Yi Xue

Protein Side-Chain Dynamics As Observed by Solution- and Solid-State NMR Spectroscopy: A Similarity Revealed

In this paper, we seek to compare the internal dynamics of a small globular protein, SH3 domain from alpha-spectrin, in solution and in a crystalline state. The comparison involves side-chain methyl 13C R1 relaxation rates that are highly sensitive to local dynamics in the vicinity of the methyl site. To conduct the relaxation measurements, protein samples have been prepared using specially labeled alpha-ketoisovalerate precursors, resulting in selective incorporation of the 1H-13C spin pair in one or both methyl groups of the valine and leucine side chains. The sparse labeling pattern in an otherwise deuterated sample makes it possible to record high-resolution 13C, 1H solid-state spectra using magic angle spinning experiment with a MAS frequency of 22 kHz. Furthermore, this labeling scheme avoids proton-driven 13C-13C spin-diffusion effects, thus allowing for accurate measurements of 13C R1 relaxation in the individual methyl groups. While the relaxation response from a polycrystalline sample is generally expected to be multiexponential, we demonstrate both theoretically and experimentally that in this particular case the relaxation profiles are, in excellent approximation, monoexponential. In fact, solid-state relaxation data can be interpreted in a model-free fashion, similar to solution data. Direct comparison between the experimentally measured solid and solution rates reveals a strong correlation, r = 0.94. Furthermore, when solution rates are corrected for the effect of the overall molecular tumbling (quantified on the basis of the solution 15N relaxation data), the results are in one-to-one agreement with the solid-state rates. This finding indicates that methyl dynamics in the solution and solid samples are quantitatively similar. More broadly, it suggests that the entire dynamic network, including motions of side chains in the protein hydrophobic core and backbone motions, is similar. This result opens interesting possibilities for combined interpretation of solid- and solution-state relaxation data, potentially leading to a detailed characterization of internal protein dynamics on a wide range of time scales.

Paramagnetic relaxation enhancements in unfolded proteins: Theory and application to drkN SH3 domain

Site‐directed spin labeling in combination with paramagnetic relaxation enhancement (PRE) measurements is one of the most promising techniques for studying unfolded proteins. Since the pioneering work of Gillespie and Shortle (J Mol Biol 1997;268:158), PRE data from unfolded proteins have been interpreted using the theory that was originally developed for rotational spin relaxation. At the same time, it can be readily recognized that the relative motion of the paramagnetic tag attached to the peptide chain and the reporter spin such as 1HN is best described as a translation. With this notion in mind, we developed a number of models for the PRE effect in unfolded proteins: (i) mutual diffusion of the two tethered spheres, (ii) mutual diffusion of the two tethered spheres subject to a harmonic potential, (iii) mutual diffusion of the two tethered spheres subject to a simulated mean‐force potential (Smoluchowski equation); (iv) explicit‐atom molecular dynamics simulation. The new models were used to predict the dependences of the PRE rates on the 1HN residue number and static magnetic field strength; the results are appreciably different from the Gillespie–Shortle model. At the same time, the Gillespie–Shortle approach is expected to be generally adequate if the goal is to reconstruct the distance distributions between 1HN spins and the paramagnetic center (provided that the characteristic correlation time is known with a reasonable accuracy). The theory has been tested by measuring the PRE rates in three spin‐labeled mutants of the drkN SH3 domain in 2M guanidinium chloride. Two modifications introduced into the measurement scheme—using a reference compound to calibrate the signals from the two samples (oxidized and reduced) and using peak volumes instead of intensities to determine the PRE rates—lead to a substantial improvement in the quality of data. The PRE data from the denatured drkN SH3 are mostly consistent with the model of moderately expanded random‐coil protein, although part of the data point toward a more compact structure (local hydrophobic cluster). At the same time, the radius of gyration reported by Choy et al. (J Mol Biol 2002;316:101) suggests that the protein is highly expanded. This seemingly contradictory evidence can be reconciled if one assumes that denatured drkN SH3 forms a conformational ensemble that is dominated by extended conformations, yet also contains compact (collapsed) species. Such behavior is apparently more complex than predicted by the model of a random‐coil protein in good solvent/poor solvent.

Comparison of solid-state dipolar couplings and solution relaxation data provides insight into protein backbone dynamics.

Analyses of solution (15)N relaxation data and solid-state (1)H(N)-(15)N dipolar couplings from a small globular protein, alpha-spectrin SH3 domain, produce a surprisingly similar pattern of order parameters. This result suggests that there is little or no ns-mus dynamics throughout most of the sequence and, in particular, in the structured portion of the backbone. At the same time, evidence of ns-mus motions is found in the flexible loops and termini. These findings, corroborated by the MD simulations of alpha-spectrin SH3 in a hydrated crystalline environment and in solution, are consistent with the picture of protein dynamics that has recently emerged from the solution studies employing residual dipolar couplings.

Motion of a disordered polypeptide chain as studied by paramagnetic relaxation enhancements, 15N relaxation, and molecular dynamics simulations: how fast is segmental diffusion in denatured ubiquitin?

Molecular dynamics (MD) simulations have been widely used to analyze dynamic conformational equilibria of folded proteins, especially in relation to NMR observables. However, this approach found little use in the studies of disordered proteins, where the sampling of vast conformational space presents a serious problem. In this paper, we demonstrate that the latest advances in computation technology make it possible to overcome this limitation. The experimentally validated (calibrated) MD models allow for new insights into structure/dynamics of disordered proteins. As a test system, we have chosen denatured ubiquitin in solution with 8 M urea at pH 2. High-temperature MD simulations in implicit solvent have been carried out for the wild-type ubiquitin as well as MTSL-tagged Q2C, D32C, and R74C mutants. To recalibrate the MD data (500 K) in relation to the experimental conditions (278 K, 8 M urea), the time axes of the MD trajectories were rescaled. The scaling factor was adjusted such as to maximize the agreement between the simulated and experimental (15)N relaxation rates. The resulting effective length of the trajectories, 311 μs, ensures good convergence properties of the MD model. The constructed MD model was validated against the array of experimental data, including additional (15)N relaxation parameters, multiple sets of paramagnetic relaxation enhancements (PREs), and the radius of gyration. In each case, a near-quantitative agreement has been obtained, suggesting that the model is successful. Of note, the MD-based approach rigorously predicts the quantities that are inherently dynamic, i.e., dependent on the motional correlation times. This cannot be accomplished, other than in empirical fashion, on the basis of static structural models (conformational ensembles). The MD model was further used to investigate the relative translational motion of the MTSL label and the individual H(N) atoms. The derived segmental diffusion coefficients proved to be nearly uniform along the peptide chain, averaging to D = 0.49-0.55 × 10(-6) cm(2)/s. This result was verified by direct analysis of the experimental PRE data using the recently proposed Ullman-Podkorytov model. In this model, MTSL and H(N) moieties are treated as two tethered spheres undergoing mutual diffusion in a harmonic potential. The fitting of the experimental data involving D as a single adjustable parameter leads to D = 0.45 × 10(-6) cm(2)/s, in good agreement with the MD-based analyses. This result can be compared with the range of estimates obtained from the resonance energy transfer experiments, D = 0.2-6.0 × 10(-6) cm(2)/s.

Role of Electrostatic Interactions in Binding of Peptides and Intrinsically Disordered Proteins to Their Folded Targets. 1. NMR and MD Characterization of the Complex between the c-Crk N-SH3 Domain and the Peptide Sos

Intrinsically disordered proteins (IDPs) often rely on electrostatic interactions to bind their structured targets. To obtain insight into the mechanism of formation of the electrostatic encounter complex, we investigated the binding of the peptide Sos (PPPVPPRRRR), which serves as a minimal model for an IDP, to the c-Crk N-terminal SH3 domain. Initially, we measured ¹⁵N relaxation rates at two magnetic field strengths and determined the binding shifts for the complex of Sos with wild-type SH3. We have also recorded a 3 μs molecular dynamics (MD) trajectory of this complex using the Amber ff99SB*-ILDN force field. The comparison of the experimental and simulated data shows that MD simulation consistently overestimates the strength of salt bridge interactions at the binding interface. The series of simulations using other advanced force fields also failed to produce any satisfactory results. To address this issue, we have devised an empirical correction to the Amber ff99SB*-ILDN force field whereby the Lennard-Jones equilibrium distance for the nitrogen-oxygen pair across the Arg-to-Asp and Arg-to-Glu salt bridges has been increased by 3%. Implementing this correction resulted in a good agreement between the simulations and the experiment. Adjusting the strength of salt bridge interactions removed a certain amount of strain contained in the original MD model, thus improving the binding of the hydrophobic N-terminal portion of the peptide. The arginine-rich C-terminal portion of the peptide, freed from the effect of the overstabilized salt bridges, was found to interconvert more rapidly between its multiple conformational states. The modified MD protocol has also been successfully used to simulate the entire binding process. In doing so, the peptide was initially placed high above the protein surface. It then arrived at the correct bound pose within ∼2 Å of the crystallographic coordinates. This simulation allowed us to analyze the details of the dynamic binding intermediate, i.e., the electrostatic encounter complex. However, an experimental characterization of this transient, weakly populated state remains out of reach. To overcome this problem, we designed the double mutant of c-Crk N-SH3 in which mutations Y186L and W169F abrogate tight Sos binding and shift the equilibrium toward the intermediate state resembling the electrostatic encounter complex. The results of the combined NMR and MD study of this engineered system will be reported in the next part of this paper.

Ensemble MD simulations restrained via crystallographic data: Accurate structure leads to accurate dynamics

Currently, the best existing molecular dynamics (MD) force fields cannot accurately reproduce the global free‐energy minimum which realizes the experimental protein structure. As a result, long MD trajectories tend to drift away from the starting coordinates (e.g., crystallographic structures). To address this problem, we have devised a new simulation strategy aimed at protein crystals. An MD simulation of protein crystal is essentially an ensemble simulation involving multiple protein molecules in a crystal unit cell (or a block of unit cells). To ensure that average protein coordinates remain correct during the simulation, we introduced crystallography‐based restraints into the MD protocol. Because these restraints are aimed at the ensemble‐average structure, they have only minimal impact on conformational dynamics of the individual protein molecules. So long as the average structure remains reasonable, the proteins move in a native‐like fashion as dictated by the original force field. To validate this approach, we have used the data from solid‐state NMR spectroscopy, which is the orthogonal experimental technique uniquely sensitive to protein local dynamics. The new method has been tested on the well‐established model protein, ubiquitin. The ensemble‐restrained MD simulations produced lower crystallographic R factors than conventional simulations; they also led to more accurate predictions for crystallographic temperature factors, solid‐state chemical shifts, and backbone order parameters. The predictions for 15N R1 relaxation rates are at least as accurate as those obtained from conventional simulations. Taken together, these results suggest that the presented trajectories may be among the most realistic protein MD simulations ever reported. In this context, the ensemble restraints based on high‐resolution crystallographic data can be viewed as protein‐specific empirical corrections to the standard force fields.

Slow conformational exchange and overall rocking motion in ubiquitin protein crystals

Proteins perform their functions in solution but their structures are most frequently studied inside crystals. Here we probe how the crystal packing alters microsecond dynamics, using solid-state NMR measurements and multi-microsecond MD simulations of different crystal forms of ubiquitin. In particular, near-rotary-resonance relaxation dispersion (NERRD) experiments probe angular backbone motion, while Bloch–McConnell relaxation dispersion data report on fluctuations of the local electronic environment. These experiments and simulations reveal that the packing of the protein can significantly alter the thermodynamics and kinetics of local conformational exchange. Moreover, we report small-amplitude reorientational motion of protein molecules in the crystal lattice with an ~3–5° amplitude on a tens-of-microseconds time scale in one of the crystals, but not in others. An intriguing possibility arises that overall motion is to some extent coupled to local dynamics. Our study highlights the importance of considering the packing when analyzing dynamics of crystalline proteins.X-ray crystallography is the main method for protein structure determination. Here the authors combine solid-state NMR measurements and molecular dynamics simulations and show that crystal packing alters the thermodynamics and kinetics of local conformational exchange as well as overall rocking motion of protein molecules in the crystal lattice.

Detection of nanosecond time scale side-chain jumps in a protein dissolved in water/glycerol solvent

In solution, the correlation time of the overall protein tumbling, τR, plays a role of a natural dynamics cutoff—internal motions with correlation times on the order of τR or longer cannot be reliably identified on the basis of spin relaxation data. It has been proposed some time ago that the ‘observation window’ of solution experiments can be expanded by changing the viscosity of solvent to raise the value of τR. To further explore this concept, we prepared a series of samples of α-spectrin SH3 domain in solvent with increasing concentration of glycerol. In addition to the conventional 15N labeling, the protein was labeled in the Val, Leu methyl positions (13CHD2 on a deuterated background). The collected relaxation data were used in asymmetric fashion: backbone 15N relaxation rates were used to determine τR across the series of samples, while methyl 13C data were used to probe local dynamics (side-chain motions). In interpreting the results, it has been initially suggested that addition of glycerol leads only to increases in τR, whereas local motional parameters remain unchanged. Thus the data from multiple samples can be analyzed jointly, with τR playing the role of experimentally controlled variable. Based on this concept, the extended model-free model was constructed with the intent to capture the effect of ns time-scale rotameric jumps in valine and leucine side chains. Using this model, we made a positive identification of nanosecond dynamics in Val-23 where ns motions were already observed earlier. In several other cases, however, only tentative identification was possible. The lack of definitive results was due to the approximate character of the model—contrary to what has been assumed, addition of glycerol led to a gradual ‘stiffening’ of the protein. This and other observations also shed light on the interaction of the protein with glycerol, which is one of the naturally occurring osmoprotectants. In particular, it has been found that the overall protein tumbling is controlled by the bulk solvent, and not by a thin solvation layer which contains a higher proportion of water.