cores. Our conclusions emerged from applying to methyl dynamics in proteins the slowly relaxing local structure (SRLS) approach of Polimeno and Freed (Polimeno, A.; Freed, J. H. J. Phys. Chem. 1995, 99, 10995-11006.), which can be considered the generalization of MF, with all the simplifications mentioned above removed. The SRLS picture derived here for the B1 immunoglobulin binding domain of peptostreptococcal protein L, studied over the temperature range of 15-45 degrees C, is fundamentally different from the MF picture. Thus, methyl dynamics is characterized structurally by rhombic local potentials with varying symmetries and dynamically by tenfold slower rates of local motion. On average, potential rhombicity decreases, mode-coupling increases, and the rate of local motion increases with increasing temperature. The average activation energy for local motion is 2.0 +/- 0.2 kcal/mol. Mode-coupling affects the analysis even at 15 degrees C. The accuracy of the results is improved by including in the experimental data set relaxation rates associated with rank 2 coherences.     

A structural mode-coupling approach to 15N NMR relaxation in proteins.

The two-body Slowly Relaxing Local Structure (SRLS) model was applied to (15)N NMR spin relaxation in proteins and compared with the commonly used original and extended model-free (MF) approaches. In MF, the dynamic modes are assumed to be decoupled, local ordering at the N-H sites is represented by generalized order parameters, and internal motions are described by effective correlation times. SRLS accounts for dynamical coupling between the global diffusion of the protein and the internal motion of the N-H bond vector. The local ordering associated with the coupling potential and the internal N-H diffusion are tensors with orientations that may be tilted relative to the global diffusion and magnetic frames. SRLS generates spectral density functions that differ from the MF formulas. The MF spectral densities can be regarded as limiting cases of the SRLS spectral density. SRLS-based model-fitting and model-selection schemes similar to the currently used MF-based ones were devised, and a correspondence between analogous SRLS and model-free parameters was established. It was found that experimental NMR data are sensitive to the presence of mixed modes. Our results showed that MF can significantly overestimate order parameters and underestimate local motion correlation times in proteins. The extent of these digressions in the derived microdynamic parameters is estimated in the various parameter ranges, and correlated with the time scale separation between local and global motions. The SRLS-based analysis was tested extensively on (15)N relaxation data from several isotropically tumbling proteins. The results of SRLS-based fitting are illustrated with RNase H from E. coli, a protein extensively studied previously with MF.     

Protein dynamics from NMR: the slowly relaxing local structure analysis compared with model-free analysis

(15)N-(1)H spin relaxation is a powerful method for deriving information on protein dynamics. The traditional method of data analysis is model-free (MF), where the global and local N-H motions are independent and the local geometry is simplified. The common MF analysis consists of fitting single-field data. The results are typically field-dependent, and multifield data cannot be fit with standard fitting schemes. Cases where known functional dynamics has not been detected by MF were identified by us and others. Recently we applied to spin relaxation in proteins the slowly relaxing local structure (SRLS) approach, which accounts rigorously for mode mixing and general features of local geometry. SRLS was shown to yield MF in appropriate asymptotic limits. We found that the experimental spectral density corresponds quite well to the SRLS spectral density. The MF formulas are often used outside of their validity ranges, allowing small data sets to be force-fitted with good statistics but inaccurate best-fit parameters. This paper focuses on the mechanism of force-fitting and its implications. It is shown that MF analysis force-fits the experimental data because mode mixing, the rhombic symmetry of the local ordering and general features of local geometry are not accounted for. Combined multifield multitemperature data analyzed with the MF approach may lead to the detection of incorrect phenomena, and conformational entropy derived from MF order parameters may be highly inaccurate. On the other hand, fitting to more appropriate models can yield consistent physically insightful information. This requires that the complexity of the theoretical spectral densities matches the integrity of the experimental data. As shown herein, the SRLS spectral densities comply with this requirement.     

Probing side-chain dynamics in high molecular weight proteins by deuterium NMR spin relaxation: an application to an 82-kDa enzyme

New NMR experiments for the measurement of side-chain dynamics in high molecular weight ( approximately 100 kDa) proteins are presented. The experiments quantify (2)H spin relaxation rates in (13)CH(2)D or (13)CHD(2) methyl isotopomers and, for applications to large systems, offer significant gains both in sensitivity (2-3-fold) and resolution over previously published HSQC schemes. The methodology has been applied to investigate Ile dynamics in the 723-residue, single polypeptide chain enzyme, malate synthase G. Methyl-axis order parameters, S(axis), characterizing the amplitudes of motion of the methyl groups, have been derived from both (13)CH(2)D and (13)CHD(2) probes and are in excellent agreement. The distribution of order parameters is trimodal, reflecting the range of dynamics that are available to Ile residues. A reasonable correlation is noted between and inverse temperature factors from X-ray studies of the enzyme. The proposed methodology significantly extends the range of protein systems for which side-chain dynamics can be studied.     

Relaxation rates of degenerate 1H transitions in methyl groups of proteins as reporters of side-chain dynamics

Experiments for quantifying the amplitudes of motion of methyl-containing side chains are presented that exploit the rich network of cross-correlated spin relaxation interactions between intra-methyl dipoles in highly deuterated, selectively 13CH2D- or 13CH3-labeled proteins. In particular, the experiments measure spin relaxation rates of degenerate 1H transitions in methyl groups that, for high-molecular-weight proteins, are very simply related to methyl three-fold symmetry axis order parameters. The methodology presented is applied to studies of dynamics in a pair of systems, including the 7.5-kDa protein L and the 82-kDa enzyme malate synthase G. Good agreement between 1H- and 2H-derived measures of side-chain order are obtained on highly deuterated proteins with correlation times exceeding approximately 10 ns (correlation coefficients greater than 0.95). Although 2H- and 13C-derived measures of side-chain dynamics are still preferred, the present work underscores the potential of using 1H relaxation for semiquantitative estimates of methyl side-chain flexibility, while the high level of consistency between the different spin probes of motion establishes the reliability of the dynamics parameters.     

Re-evaluation of the model-free analysis of fast internal motion in proteins using NMR relaxation

NMR spin relaxation retains a central role in the characterization of the fast internal motion of proteins and their complexes. Knowledge of the distribution and amplitude of the motion of amino acid side chains is critical for the interpretation of the dynamical proxy for the residual conformational entropy of proteins, which can potentially significantly contribute to the entropy of protein function. A popular treatment of NMR relaxation phenomena in macromolecules dissolved in liquids is the so-called model-free approach of Lipari and Szabo. The robustness of the mode-free approach has recently been strongly criticized and the remarkable range and structural context of the internal motion of proteins, characterized by such NMR relaxation techniques, attributed to artifacts arising from the model-free treatment, particularly with respect to the symmetry of the underlying motion. We develop an objective quantification of both spatial and temporal asymmetry of motion and re-examine the foundation of the model-free treatment. Concerns regarding the robustness of the model-free approach to asymmetric motion appear to be generally unwarranted. The generalized order parameter is robustly recovered. The sensitivity of the model-free treatment to asymmetric motion is restricted to the effective correlation time, which is by definition a normalized quantity and not a true time constant and therefore of much less interest in this context. With renewed confidence in the model-free approach, we then examine the microscopic distribution of side chain motion in the complex between calcium-saturated calmodulin and the calmodulin-binding domain of the endothelial nitric oxide synthase. Deuterium relaxation is used to characterize the motion of methyl groups in the complex. A remarkable range of Lipari-Szabo model-free generalized order parameters are seen with little correlation with basic structural parameters such as the depth of burial. These results are contrasted with the homologous complex with the neuronal nitric oxide synthase calmodulin-binding domain, which has distinctly different thermodynamic origins for high affinity binding.     

The stereochemistry of polyporenic acid a methyl ester

The absolute configuration of the terminal asymmetric carbon centre in the side-chain of the methyl ester of polyporenic acid A, from $\text{Piptoporus betulinus}$ Fries, is shown to be 25(S)(2).     

Methyl side-chain dynamics in proteins using selective enrichment with a single isotopomer

13C relaxation studies on side-chain methyl groups in proteins typically involve measurements on (13)CHD(2) isotopomers, where the (13)C relaxation mechanism is particularly straightforward in the presence of a single proton. While such isotopomers can be obtained in proteins overexpressed in bacteria by use of (13)C enriched and fractionally deuterated media, invariably all possible (2)H isotopomers are obtained. This results in a loss of both resolution and sensitivity, which becomes particularly severe for larger proteins. We describe an approach that overcomes this problem by chemical synthesis of amino acids containing a pure (13)CHD(2) isotopomer. We illustrate the benefits of this approach in (13)C side-chain relaxation measurements on the mouse major urinary protein selectively enriched with [gamma(1),gamma(2)-(13)C(2),alpha,beta,gamma(1),gamma(1),gamma(2),gamma(2)-(2)H(6)] valine. Relaxation measurements in the absence and presence of pyrazine-derived ligands suggest that valine side-chain dynamics do not contribute significantly to binding entropy.     

On the internal rotations in p-cresol in its ground and first electronically excited states

The overall rotation and internal rotation of p-cresol (4-methyl-phenol) has been studied by comparison of the microwave spectrum with accurate ab initio calculations using the principal axis method in the electronic ground state. Both internal rotations, the torsions of the methyl and the hydroxyl groups relative to the aromatic ring, have been investigated. The internal rotation of the hydroxyl group can be approximately described as the motion of a symmetrical rotor on an asymmetric frame. For the methyl group it has been found that the potential barrier hindering its internal rotation is very small with the first two nonvanishing Fourier coefficients of the potential V(3) and V(6) in the same order of magnitude. Different splittings of b-type transitions for the A and E species of the methyl torsion indicate a top-top interaction between both internal rotors through the benzene ring. An effective coupling potential for the top-top interaction could be estimated. The hindering barriers of the hydroxyl and methyl rotation have been calculated using second-order Moller-Plesset perturbation theory and the approximate coupled-cluster singles-and-doubles model (CC2) in the ground state and using CC2 and the algebraic diagrammatic construction through second order in the first electronically excited state. The results are in excellent agreement with the experimental values.     

Comparison of methyl rotation axis order parameters derived from model-free analyses of (2)H and (13)C longitudinal and transverse relaxation rates measured in the same protein sample.

Recombinant HIV-1 protease was obtained from bacteria grown on a 98% D(2)O medium containing 3-(13)C pyruvic acid as the sole source of (13)C and (1)H. The purified protein is highly deuterated at non-methyl carbons, but contains significant populations of (13)CHD(2) and (13)CH(2)D methyl isotopomers. This pattern of isotope labeling permitted measurements of (1)H and (13)C relaxation rates of (13)CHD(2) isotopomers and (2)H (D) relaxation rates of (13)CH(2)D isotopomers using a single sample. The order parameters S(axis)(2), which characterize the motions of the methyl rotation axes, were derived from model-free analyses of R(1) and R(2) data sets measured for (13)C and (2)H spins. Our primary goal was to compare the S(axis)(2) values derived from the two independent types of data sets to test our understanding of the relaxation mechanisms involved. However, S(axis)(2) values derived from the analyses depend strongly on the geometry of the methyl group, the sizes of the quadrupolar and dipolar couplings, and the effects of bond vibrations and librations on these couplings. Therefore uncertainties in these basic physical parameters complicate comparison of the order parameters. This problem was circumvented by using an experimental relationship, between the methyl quadrupolar, (13)C-(13)C and (13)C-(1)H dipolar couplings, derived from independent measurements of residual static couplings of weakly aligned proteins by Ottiger and Bax (J. Am. Chem. Soc. 1999, 121, 4690-4695) and Mittermaier and Kay (J. Am. Chem. Soc. 1999, 121, 10608-10613). This approach placed a tight experimental restraint on the values of the (2)H quadrupolar and (13)C-(1)H dipolar interactions and greatly facilitated the accurate comparison of the relative values of the order parameters. When applied to our data this approach yielded satisfactory agreement between the S(axis)(2) values derived from the (13)C and (2)H data sets.     

Backbone and side-chain ordering in a small protein

We investigate the relation between backbone and side-chain ordering in a small protein. For this purpose, we have performed multicanonical simulations of the villin headpiece subdomain HP-36, an often used toy model in protein studies. Concepts of circular statistics are introduced to analyze side-chain fluctuations. In contrast to earlier studies on homopolypeptides [Wei et al., J. Phys. Chem. B 111, 4244 (2007)], we do not find collective effects leading to a separate transition. Rather, side-chain ordering is spread over a wide temperature range. Our results indicate a thermal hierarchy of ordering events, with side-chain ordering appearing at temperatures below the helix-coil transition but above the folding transition. We conjecture that this thermal hierarchy reflects an underlying temporal order, and that side-chain ordering facilitates the search for the correct backbone topology.     

Differential ordering of the protein backbone and side chains during protein folding revealed by site-specific recombinant infrared probes

The time scale for ordering of the polypeptide backbone relative to the side chains is a critical issue in protein folding. The interplay between ordering of the backbone and ordering of the side chains is particularly important for the formation of β-sheet structures, as the polypeptide chain searches for the native stabilizing cross-strand interactions. We have studied these issues in the N-terminal domain of protein L9 (NTL9), a model protein with mixed α/β structure. We have developed a general approach for introducing site-specific IR probes for the side chains (azide) and backbone ((13)C═(18)O) using recombinant protein expression. Temperature-jump time-resolved IR spectroscopy combined with site-specific labeling enables independent measurement of the respective backbone and side-chain dynamics with single residue resolution. We have found that side-chain ordering in a key region of the β-sheet structure occurs on a slower time scale than ordering of the backbone during the folding of NTL9, likely as a result of the transient formation of non-native side-chain interactions.     

Field response and switching times in biaxial nematics

We study by means of virtual molecular dynamics computer experiments the response of a bulk biaxial nematic to an applied external field and, in particular, the relative speed of reorientation of the principal director axis and of the secondary one, typical of these new materials, upon a pi2 field switch. We perform the simulations setting up and integrating the equations of motion for biaxial Gay-Berne particles using quaternions and a suitable time reversible symplectic integrator. We find that switching of the secondary axis is up to an order of magnitude faster than that of the principal axis, and that under fields above a certain strength a reorganization of local domains, temporarily disrupting the nematic and biaxial ordering, rather than a collective concerted reorientation occurs.     

Insights into the mobility of methyl-bearing side chains in proteins from (3)J(CC) and (3)J(CN) couplings

Side-chain dynamics in proteins can be characterized by the NMR measurement of (13)C and (2)H relaxation rates. Evaluation of the corresponding spectral densities limits the slowest motions that can be studied quantitatively to the time scale on which the overall molecular tumbling takes place. A different measure for the degree of side-chain order about the C(alpha)-C(beta) bond (chi(1) angle) can be derived from (3)J(C)(')(-)(C)(gamma) and (3)J(N)(-)(C)(gamma) couplings. These couplings can be measured at high accuracy, in particular for Thr, Ile, and Val residues. In conjunction with the known backbone structures of ubiquitin and the third IgG-binding domain of protein G, and an extensive set of (13)C-(1)H side-chain dipolar coupling measurements in oriented media, these (3)J couplings were used to parametrize empirical Karplus relationships for (3)J(C)(')(-)(C)(gamma) and (3)J(N)(-)(C)(gamma). These Karplus curves agree well with results from DFT calculations, including an unusual phase shift, which causes the maximum (3)J(CC) and (3)J(CN) couplings to occur for dihedral angles slightly smaller than 180 degrees, particularly noticeable in Thr residues. The new Karplus curves permit determination of rotamer populations for the chi(1) torsion angles. Similar rotamer populations can be derived from side-chain dipolar couplings. Conversion of these rotamer populations into generalized order parameters, S(J)(2) and S(D)(2), provides a view of side-chain dynamics that is complementary to that obtained from (13)C and (2)H relaxation. On average, results agree well with literature values for (2)H-relaxation-derived S(rel)(2) values in ubiquitin and HIV protease, but also identify a fraction of residues for which S(J,D)(2) < S(rel)(2). This indicates that some of the rotameric averaging occurs on a time scale too slow to be observable in traditional relaxation measurements.     

Studies of magnetic resonance phenomena in polymers. II. Molecular motions in poly(methyl methacrylate) as studied by spin-probe and spin-label methods

Thin films of spin-probed and spin-labeled poly(methyl methacrylate) (PMMA) have been examined by electron spin resonance (ESR) in the temperature range of 77–520°K. The rotational correlation times of nitroxides used as spin probes and labels have been determined as a function of temperature from which activation energies are also determined. The nitroxide rotational times are found to strongly correlate with local segmental and side-chain motions of the host PMMA matrix. Five discrete molecular motions are detected in PMMA along with their activation energies as measured: side-chain CH₃ rotation (1 Kcal/mol), main-chain CH₃ rotation (2 Kcal/mol), ester side-chain COOCH₃ rotation around the C? C bond (4 Kcal/mol), main-chain C? C bond rotation (6 Kcal/mol), and side-chain OCH₃ rotation around the C? O bond (18 Kcal/mol). The activation energies determined by ESR are consistent with the potential-energy barriers calculated theoretically for various rotations in PMMA. It is concluded that the probe and label rotational motions do respond to localized, small-scale segmental and side-chain motions of host polymers but are relatively ineffective in response to the large-scale segmental motion with an activation energy larger than 20 Kcal/mol in the case of PMMA.     

Side-chain and backbone ordering in homopolymers

In order to study the relation between backbone and side-chain ordering in proteins, we have performed multicanonical simulations of deka-peptide chains with various side groups. Glu(10), Gln(10), Asp(10), Asn(10), and Lys(10) were selected to cover a wide variety of possible interactions between the side chains of the monomers. All homopolymers undergo helix-coil transitions. We found that peptides with long side chains that are capable of hydrogen bonding, i.e., Glu(10), and Gln(10), exhibit a second transition at lower temperatures connected with side-chain ordering. This occurs in the gas phase as well as in solvent, although the character of the side-chain structure is different in each case. However, in polymers with short side chains capable of hydrogen bonding, i.e., Asp(10) and Asn(10), side-chain ordering takes place over a wide temperature range and exhibits no phase transition-like character. Moreover, non-backbone hydrogen bonds show enhanced formation and fluctuations already at the helix-coil transition temperature, indicating competition between side-chain and backbone hydrogen bond formation. Again, these results are qualitatively independent of the environment. Side-chain ordering in Lys(10), whose side groups are long and polar, also takes place over a wide temperature range and exhibits no phase transition-like character in both environments. Reasons for the observed chain length threshold and consequences from these results for protein folding are discussed.     

Probing side-chain dynamics in the proteasome by relaxation violated coherence transfer NMR spectroscopy

A pair of experiments is presented for measuring intra-methyl 1H-1H dipolar cross-correlated spin relaxation rates in highly deuterated, methyl protonated proteins with significantly improved sensitivity relative to previously developed experiments that measure dynamics via 1H spin relaxation. In applications to proteins with correlation times in the macromolecular limit, these cross-correlation rates are related directly to order parameters, characterizing the amplitude of motion of methyl-containing side-chains. The experimental approach is validated by comparing extracted order parameters with those obtained via 2H and 13C spin relaxation methods for both protein L (7.5 kDa) and malate synthase G (82 kDa), with excellent correlations obtained. The methodology is applied to study Ile, Leu, and Val side-chain dynamics in a 360 kDa "half-proteasome" complex. In particular, order parameters obtained from the WT complex and from a second complex where the proteasome gating residues are deleted establish that the relative levels of dynamics in each of the two molecules are very similar. It thus becomes clear that there is no communication between gating residues and other regions of the molecule involving pico- to nanosecond time-scale dynamics of these methyl-containing side-chains.     

含乙烯氧基柔链的苯并菲盘状液晶清亮点的平均场理论研究

我们前期的合成和实验发现, 对于一系列含端烯氧基醚链的苯并菲分子, 它们没有分子间氢键, 其生成的液晶的清亮点的高低与端烯氧基醚链的数目有关. 本工作采用Gay-Berne势模拟液晶分子的双体势, 用量子化学和分子力学相结合的ONIOM(MP2/6-31G*(0.25):UFF)方法优化含端烯氧基醚链的苯并菲分子的单体和双体的构型和能量, 从而获得Gay-Berne势的参数. 在此基础上, 根据平均场理论, 解一个关于序参量和温度的积分方程, 求出液晶的清亮点. 计算结果与实验趋势相同, 可以解释清亮点和分子端烯氧基醚链数目的关系.     

N-isopropylsulfinylimines as useful intermediates in the synthesis of chiral amines: expeditive asymmetric synthesis of the calcimimetic (+)-NPS R-568

An efficient and high-yielding approach for the asymmetric synthesis of calcimimetic (+)-NPS R-568 (1) has been developed. The key step of the synthesis is the highly diastereoselective addition of methyl Grignard to the (SS,E)-N-(3-methoxybenzylidene)-2-propanesulfinamide [5(S)], which afforded a single diastereoisomer in high yield in short reaction time.