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.     

Characterization of NMR relaxation-active motions of a partially folded A-state analogue of ubiquitin

The dominant dynamics of a partially folded A-state analogue of ubiquitin that give rise to NMR 15N spin relaxation have been investigated using molecular dynamics (MD) computer simulations and reorientational quasiharmonic analysis. Starting from the X-ray structure of native ubiquitin with a protonation state corresponding to a low pH, the A-state analogue was generated by a MD simulation of a total length of 33 ns in a 60%/40% methanol/water mixture using a variable temperature scheme to control and speed up the structural transformation. The N-terminal half of the A-state analogue consists of loosely coupled native-like secondary structural elements, while the C-terminal half is mostly irregular in structure. Analysis of dipolar N-H backbone correlation functions reveals reorientational amplitudes and time-scale distributions that are comparable to those observed experimentally. Thus, the trajectory provides a realistic picture of a partially folded protein that can be used for gaining a better understanding of the various types of reorientational motions that are manifested in spin-relaxation parameters of partially folded systems. For this purpose, a reorientational quasiharmonic reorientational analysis was performed on the final 5 ns of the trajectory of the A-state analogue, and for comparison on a 5 ns trajectory of native ubiquitin. The largest amplitude reorientational modes show a markedly distinct behavior for the two states. While for native ubiquitin, such motions have a more local character involving loops and the C-terminal end of the polypeptide chain, the A-state analogue shows highly collective motions in the nanosecond time-scale range corresponding to larger-scale movements between different segments. Changes in reorientational backbone entropy between the A-state analogue and the native state of ubiquitin, which were computed from the reorientational quasiharmonic analyses, are found to depend significantly on motional correlation effects.     

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.     

Assessment of protein reorientational diffusion in solution by 13C off-resonance rotating frame spin-lattice relaxation: effect of anisotropic tumbling

The 13C off-resonance rotating frame spin-lattice relaxation technique is applicable to the study of protein rotational diffusion behavior in a variety of experimental situations. The original formalism of James and co-workers (1978) (J. Amer. Chem. Soc. 100, 3590-3594) was constrained by the assumption of random isotropic reorientational motion. Here we include in the formalism anisotropic tumbling, and present the results of computer simulations illustrating the differences between anisotropic and isotropic reorientational motion for the off-resonance rotating frame spin-lattice relaxation experiment. In addition, we have included chemical shift anisotropy of the peptide carbonyl carbon as an additional relaxation mechanism contribution, to permit high-field nmr protein rotational diffusion measurements.     

Water and Backbone Dynamics in a Hydrated Protein

Rotational immobilization of proteins permits characterization of the internal peptide and water molecule dynamics by magnetic relaxation dispersion spectroscopy. Using different experimental approaches, we have extended measurements of the magnetic field dependence of the proton-spin-lattice-relaxation rate by one decade from 0.01 to 300 MHz for ¹H and showed that the underlying dynamics driving the protein ¹H spin-lattice relaxation is preserved over 4.5 decades in frequency. This extension is critical to understanding the role of ¹H₂O in the total proton-spin-relaxation process. The fact that the protein-proton-relaxation-dispersion profile is a power law in frequency with constant coefficient and exponent over nearly 5 decades indicates that the characteristics of the native protein structural fluctuations that cause proton nuclear spin-lattice relaxation are remarkably constant over this wide frequency and length-scale interval. Comparison of protein-proton-spin-lattice-relaxation rate constants in protein gels equilibrated with ²H₂O rather than ¹H₂O shows that water protons make an important contribution to the total spin-lattice relaxation in the middle of this frequency range for hydrated proteins because of water molecule dynamics in the time range of tens of ns. This water contribution is with the motion of relatively rare, long-lived, and perhaps buried water molecules constrained by the confinement. The presence of water molecule reorientational dynamics in the tens of ns range that are sufficient to affect the spin-lattice relaxation driven by ¹H dipole-dipole fluctuations should make the local dielectric properties in the protein frequency dependent in a regime relevant to catalytically important kinetic barriers to conformational rearrangements.     

Investigation of the local structure and dynamics of the H subunit of the mitochondrial glycine decarboxylase using heteronuclear NMR spectroscopy.

The lipoate-dependent H protein plays a pivotal role in the catalytic cycle of the glycine decarboxylase complex (GDC), undergoing reducing methylamination, methylene transfer, and oxidation. The local structure and backbone dynamics of the methylamine-loaded H (Hmet), oxidized H (Hox), and H apoprotein (Hapo) have been investigated in solution. Filtered NOESY experiments using a [13C]Hmet as well as comparison of the heteronuclear shifts between the Hox and Hmet proteins demonstrate that the methylamine group is located inside a cleft of the protein. Furthermore, this group appears to be locked in this configuration as indicated by the high value of the activation energy (37 kcal/mol) of the global unloading reaction and by its restricted mobility, deduced from 13C relaxation measurements. Comparisons of the 1H and 15N chemical shifts and 15N relaxation in the three forms suggest that part of the lipoyl-lysine arm interacts with the protein polypeptide in the Hox and Hmet. The major change induced by the loading of the methylamine group concerns the C-terminal helix whose mobility becomes completely restricted compared to those of the Hox and Hapo. This C-terminal helix exhibits different reorientational characteristics in the three forms, which can be explained in the Hapo by a model consisting of a twisting motion about an axis passing through the helix. Our results indicate that the model of a freely swinging arm proposed for other lipoate-containing proteins is not acceptable in solution for the GDC. The implication of this observation in terms of the mechanism of the interaction of the H protein with the T protein, its physiological partner during the catalytic cycle, is discussed.     

Microviscosity of human erythrocytes studied using hypophosphite two-spin order relaxation.

A new 31P NMR method is used to probe the cytoplasmic viscosity of human erythrocytes. The method is based on observing two-spin order relaxation of the 31P atom of the hypophosphite ion. This method is superior to our previous method, using the longitudinal relaxation time of the ion, because random field effects such as intermolecular dipole-dipole relaxation can be separated from intramolecular relaxation. This allows a more accurate determination of the effective reorientational correlation time from the measured intramolecular relaxation because it is now unaffected by random field effects. The new method also provides a means by which to estimate the random field effects. Both two-spin order and proton-decoupled T1 measurements were conducted on hypophosphite in water solutions at various temperatures, glycerol solutions of various viscosities, and in erythrocyte samples of various cell volumes. The results show that the effective reorientational correlation time of the hypophosphite ion varies from 7.2 to 15.2 ps in the cytoplasm of cells ranging in volume from 102 to 56 fl cells.     

Interpretation of NMR relaxation properties of Pin1, a two-domain protein, based on Brownian dynamic simulations

Many important proteins contain multiple domains connected by flexible linkers. Inter-domain motion is suggested to play a key role in many processes involving molecular recognition. Heteronuclear NMR relaxation is sensitive to motions in the relevant time scales and could provide valuable information on the dynamics of multi-domain proteins. However, the standard analysis based on the separation of global tumbling and fast local motions is no longer valid for multi-domain proteins undergoing internal motions involving complete domains and that take place on the same time scale than the overall motion.The complexity of the motions experienced even for the simplest two-domain proteins are difficult to capture with simple extensions of the classical Lipari-Szabo approach. Hydrodynamic effects are expected to dominate the motion of the individual globular domains, as well as that of the complete protein. Using Pin1 as a test case, we have simulated its motion at the microsecond time scale, at a reasonable computational expense, using Brownian Dynamic simulations on simplified models. The resulting trajectories provide insight on the interplay between global and inter-domain motion and can be analyzed using the recently published method of isotropic Reorientational Mode Dynamics which offer a way of calculating their contribution to heteronuclear relaxation rates. The analysis of trajectories computed with Pin1 models of different flexibility provides a general framework to understand the dynamics of multi-domain proteins and explains some of the observed features in the relaxation rate profile of free Pin1.     

1H nuclear magnetic relaxation dispersion of Cu,Zn superoxide dismutase in the native and guanidinium-induced unfolded forms

Potentialities and limitations of the use of (1)H NMRD technique for the characterization of the hydration properties of unfolded or partially folded states of proteins are discussed. The copper(I) form of monomeric Cu,Zn superoxide dismutase in its folded state and in the presence of 4M guanidinium chloride is taken as case system. The dispersion profile, analyzed with an extended relaxation matrix analysis, indicates the presence of long-lived water molecules in the folded state. The observed increase in relaxation at high field upon addition of guanidinium chloride indicates an increase in the number of solvation protons interacting with the protein and exchanging with a time shorter than the protein reorientational time. The observed effect is consistent with an exposed protein surface of SOD in the presence of 4M guanidinium chloride smaller than what could be expected for a random coil.     

Molecular dynamics simulations of heme reorientational motions in myoglobin.

Molecular dynamics simulations of 2-ns duration were performed on carbonmonoxymyoglobin and deoxymyoglobin in vacuo to study the reorientational dynamics of the heme group. The heme in both simulations undergoes reorientations of approximately 5 degrees amplitude on a subpicosecond time scale, which produce a rapid initial decay in the reorientational correlation function to about 0.99. The heme also experiences infrequent changes in average orientation of approximately 10 degrees amplitude, which lead to a larger slow decay of the reorientational correlation function over a period of hundreds of picoseconds. The simulations have not converged with respect to these infrequent transitions. However, an estimate of the order parameter for rapid internal motions of the heme from those orientations which are sampled by the simulations suggests that the subnanosecond orientational dynamics of the heme accounts for at least 30% of the unresolved initial anisotropy decay observed in the nanosecond time-resolved optical absorption experiments on myoglobin reported by Ansari et al. in a companion paper (Ansari, A., C.M. Jones, E.R. Henry, J. Hofrichter, and W.A. Eaton. 1992. Biophys. J. 64:852-868.). A more complete sampling of the accessible heme orientations would most likely increase this fraction further. The simulation of the liganded molecule also suggests that the conformational dynamics of the CO ligand may contribute significantly to discrepancies between the ligand conformation as probed by x-ray diffraction and by infrared-optical photoselection experiments. The protein back-bone explores multiple conformations during the simulations, with the largest structural changes appearing in the E and F helices, which are in contact with the heme. The variations in the heme orientation correlate with the conformational dynamics of the protein on a time scale of hundreds of picoseconds, suggesting that the heme orientation may provide a useful probe of dynamical processes in the protein.     

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.     

Theory of photoselection by intense light pulses. Influence of reorientational dynamics and chemical kinetics on absorbance measurements.

The theory of absorbance measurements on a system (e.g., chromophore(s) in a protein) that undergoes a sequence of reactions initiated by a linearly polarized light pulse is developed for excitation pulses of arbitrary intensity. This formalism is based on a set of master equations describing the time evolution of the orientational distribution function of the various species resulting from excitation, reorientational dynamics, and chemical kinetics. For intense but short excitation pulses, the changes in absorbance (for arbitrary polarization directions of the excitation and probe pulses) and the absorption anisotropy are expressed in terms of reorientational correlation functions. The influence of the internal motions of the chromophore as well as the overall motions of the molecules is considered. When the duration of the excitation pulse is long compared to the time-scale of internal motions but comparable to the overall correlation time of the molecule that is reorienting isotropically, the problem of calculating the changes in absorbance is reduced to the solution of a set of first-order coupled differential equations. Emphasis is placed on obtaining explicit results for quantities that are measured in photolysis and fluorescence experiments so as to facilitate the analysis of experimental data.     

Probing protein side chain dynamics via 13C NMR relaxation

Protein side chain dynamics is associated with protein stability, folding, and intermolecular interactions. Detailed dynamics information is crucial for the understanding of protein function and biochemical and biophysical properties, which can be obtained using NMR relaxation techniques. In this review, (13)C relaxation of methine, methylene and methyl groups with and without (1)H decoupling are described briefly for a better understanding of how spin relaxation is associated with motional (dynamics) parameters. Developments in the measurement and interpretation of (13)C auto-relaxation and cross-correlated relaxation data are presented too. Finally, recent progress in the use of (13)C relaxation to probe the dynamics of protein side chains is detailed mainly for the dynamics of non-deuterated proteins on picoseconds-nanosecond timescales.     

The membrane fluidity concept revisited by polarized fluorescence spectroscopy on different model membranes containing unsaturated lipids and sterols

Quantitative analysis of time-resolved anisotropy measurements of DPH or TMA-DPH in lipid vesicles yields more than one mathematically correct solution. The solutions differ with respect to the average orientation and to the reorientational dynamics of the probe molecules in the bilayer. This leads to quite opposite results regarding the effects of cholesterol on membrane fluidity. One solution predicts an increase in fluidity, the other a decrease. Angle-resolved fluorescence depolarization (AFD) measurements of probes in oriented lipid bilayers enable determination of the average orientation of the probes in the bilayer and, if the fluorescence decay function is known, of the reorientational dynamics. Analysis of AFD measurements of DPH and TMA-DPH show that increasing unsaturation leads to a decrease in molecular order and a decrease in reorientational dynamics (= fluidity) of the probes. At temperatures above the phase transition of the lipids, the addition of cholesterol causes an increase in molecular order and an increase in reorientational dynamics (= fluidity). The plant sterol stigmaterol, which is structurally closely related to cholesterol, has different effects than cholesterol. The effects vary with the structure of the surrounding lipids. The membrane fluidity concept as it was originally proposed by Chapman attempts to describe the structural and dynamic properties of lipids in a membrane using one single parameter indicated as 'membrane fluidity'. Our results show that it is necessary to distinguish between structural parameters describing molecular order and motion parameters describing molecular dynamics, thus supporting a similar suggestion by Seelig and Seelig. In order to be useful, the membrane fluidity concept has to be limited to the parameters describing molecular dynamics.     

Conformational dynamics in loop swap mutants of homologous fibronectin type III domains

Fibronectin type III (FN-III) domains are autonomously folded modules found in a variety of multidomain proteins. The 10th FN-III domain from fibronectin (fnFN10) and the 3rd FN-III domain from tenascin-C (tnFN3) have 27% sequence identity and the same overall fold; however, the CC' loop has a different pattern of backbone hydrogen bonds and the FG loop is longer in fnFN10 compared to tnFN3. To examine the influence of length, sequence, and context in determining dynamical properties of loops, CC' and FG loops were swapped between fnFN10 and tnFN3 to generate four mutant proteins and backbone conformational dynamics on ps-ns and mus-ms timescales were characterized by solution (15)N-NMR spin relaxation spectroscopy. The grafted loops do not strongly perturb the properties of the protein scaffold; however, specific effects of the mutations are observed for amino acids that are proximal in space to the sites of mutation. The amino acid sequence primarily dictates conformational dynamics when the wild-type and grafted loop have the same length, but both sequence and context contribute to conformational dynamics when the loop lengths differ. The results suggest that changes in conformational dynamics of mutant proteins must be considered in both theoretical studies and protein design efforts.     

The relation of the X-ray B-factor to protein dynamics: insights from recent dynamic solid-state NMR data

In addressing the potential use of B-factors derived from X-ray scattering data of proteins for the understanding the (functional) dynamics of proteins, we present a comparison of B-factors of five different proteins (SH3 domain, Crh, GB1, ubiquitin and thioredoxin) with data from recent solid-state nuclear magnetic resonance experiments reflecting true (rotational) dynamics on well-defined timescales. Apart from trivial correlations involving mobile loop regions and chain termini, we find no significant correlation of B-factors with the dynamic data on any of the investigated timescales, concluding that there is no unique and general correlation of B-factors with the internal reorientational dynamics of proteins.     

The relation of the X-ray B-factor to protein dynamics: insights from recent dynamic solid-state NMR data

In addressing the potential use of B-factors derived from X-ray scattering data of proteins for the understanding the (functional) dynamics of proteins, we present a comparison of B-factors of five different proteins (SH3 domain, Crh, GB1, ubiquitin and thioredoxin) with data from recent solid-state nuclear magnetic resonance experiments reflecting true (rotational) dynamics on well-defined timescales. Apart from trivial correlations involving mobile loop regions and chain termini, we find no significant correlation of B-factors with the dynamic data on any of the investigated timescales, concluding that there is no unique and general correlation of B-factors with the internal reorientational dynamics of proteins.     

Conformational exchange of aromatic side chains characterized by L-optimized TROSY-selected 13C CPMG relaxation dispersion

Protein dynamics on the millisecond time scale commonly reflect conformational transitions between distinct functional states. NMR relaxation dispersion experiments have provided important insights into biologically relevant dynamics with site-specific resolution, primarily targeting the protein backbone and methyl-bearing side chains. Aromatic side chains represent attractive probes of protein dynamics because they are over-represented in protein binding interfaces, play critical roles in enzyme catalysis, and form an important part of the core. Here we introduce a method to characterize millisecond conformational exchange of aromatic side chains in selectively (13)C labeled proteins by means of longitudinal- and transverse-relaxation optimized CPMG relaxation dispersion. By monitoring (13)C relaxation in a spin-state selective manner, significant sensitivity enhancement can be achieved in terms of both signal intensity and the relative exchange contribution to transverse relaxation. Further signal enhancement results from optimizing the longitudinal relaxation recovery of the covalently attached (1)H spins. We validated the L-TROSY-CPMG experiment by measuring fast folding-unfolding kinetics of the small protein CspB under native conditions. The determined unfolding rate matches perfectly with previous results from stopped-flow kinetics. The CPMG-derived chemical shift differences between the folded and unfolded states are in excellent agreement with those obtained by urea-dependent chemical shift analysis. The present method enables characterization of conformational exchange involving aromatic side chains and should serve as a valuable complement to methods developed for other types of protein side chains.