Analysis of side chain mobility among protein G B1 domain mutants with widely varying stabilities

"Host-guest" studies of the B1 domain from Streptococcal protein G have been used previously to establish a thermodynamic scale for the beta-sheet-forming propensities of the 20 common amino acids. To investigate the contribution of side chain conformational entropy to the relative stabilities of B1 domain mutants, we have determined the dynamics of side chain methyl groups in 10 of the 20 mutants used in a previous study. Deuterium relaxation rates were measured using two-dimensional NMR techniques for 13CH2D groups. Analysis of the relaxation data using the Lipari-Szabo model-free formalism showed that mutations introduced at the guest position caused small but statistically significant changes in the methyl group dynamics. In addition, there was a low level of covariation of the Lipari-Szabo order parameters among the 10 mutants. The variations in conformational free energy estimated from the order parameters were comparable in magnitude to the variations in global stability of the 10 mutants but did not correlate with the global stability of the domain or with the structural properties of the guest amino acids. The data support the view that conformational entropy in the folded state is one of many factors that can influence the folding thermodynamics of proteins.     

Conformational entropy changes upon lactose binding to the carbohydrate recognition domain of galectin-3

The conformational entropy of proteins can make significant contributions to the free energy of ligand binding. NMR spin relaxation enables site-specific investigation of conformational entropy, via order parameters that parameterize local reorientational fluctuations of rank-2 tensors. Here we have probed the conformational entropy of lactose binding to the carbohydrate recognition domain of galectin-3 (Gal3), a protein that plays an important role in cell growth, cell differentiation, cell cycle regulation, and apoptosis, making it a potential target for therapeutic intervention in inflammation and cancer. We used ¹⁵N spin relaxation experiments and molecular dynamics simulations to monitor the backbone amides and secondary amines of the tryptophan and arginine side chains in the ligand-free and lactose-bound states of Gal3. Overall, we observe good agreement between the experimental and computed order parameters of the ligand-free and lactose-bound states. Thus, the ¹⁵N spin relaxation data indicate that the molecular dynamics simulations provide reliable information on the conformational entropy of the binding process. The molecular dynamics simulations reveal a correlation between the simulated order parameters and residue-specific backbone entropy, re-emphasizing that order parameters provide useful estimates of local conformational entropy. The present results show that the protein backbone exhibits an increase in conformational entropy upon binding lactose, without any accompanying structural changes.     

15N backbone dynamics of the S-peptide from ribonuclease A in its free and S-protein bound forms: toward a site-specific analysis of entropy changes upon folding.

Backbone 15N relaxation parameters (R1, R2, 1H-15N NOE) have been measured for a 22-residue recombinant variant of the S-peptide in its free and S-protein bound forms. NMR relaxation data were analyzed using the "model-free" approach (Lipari & Szabo, 1982). Order parameters obtained from "model-free" simulations were used to calculate 1H-15N bond vector entropies using a recently described method (Yang & Kay, 1996), in which the form of the probability density function for bond vector fluctuations is derived from a diffusion-in-a-cone motional model. The average change in 1H-15N bond vector entropies for residues T3-S15, which become ordered upon binding of the S-peptide to the S-protein, is -12.6+/-1.4 J/mol.residue.K. 15N relaxation data suggest a gradient of decreasing entropy values moving from the termini toward the center of the free peptide. The difference between the entropies of the terminal and central residues is about -12 J/mol residue K, a value comparable to that of the average entropy change per residue upon complex formation. Similar entropy gradients are evident in NMR relaxation studies of other denatured proteins. Taken together, these observations suggest denatured proteins may contain entropic contributions from non-local interactions. Consequently, calculations that model the entropy of a residue in a denatured protein as that of a residue in a di- or tri-peptide, might over-estimate the magnitude of entropy changes upon folding.     

Prediction of methyl-side Chain Dynamics in Proteins

A simple analytical model is presented for the prediction of methyl-side chain dynamics in comparison with S(2) order parameters obtained by NMR relaxation spectroscopy. The model, which is an extension of the local contact model for backbone order parameter prediction, uses a static 3D protein structure as input. It expresses the methyl-group S(2) order parameters as a function of local contacts of the methyl carbon with respect to the neighboring atoms in combination with the number of consecutive mobile dihedral angles between the methyl group and the protein backbone. For six out of seven proteins the prediction results are good when compared with experimentally determined methyl-group S(2) values with an average correlation coefficient r = 0.65+/-0.14. For the unusually rigid cytochrome c(2) no significant correlation between prediction and experiment is found. The presented model provides independent support for the reliability of current side-chain relaxation methods along with their interpretation by the model-free formalism.     

Thermal coefficients of the methyl groups within ubiquitin

Physiological processes such as protein folding and molecular recognition are intricately linked to their dynamic signature, which is reflected in their thermal coefficient. In addition, the local conformational entropy is directly related to the degrees of freedom, which each residue possesses within its conformational space. Therefore, the temperature dependence of the local conformational entropy may provide insight into understanding how local dynamics may affect the stability of proteins. Here, we analyze the temperature dependence of internal methyl group dynamics derived from the cross-correlated relaxation between dipolar couplings of two CH bonds within ubiquitin. Spanning a temperature range from 275 to 308 K, internal methyl group dynamics tend to increase with increasing temperature, which translates to a general increase in local conformational entropy. With this data measured over multiple temperatures, the thermal coefficient of the methyl group order parameter, the characteristic thermal coefficient, and the local heat capacity were obtained. By analyzing the distribution of methyl group thermal coefficients within ubiquitin, we found that the N-terminal region has relatively high thermostability. These results indicate that methyl groups contribute quite appreciably to the total heat capacity of ubiquitin through the regulation of local conformational entropy.     

What contributions to protein side-chain dynamics are probed by NMR experiments? A molecular dynamics simulation analysis

Molecular dynamics simulations of the structurally homologous proteins TNfn3 and FNfn10 have been used to investigate the contributions to side-chain dynamics measured by NMR relaxation experiments. The results reproduce the variation in core side-chain dynamics observed by NMR and highlight the relevance of anharmonic motion and transitions between local minima for explaining NMR side-chain order parameters. A method is described for calculating converged order parameters by use of replica exchange molecular dynamics in conjunction with an implicit solvent model. These simulations allow the influence of various factors, such as the flexibility of side-chains and their free volume, on the mobility to be tested by perturbing the system. Deletion mutations are found to have the largest effect on the more densely packed FNfn10. Some counterintuitive effects are seen, such as an increase in order parameters close to deletion mutation sites, but these can be rationalized in terms of direct interactions with the modified side-chains. A statistical analysis of published order parameters supports the conclusions drawn from the simulations.     

Correlation between changes in nuclear magnetic resonance order parameters and conformational entropy: molecular dynamics simulations of native and denatured staphylococcal nuclease

Recent work has suggested that changes in NMR order parameters may quantitatively reflect changes in the conformational entropy of a protein ensemble. The extent of the mathematical relationship between local entropy changes as seen by NMR order parameters and the full protein entropy change is a complex issue. As a step towards a fuller understanding of this problem, molecular dynamics calculations of both native and denatured staphylococcal nuclease were performed. The N-H bond vector motion, in both explicit and implicit solvent, was analyzed to estimate local and global entropy changes. The calculated N-H bond vector order parameters from simulation agreed on average with experimental values for both native and denatured structures. However, the inverted-U profile of order parameters versus residue number observed experimentally for denatured nuclease was only partially reproduced by simulation of compact denatured structures. Comparisons made across the full set of simulations revealed a correlation between the N-H order parameter-based conformational entropy change and the total quasiharmonic-based conformational entropy change between the native and denatured structures. The calculations showed that about 25% of the total entropy change was reflected by changes in simulated S2 values. This result suggests that NMR-derived order parameters may be used to provide a reasonable estimate of the total conformational entropy change on protein folding.     

Temperature dependence of the internal dynamics of a calmodulin-peptide complex

The temperature dependence of the fast internal dynamics of calcium-saturated calmodulin in complex with a peptide corresponding to the calmodulin-binding domain of the smooth muscle myosin light chain kinase is examined using 15N and 2H NMR relaxation methods. NMR relaxation studies of the complex were carried out at 13 temperatures that span 288-346 K. The dynamics of the backbone and over four dozen methyl-bearing side chains, distributed throughout the calmodulin molecule, were probed. The side chains show a much more variable and often considerably larger response to temperature than the backbone. A significant variation in the temperature dependence of the amplitude of motion of individual side chains is seen. The amplitude of motion of some side chains is essentially temperature-independent while many show a simple roughly linear temperature dependence. In a few cases, angular order increases with temperature, which is interpreted as arising from interactions with neighboring residues. In addition, a number of side chains display a nonlinear temperature dependence. The significance of these and other results is illuminated by several simple interpretative models. Importantly, analysis of these models indicates that changes in generalized order parameters can be robustly related to corresponding changes in residual entropy. A simple cluster model that incorporates features of cooperative or conditional motion reproduces many of the unusual features of the experimentally observed temperature dependence and illustrates that side chain interactions result in a dynamically changing environment that significantly influences the motion of internal side chains. This model also suggests that the intrinsic entropy of interacting clusters of side chains is only modestly reduced from that of independent side chain motion. Finally, estimates of protein heat capacity support the view that the major contribution to the heat capacity of protein solutions largely arises from local bond vibrations and solvent interactions and not from torsional oscillations of side chains.     

Dynamics in natural and designed elastins and their relation to elastic fiber structure and recoil

Elastin fibers assemble in the extracellular matrix from the precursor protein tropoelastin and provide the flexibility and spontaneous recoil required for arterial function. Unlike many proteins, a structure-function mechanism for elastin has been elusive. We have performed detailed NMR relaxation studies of the dynamics of the minielastins 24x′ and 20x′ using solution NMR, and of purified bovine elastin fibers in the presence and absence of mechanical stress using solid state NMR. The low sequence complexity of the minielastins enables us to determine average dynamical timescales and degrees of local ordering in the cross-link and hydrophobic modules separately using NMR relaxation by taking advantage of their residue-specific resolution. We find an extremely high degree of disorder, with order parameters for the entirety of the hydrophobic domains near zero, resembling that of simple chemical polymers and less than the order parameters that have been observed in other intrinsically disordered proteins. We find that average backbone order parameters in natural, purified elastin fibers are comparable to those found in 24x′ and 20x′ in solution. The difference in dynamics, compared with the minielastins, is that backbone correlation times are significantly slowed in purified elastin. Moreover, when elastin is mechanically stretched, the high chain disorder in purified elastin is retained, showing that any change in local ordering is below that detectable in our experiment. Combined with our previous finding of a 10-fold increase in the ordering of water when fully hydrated elastin fibers are stretched by 50%, these results support the hypothesis that stretch induced solvent ordering, i.e., the hydrophobic effect, is a key player in the elastic recoil of elastin as opposed to configurational entropy loss.     

Smoluchowski dynamics of the vnd/NK‐2 homeodomain from Drosophila melanogaster: First‐order mode‐coupling approximation

This work is the first in a series devoted to applying mode coupling diffusion theory to the derivation of local dynamics properties of proteins in solution. The first‐order mode‐coupling approximation, or optimized Rouse–Zimm local dynamics (ORZLD), is applied here to derive the rotational dynamics of the bonds and compare the calculated with the experimental nmr ¹⁵N spin–lattice relaxation time behavior of the vnd/NK‐2 homeodomain from Drosophila melanogaster. The starting point for the calculations is the experimental three‐dimensional structure of the homeodomain determined by multidimensional nmr spectroscopy. The results of the computations are compared with experimentally measured ¹⁵N spin–lattice relaxation times T₁, at 34.5 and 60.8 MHz, to check the first‐order approximation. To estimate the relative importance of internal and overall rotation, both rigid and fluctuating dynamic models are examined, with fluctuations evaluated using molecular dynamics (MD) simulations. The correlation times for the fundamental bond vector time correlation function and for the second‐order bond orientational TCF are obtained as a function of the residue number for vnd/NK‐2. The stability of the corresponding local dynamics pattern for the fluctuating structure as a function of the length of the MD trajectory is presented. Diffusive dynamics, which is essentially free of model parameters even at first order in the mode‐coupling diffusion approach, confirm that local dynamics of proteins can be described in terms of rotational diffusion of a fluctuating quasi‐rigid structure. The comparison with the nmr data shows that the first‐order mode coupling diffusion approximation accounts for the correct order of magnitude of the results and of important qualitative aspects of the data sensitive to conformational changes. Indications are obtained from this study to efficiently extend the theory to higher order in the mode‐coupling expansion. These results demonstrate the promise of the mode‐coupling approach, where the local dynamics of proteins is described in terms of rotational diffusion of a fluctuating quasi‐rigid structure, to analyze nmr spin–lattice relaxation behavior. © 1999 John Wiley & Sons, Inc. Biopoly 49: 235–254, 1999     

Redistribution and loss of side chain entropy upon formation of a calmodulin-peptide complex

The response of the internal dynamics of calcium-saturated calmodulin to the formation of a complex with a peptide model of the calmodulin-binding domain of the smooth muscle myosin light chain kinase has been studied using NMR relaxation methods. The backbone of calmodulin is found to be unaffected by the binding of the domain, whereas the dynamics of side chains are significantly perturbed. The changes in dynamics are interpreted in terms of a heterogeneous partitioning between structure (enthalpy) and dynamics (entropy). These data provide a microscopic view of the residual entropy of a protein in two functional states and suggest extensive enthalpy/entropy exchange during the formation of a protein-protein interface.     

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.     

Accuracy and precision of NMR relaxation experiments and MD simulations for characterizing protein dynamics

Model-free parameters obtained from nuclear magnetic resonance (NMR) relaxation experiments and molecular dynamics (MD) simulations commonly are used to describe the intramolecular dynamical properties of proteins. To assess the relative accuracy and precision of experimental and simulated model-free parameters, three independent data sets derived from backbone ¹⁵N NMR relaxation experiments and two independent data sets derived from MD simulations of Escherichia coli ribonuclease HI are compared. The widths of the distributions of the differences between the order parameters for pairs of NMR data sets are congruent with the uncertainties derived from statistical analyses of individual data sets; thus, current protocols for analyzing NMR data encapsulate random uncertainties appropriately. Large differences in order parameters for certain residues are attributed to systematic differences between samples for intralaboratory comparisons and unknown, possibly magnetic field-dependent, experimental effects for interlaboratory comparisons. The widths of distributions of the differences between the order parameters for two NMR sets are similar to widths of distributions for an NMR and an MD set or for two MD sets. The linear correlations between the order parameters for an MD set and an NMR set are within the range of correlations observed between pairs of NMR sets. These comparisons suggest that the NMR and MD generalized order parameters for the backbone amide N—H bond vectors are of comparable accuracy for residues exhibiting motions on a fast time scale (<100 ps). Large discrepancies between NMR and MD order parameters for certain residues are attributed to the occurrence of “rare” motional events over the simulation trajectories, the disruption of an element of secondary structure in one of the simulations, and lack of consensus among the experimental data sets. Consequently, (easily detectable) severe distortions of local protein structure and infrequent motional events in MD simulations appear to be the most serious artifacts affecting the accuracy and precision, respectively, of MD order parameters relative to NMR values. In addition, MD order parameters for motions on a fast (<100 ps) timescale are more precisely determined than their NMR counterparts, thereby permitting more detailed dynamic characterization of biologically important residues by MD simulation than is sometimes possible by experimental methods. Proteins 28:481–493, 1997. © 1997 Wiley-Liss, Inc.     

Backbone dynamics of the human CC-chemokine eotaxin

Eotaxin is a CC chemokine with potent chemoattractant activity towards eosinophils. ¹⁵N NMR relaxation data have been used to characterize the backbone dynamics of recombinant human eotaxin. ¹⁵N longitudinal (R₁) and transverse (R₂) auto relaxation rates, heteronuclear ¹H-¹⁵N steady-state NOEs, and transverse cross-relaxation rates (_xy) were obtained at 30 °C for all resolved backbone secondary amide groups using ¹ H-detected two-dimensional NMR experiments. Ratios of transverse auto and cross relaxation rates were used to identify NH groups influenced by slow conformational rearrangement. Relaxation data were fit to the extended model free dynamics formalism, yielding parameters describing axially symmetric molecular rotational diffusion and the internal dynamics of each NH group. The molecular rotational correlation time (_m) is 5.09±0.02 ns, indicating that eotaxin exists predominantly as a monomer under the conditions of the NMR study. The ratio of diffusion rates about unique and perpendicular axes (D/D) is 0.81±0.02. Residues with large amplitudes of subnanosecond motion are clustered in the N-terminal region (residues 1–19), the C-terminus (residues 68–73) and the loop connecting the first two -strands (residues 30–37). N-terminal flexibility appears to be conserved throughout the chemokine family and may have implications for the mechanism of chemokine receptor activation. Residues exhibiting significant dynamics on the microsecond–millisecond time scale are located close to the two conserved disulfide bonds, suggesting that these motions may be coupled to disulfide bond isomerization.     

Reorientational contact-weighted elastic network model for the prediction of protein dynamics: comparison with NMR relaxation

A new model for the prediction of protein backbone motions is presented. The model, termed reorientational contact-weighted elastic network model, is based on a multidimensional reorientational harmonic potential of the backbone amide bond vector orientations and it is applied to the interpretation of dynamics parameters obtained from NMR relaxation data. The individual energy terms are weighted as a function of the intervector distances and by the contact strengths of each bond vector with respect to its local environment. Correlated reorientational motional properties of the bond vectors are obtained by means of normal mode analysis. Application to a set of proteins with known three-dimensional structures yields good to excellent agreement between predicted and experimental NMR order parameters presenting an improvement over the local contact model. The reorientational eigenmodes of the reorientational contact-weighted elastic network model method provide direct information on the collective nature of protein backbone motions. The dominant eigenmodes have a notably low collectivity, which is consistent with the behavior found for reorientational eigenmodes from molecular dynamics simulations.     

Relaxation data in NMR structure determination: model calculations for the lysozyme-Gd3+ complex

The effect of including paramagnetic relaxation data as additional restraints in the determination of protein tertiary structures from NMR data has been explored by a systematic series of model calculations. The system used for testing the method was the 2.0 A resolution tetragonal crystal structure of hen egg white lysozyme (129 amino acid residues) and structures were generated using a version of the hybrid "distance geometry-dynamic simulated annealing" procedure. A limited set of 769 NOEs was used as restraints in all the calculations; the strengths of these were categorized into three classes on the basis of distances observed in the crystal structure. The values of 50 phi angles were also restrained on the basis of amide-alpha coupling constants calculated from the X-ray structure. Five sets of 12 structures were determined using differing sets of paramagnetic relaxation data as restraints additional to those involving the NOE and coupling constant data. The paramagnetic relaxation data were modeled on the basis of the distances of defined protons from the crystallographic binding site of Gd3+ in lysozyme. Analysis of the results showed that the relaxation data significantly improved the correspondence between the set of generated structures and the crystal structure, and that the more well defined the relaxation data, the more significant the improvement in the quality of the structures. The results suggest that the inclusion of paramagnetic relaxation restraints could be of significant value for the experimental determination of protein structures from NMR data.     

Sodium-23 and potassium-39 nuclear magnetic resonance relaxation in eye lens. Examples of quadrupole ion magnetic relaxation in a crowded protein environment.

Single and multiple quantum nuclear magnetic resonance (NMR) spectroscopic techniques were used to investigate the motional dynamics of sodium and potassium ions in concentrated protein solution, represented in this study by cortical and nuclear bovine lens tissue homogenates. Both ions displayed homogeneous biexponential magnetic relaxation behavior. Furthermore, the NMR relaxation behavior of these ions in lens homogenates was consistent either with a model that assumed the occurrence of two predominant ionic populations, "free" and "bound," in fast exchange with each other or with a model that assumed an asymmetric Gaussian distribution of correlation times. Regardless of the model employed, both ions were found to occur in a predominantly "free" or "unbound" rapidly reorienting state. The fraction of "bound" 23Na+, assuming a discrete two-site model, was approximately 0.006 and 0.017 for cortical and nuclear homogenates, respectively. Corresponding values for 39K+ were 0.003 and 0.007, respectively. Estimated values for the fraction of "bound" 23Na+ or 39K+ obtained from the distribution model (tau C greater than omega L-1) were less than or equal to 0.05 for all cases examined. The correlation times of the "bound" ions, derived using either a two-site or distribution model, yielded values that were at least one order of magnitude smaller than the reorientational motion of the constituent lens proteins. This observation implies that the apparent correlation time for ion binding is dominated by processes other than protein reorientational motion, most likely fast exchange between "free" and "bound" environments. The results of NMR visibility studies were consistent with the above findings, in agreement with other studies performed by non-NMR methods. These studies, in combination with those presented in the literature, suggest that the most likely role for sodium and potassium ions in the lens appears to be the regulation of cell volume by affecting the intralenticular water chemical potential.     

Addition of hydrophilic and lipophilic compounds of biological relevance to the monoolein/water system II - 13C NMR relaxation study

The addition of hydrophilic and hydrophobic molecules to the 1-monooleoyl glycerol (MO)/water (W) system has been investigated at a molecular level by 13C nuclear magnetic resonance (NMR) relaxation. Depending on the nature of the additive, the liquid crystalline phases of the MO/W binary system are modified. The 13C NMR spin lattice relaxation rates of the various MO carbons were determined in the presence of the additives for different types of L(2) and liquid crystalline phases. Data revealed that local dynamics are independent of type and amount of additive (within 5 wt.%), and also of the type of the structural arrangement. The curvature of the interface does not affect the local mobility of MO carbons, with the exception of the glycerol G3 and the carboxylic C1 carbons. Moreover, the presence of the double bond in the mid part of the hydrocarbon chain induces a levelling in the relaxation rates on the neighboring carbons. The 13C NMR spin lattice relaxation rates at two magnetic field strengths and the Overhauser enhancement were measured in the L(2) phase of the MO/W/sodium decanoate system. The use of a two-step model of relaxation allowed to estimate order parameters, and slow and fast motions of MO in the structured aggregate.