Relationships between protein structure and dynamics from a database of NMR-derived backbone order parameters

Intramolecular dynamics of low molecular weight protein tyrosine phosphatase in monomer-dimer equilibrium studied by NMR: a model for changes in dynamics upon target binding

Low molecular weight protein tyrosine phosphatase (LMW-PTP) dimerizes in the phosphate-bound state in solution with a dissociation constant of K(d)=1.5(+/-0.1)mM and an off-rate on the order of 10(4)s(-1). 1H and 15N NMR chemical shifts identify the dimer interface, which is in excellent agreement with that observed in the crystal structure of the dimeric S19A mutant. Two tyrosine residues of each molecule interact with the active site of the other molecule, implying that the dimer may be taken as a model for a complex between LMW-PTP and a target protein. 15N relaxation rates for the monomeric and dimeric states were extrapolated from relaxation data acquired at four different protein concentrations. Relaxation data of satisfactory precision were extracted for the monomer, enabling model-free analyses of backbone fluctuations on pico- to nanosecond time scales. The dimer relaxation data are of lower quality due to extrapolation errors and the possible presence of higher-order oligomers at higher concentrations. A qualitative comparison of order parameters in the monomeric and apparent dimeric states shows that loops forming the dimer interface become rigidified upon dimerization. Qualitative information on monomer-dimer exchange and intramolecular conformational exchange was obtained from the concentration dependence of auto- and cross-correlated relaxation rates. The loop containing the catalytically important Asp129 fluctuates between different conformations in both the monomeric and dimeric (target bound) states. The exchange rate compares rather well with that of the catalyzed reaction step, supporting existing hypotheses that catalysis and enzyme dynamics may be coupled. The side-chain of Trp49, which is important for substrate specificity, exhibits conformational dynamics in the monomer that are largely quenched upon formation of the dimer, suggesting that binding is associated with the selection of a single side-chain conformer.

Modern protein force fields behave comparably in molecular dynamics simulations

Several molecular dynamics simulations were performed on three proteins--bovine apo-calbindin D9K, human interleukin-4 R88Q mutant, and domain IIA of bacillus subtilis glucose permease--with each of the AMBER94, CHARMM22, and OPLS-AA force fields as implemented in CHARMM. Structural and dynamic properties such as solvent-accessible surface area, radius of gyration, deviation from their respective experimental structures, secondary structure, and backbone order parameters are obtained from each of the 2-ns simulations for the purpose of comparing the protein portions of these force fields. For one of the proteins, the interleukin-4 mutant, two independent simulations were performed using the CHARMM22 force field to gauge the sensitivity of some of these properties to the specific trajectory. In general, the force fields tested performed remarkably similarly with differences on the order of those found for the two independent trajectories of interleukin-4 with CHARMM22. When all three proteins are considered together, no force field showed any consistent trend in variations for most of the properties monitored in the study.

Temperature-dependent dynamics of the villin headpiece helical subdomain, an unusually small thermostable protein

(15)N spin relaxation experiments were used to measure the temperature-dependence of protein backbone conformational fluctuations in the thermostable helical subdomain, HP36, of the F-actin-binding headpiece domain of chicken villin. HP36 is the smallest domain of a naturally occurring protein that folds cooperatively to a compact native state. Spin-lattice, spin-spin, and heteronuclear nuclear Overhauser effect relaxation data for backbone amide (15)N spins were collected at five temperatures in the range of 275-305 K. The data were analyzed using a model-free formalism to determine generalized order parameters, S, that describe the distribution of N-H bond vector orientations in a molecular reference frame. A novel parameter, Lambda=dln(1-S)/dln T is introduced to characterize the temperature-dependence of S. An average value of Lambda=4.5 is obtained for residues in helical conformations in HP36. This value of Lambda is not reproduced by model potential energy functions commonly used to parameterize S. The maximum entropy principle was used to derive a new model potential function that reproduces both S and Lambda. Contributions to the entropy, S(r), and heat capacity, C(r)(p), from reorientational conformational fluctuations were analyzed using this potential energy function. Values of S(r) show a qualitative dependence on S similar to that obtained for the diffusion-in-a-cone model; however, quantitative differences of up to 0.5k, in which k is the Boltzmann constant, are observed. Values of C(r)(p) approach zero for small values of S and approach k for large values of S; the largest values of C(r)(p) are predicted to occur for intermediate values of S. The results suggest that backbone dynamics, as probed by relaxation measurements, make very little contribution to the heat capacity difference between folded and unfolded states for HP36.

Molecular dynamics and NMR spin relaxation in proteins

Molecular dynamics simulations often play a central role in the analysis of biomolecular NMR data. The focus here is on NMR spin-relaxation, which can provide unique insights into the time-dependence of conformational fluctuations, especially on picosecond to nanosecond time scales which can be directly probed by simulations. A great deal has been learned from such simulations about the general nature of such motions and their impact on NMR observables. In principle, relaxation measurements should also provide valuable benchmarks for judging the quantitative accuracy of simulations, but there are a variety of experimental and computational obstacles to making useful direct comparisons. It seems likely that simulations on time scales that are just now becoming generally feasible may provide important new information on internal motions, overall rotational diffusion, and the coupling between internal and rotational motion. Such information could provide a sound foundation for a new generation of detailed interpretation of NMR spin-relaxation results.

A new spin on protein dynamics

Site-directed spin labeling is a general method for investigating structure and conformational switching in soluble and membrane proteins. It will also be an important tool for exploring protein backbone dynamics. A semi-empirical analysis of nitroxide sidechain dynamics in spin-labeled proteins reveals contributions from fluctuations in backbone dihedral angles and rigid-body (collective) motions of alpha helices. Quantitative analysis of sidechain dynamics is sometimes possible, and contributions from backbone modes can be expressed in terms of relative order parameters and rates. Dynamic sequences identified by site-directed spin labeling correlate with functional domains, and so nitroxide scanning could provide an efficient strategy for identifying such domains in high-molecular weight proteins, supramolecular complexes and membrane proteins.

NMR studies of the backbone flexibility and structure of human growth hormone: a comparison of high and low pH conformations

(15)N NMR relaxation parameters and amide (1)H/(2)H-exchange rates have been used to characterize the structural flexibility of human growth hormone (rhGH) at neutral and acidic pH. Our results show that the rigidity of the molecule is strongly affected by the solution conditions. At pH 7.0 the backbone dynamics parameters of rhGH are uniform along the polypeptide chain and their values are similar to those of other folded proteins. In contrast, at pH 2.7 the overall backbone flexibility increases substantially compared to neutral pH and the average order parameter approaches the lower limit expected for a folded protein. However, a significant variation of the backbone dynamics through the molecule indicates that under acidic conditions the mobility of the residues becomes more dependent on their location within the secondary structure units. In particular, the order parameters of certain loop regions decrease dramatically and become comparable to those found in unfolded proteins. Furthermore, the HN-exchange rates at low pH reveal that the residues most protected from exchange are clustered at one end of the helical bundle, forming a stable nucleus. We suggest that this nucleus maintains the overall fold of the protein under destabilizing conditions. We therefore conclude that the acid state of rhGH consists of a structurally conserved, but dynamically more flexible helical core surrounded by an aura of highly mobile, unstructured loops. However, in spite of its prominent flexibility the acid state of rhGH cannot be considered a "molten globule" state because of its high stability. It appears from our work that under certain conditions, a protein can tolerate a considerable increase in flexibility of its backbone, along with an increased penetration of water into its core, while still maintaining a stable folded conformation.

Flexibility and packing in proteins

Structural flexibility is an essential attribute, without which few proteins could carry out their biological functions. Much information about protein flexibility has come from x-ray crystallography, in the form of atomic mean-square displacements (AMSDs) or B factors. Profiles showing the AMSD variation along the polypeptide chain are usually interpreted in dynamical terms but are ultimately governed by the local features of a highly complex energy landscape. Here, we bypass this complexity by showing that the AMSD profile is essentially determined by spatial variations in local packing density. On the basis of elementary statistical mechanics and generic features of atomic distributions in proteins, we predict a direct inverse proportionality between the AMSD and the contact density, i.e., the number of noncovalent neighbor atoms within a local region of approximately 1.5 nm(3) volume. Testing this local density model against a set of high-quality crystal structures of 38 nonhomologous proteins, we find that it accurately and consistently reproduces the prominent peaks in the AMSD profile and even captures minor features, such as the periodic AMSD variation within alpha helices. The predicted rigidifying effect of crystal contacts also agrees with experimental data. With regard to accuracy and computational efficiency, the model is clearly superior to its predecessors. The quantitative link between flexibility and packing density found here implies that AMSDs provide little independent information beyond that contained in the mean atomic coordinates.

Continuum secondary structure captures protein flexibility

The DSSP program assigns protein secondary structure to one of eight states. This discrete assignment cannot describe the continuum of thermal fluctuations. Hence, a continuous assignment is proposed. Technically, the continuum results from averaging over ten discrete DSSP assignments with different hydrogen bond thresholds. The final continuous assignment for a single NMR model successfully reflected the structural variations observed between all NMR models in the ensemble. The structural variations between NMR models were verified to correlate with thermal motion; these variations were captured by the continuous assignments. Because the continuous assignment reproduces the structural variation between many NMR models from one single model, functionally important variation can be extracted from a single X-ray structure. Thus, continuous assignments of secondary structure may affect future protein structure analysis, comparison, and prediction.

Thermodynamic insights into proteins from NMR spin relaxation studies

NMR spin relaxation measurements of picosecond to nanosecond timescale backbone and sidechain fluctuations of protein molecules, and subsequent entropic interpretation yield interesting, but sometimes counterintuitive, insights into proteins. The stabilities of proteins and protein interactions are achieved through enthalpy-entropy compensation, which is partitioned between the backbone and sidechains depending on the nature of the system.

Nmr probes of molecular dynamics: overview and comparison with other techniques

NMR spin relaxation spectroscopy is a powerful approach for characterizing intramolecular and overall rotational motions in proteins. This review describes experimental methods for measuring laboratory frame spin relaxation rate constants by high-resolution solution-state NMR spectroscopy, together with theoretical approaches for interpreting spin relaxation data in order to quantify protein conformational dynamics on picosecond-nanosecond time scales. Recent applications of these techniques to proteins are surveyed, and investigations of the contribution of conformational chain entropy to protein function are highlighted. Insights into the dynamical properties of proteins obtained from NMR spin relaxation spectroscopy are compared with results derived from other experimental and theoretical techniques.

Protein flexibility predictions using graph theory

Techniques from graph theory are applied to analyze the bond networks in proteins and identify the flexible and rigid regions. The bond network consists of distance constraints defined by the covalent and hydrogen bonds and salt bridges in the protein, identified by geometric and energetic criteria. We use an algorithm that counts the degrees of freedom within this constraint network and that identifies all the rigid and flexible substructures in the protein, including overconstrained regions (with more crosslinking bonds than are needed to rigidify the region) and underconstrained or flexible regions, in which dihedral bond rotations can occur. The number of extra constraints or remaining degrees of bond-rotational freedom within a substructure quantifies its relative rigidity/flexibility and provides a flexibility index for each bond in the structure. This novel computational procedure, first used in the analysis of glassy materials, is approximately a million times faster than molecular dynamics simulations and captures the essential conformational flexibility of the protein main and side-chains from analysis of a single, static three-dimensional structure. This approach is demonstrated by comparison with experimental measures of flexibility for three proteins in which hinge and loop motion are essential for biological function: HIV protease, adenylate kinase, and dihydrofolate reductase.

Backbone dynamics of the regulatory domain of calcium vector protein, studied by (15)N relaxation at four fields, reveals unique mobility characteristics of the intermotif linker

CaVP is a calcium-binding protein from amphioxus. It has a modular composition with two domains, but only the two EF-hand motifs localized in the C-terminal domain are functional. We recently determined the solution structure of this regulatory half (C-CaVP) in the Ca(2+)-saturated form and characterized the stepwise ion binding. This paper reports the (15)N nuclear relaxation rates of the Ca(2+)-saturated C-CaVP, measured at four different NMR fields (9.39, 11.74, 14.1, and 18.7 T), which were used to map the spectral density function for the majority of the amide H(N)-N vectors. Fitting the spectral density values at eight frequencies by a model-free approach, we obtained the microdynamic parameters characterizing the global and internal movements of the polypeptide backbone. The two EF-hand motifs, including the ion binding loops, behave like compact structural units with restricted mobility as reflected in the quite uniform order parameter and short internal correlation time (< 20 nsec). Comparative analysis of the two Ca(2+) binding sites shows that site III, having a larger affinity for the metal ion, is generally more rigid, and the amide vector in the second residue of each loop is significantly less restricted. The linker fragment is animated simultaneously by a larger amplitude fast motion and a slow conformational exchange on a microsecond to millisecond time scale. The backbone dynamics of C-CaVP characterized here is discussed in relation with other well-characterized Ca(2+)-binding proteins.

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Fluctuations in ion pairs and their stabilities in proteins

This report investigates the effect of systemic protein conformational flexibility on the contribution of ion pairs to protein stability. Toward this goal, we use all NMR conformer ensembles in the Protein Data Bank (1) that contain at least 40 conformers, (2) whose functional form is monomeric, (3) that are nonredundant, and (4) that are large enough. We find 11 proteins adhering to these criteria. Within these proteins, we identify 22 ion pairs that are close enough to be classified as salt bridges. These are identified in the high-resolution crystal structures of the respective proteins or in the minimized average structures (if the crystal structures are unavailable) or, if both are unavailable, in the "most representative" conformer of each of the ensembles. We next calculate the electrostatic contribution of each such ion pair in each of the conformers in the ensembles. This results in a comprehensive study of 1,201 ion pairs, which allows us to look for consistent trends in their electrostatic contributions to protein stability in large sets of conformers. We find that the contributions of ion pairs vary considerably among the conformers of each protein. The vast majority of the ion pairs interconvert between being stabilizing and destabilizing to the structure at least once in the ensembles. These fluctuations reflect the variabilities in the location of the ion pairing residues and in the geometric orientation of these residues, both with respect to each other, and with respect to other charged groups in the remainder of the protein. The higher crystallographic B-factors for the respective side-chains are consistent with these fluctuations. The major conclusion from this study is that salt bridges observed in crystal structure may break, and new salt bridges may be formed. Hence, the overall stabilizing (or, destabilizing) contribution of an ion pair is conformer population dependent.

NMR relaxation studies of the role of conformational entropy in protein stability and ligand binding

Recent advances in the measurement and analysis of protein NMR relaxation data have made it possible to characterize the dynamical properties of many backbone and side chain groups. With certain caveats, changes in flexibility that occur upon ligand binding, mutation, or changes in sample conditions can be interpreted in terms of contributions to conformational entropy. Backbone and side chain flexibility can either decrease or increase upon ligand binding. Decreases are often associated with "enthalpy-entropy compensation" and "induced fit" binding, whereas increases in conformational entropy can contribute to stabilization of complexes. In certain cases, conformational entropy appears to play a role in cooperative binding and enzyme catalysis. In addition, variations in conformational entropy and heat capacity may both be important in stabilizing the folded structures of proteins.

Relationship of DNA structure to internal dynamics: correlation of helical parameters from NOE-based NMR solution structures of d(GCGTACGC)(2) and d(CGCTAGCG)(2) with (13)C order parameters implies conformational coupling in dinucleotide units

The coupling between the conformational properties of double-stranded DNA and its internal dynamics has been examined. The solution structures of the isomeric DNA oligomers d(GCGTACGC)(2) (UM) and d(CGCTAGCG)(2) (CTSYM) were determined with (1)H NMR spectroscopy by utilizing distance restraints from total relaxation matrix analysis of NOESY cross-peak intensities in restrained molecular dynamics calculations. The root-mean-square deviation of the coordinates for the ensemble of structures was 0.13 A for UM and 0.49 A for CTSYM, with crystallographic equivalent R(c)=0.41 and 0.39 and sixth-root residual R(x)=0.11 and 0.10 for UM and CTSYM, respectively. Both UM and CTSYM are B-form with straight helical axes and show sequence-dependent variations in conformation. The internal dynamics of UM and CTSYM were previously determined by analysis of (13)C relaxation parameters in the context of the Lipari & Szabo model-free formalism. Helical parameters for the two DNA oligomers were examined for linear correlations with the order parameters (S(2)) of groups of (13)C spins in base-pairs and dinucleotide units of UM and CTSYM. Correlations were found for six interstrand base-pair parameters tip, y-displacement, inclination, buckle and stretch with various combinations of S(2) for atoms in Watson-Crick base-pairs and for two inter-base-pair parameters, rise and roll with various combinations of S(2) for atoms in dinucleotides. The correlations for the interstrand base-pair helical parameters indicate that the conformations of the deoxyribose residues of each strand are dynamically coupled. Also, the inter-base-pair separation has a profound effect on the local internal motions available to the DNA, supporting the idea that rise is a principal degree of freedom for DNA conformational variability. The correlations indicate collective atomic motions of spins that may represent specific motional modes in DNA, and that base sequence has a predictable effect on the relative order of groups of spins both in the bases and in the deoxyribose ring of the DNA backbone. These observations suggest that an important functional outcome of DNA base sequence is the modulation of both the conformation and dynamic behavior of the DNA backbone.

Backbone dynamics of a module pair from the ligand-binding domain of the LDL receptor

The ligand-binding domain of the LDL receptor consists of seven contiguous LDL-A modules. The fifth of these ligand-binding modules is absolutely required for recognition of both LDL and beta-VLDL particles. A four-residue linker of variable sequence connects each pair of modules, except for modules four and five, which are connected by a 12-residue linker. To provide a more detailed understanding of the structural relationship in a typical pair of functionally important LDL-A repeats of the LDLR, we investigated the backbone dynamics of repeats five (LR5) and six (LR6) alone and in the context of the covalently connected LR5-6 pair. Our results reveal substantial flexibility in the four-residue linker connecting the two repeats in the LR5-6 pair. The intrinsic dynamic behavior of each repeat is essentially unchanged when the repeats are covalently connected. These observations indicate that the relative orientation of repeats in LR5-6 is not fixed. Modeled in an extended conformation, the linker can separate LR5 and LR6 by up to 15 A, a distance that would allow substantial freedom of motion of each repeat with respect to the other in the pair.

Solution structure and dynamics of an open beta-sheet, glycolytic enzyme, monomeric 23.7 kDa phosphoglycerate mutase from Schizosaccharomyces pombe

The structure and backbone dynamics of a double labelled (15N,13C) monomeric, 23.7 kD phosphoglycerate mutase (PGAM) from Schizosaccharomyces pombe have been investigated in solution using NMR spectroscopy. A set of 3125 NOE-derived distance restraints, 148 restraints representing inferred hydrogen bonds and 149 values of (3)J(HNHalpha) were used in the structure calculation. The mean rmsd from the average structure for all backbone atoms from residues 6-205 in the best 21 calculated structures was 0.59 A. The core of the enzyme includes an open, twisted, six-stranded beta-sheet flanked by four alpha-helices and a short 3(10)-helix. An additional smaller domain contains two short antiparallel beta-strands and a further pair of alpha-helices. The C(alpha) atoms of the S. pombe PGAM may be superimposed on their equivalents in one of the four identical subunits of Saccharomyces cerevisiae PGAM with an rmsd of 1.34 A (0.92 A if only the beta-sheet is considered). Small differences between the two structures are attributable partly to the deletion in the S. pombe sequence of a 25 residue loop involved in stabilising the S. cerevisiae tetramer. Analysis of 15N relaxation parameters indicates that PGAM tumbles isotropically with a rotational correlation time of 8.7 ns and displays a range of dynamic features. Of 178 residues analysed, only 77 could be fitted without invoking terms for fast internal motion or chemical exchange, and out of the remainder, 77 required a chemical exchange term. Significantly, 46 of the slowly exchanging (milli- to microsecond) residues lie in helices, and these account for two-thirds of all analysed helix residues. On the contrary, only one beta-sheet residue required an exchange term. In contrast to other analyses of backbone dynamics reported previously, residues in slow exchange appeared to correlate with architectural features of the enzyme rather than congregating close to ligand binding sites.