Propagation of experimental uncertainties using the Lipari-Szabo model-free analysis of protein dynamics

In this paper we make use of the graphical procedure previously described [Jin, D. et al. (1997) J. Am. Chem. Soc., 119, 6923–6924] to analyze NMR relaxation data using the Lipari-Szabo model-free formalism. The graphical approach is advantageous in that it allows the direct visualization of the experimental uncertainties in the motional parameter space. Some general rules describing the relationship between the precision of the relaxation measurements and the precision of the model-free parameters and how this relationship changes with the overall tumbling time (m) are summarized. The effect of the precision in the relaxation measurements on the detection of internal motions not close to the extreme narrowing limit is analyzed. We also show that multiple timescale internal motions may be obscured by experimental uncertainty, and that the collection of relaxation data at very high field strength can improve the ability to detect such deviations from the simple Lipari-Szabo model.     

Refolding the unfoldable: A systematic approach for renaturation of Bacillus circulans xylanase

Xylanases are important polysaccharide‐cleaving catalysts for the pulp and paper, animal feeds and biofuels industries. They have also proved to be valuable model systems for understanding enzymatic catalysis, with one of the best studied being the GH11 xylanase from Bacillus circulans (Bcx). However, proteins from this class are very recalcitrant to refolding in vitro. This both limits their high level expression in heterologous hosts, and prevents experimental approaches, such as peptide ligation or chemical modifications, to probe and engineer their stability and function. To solve this problem, a systematic screening approach was employed to identify suitable buffer conditions for renaturing Bcx in vitro. The fractional factorial screen employed identified starting conditions for refolding, which were then refined and developed into a generic protocol for renaturing preparative amounts of active Bcx in a 50–60% yield from inclusion bodies. The method is robust and proved equally proficient at refolding circularly permuted versions that carry cysteine mutations. This general approach should be applicable to related GH11 xylanases, as well as proteins adopting a similar β‐jellyroll fold, that are otherwise recalcitrant to refolding in vitro.     

Mechanism-based labeling defines the free energy change for formation of the covalent glycosyl-enzyme intermediate in a xyloglucan endo-transglycosylase

Xyloglucan endo-transglycosylases (XETs) are key enzymes involved in the restructuring of plant cell walls during morphogenesis. As members of glycoside hydrolase family 16 (GH16), XETs are predicted to employ the canonical retaining mechanism of glycosyl transfer involving a covalent glycosyl-enzyme intermediate. Here, we report the accumulation and direct observation of such intermediates of PttXET16-34 from hybrid aspen by electrospray mass spectrometry in combination with synthetic "blocked" substrates, which function as glycosyl donors but are incapable of acting as glycosyl acceptors. Thus, GalGXXXGGG and GalGXXXGXXXG react with the wild-type enzyme to yield relatively stable, kinetically competent, covalent GalG-enzyme and GalGXXXG-enzyme complexes, respectively (Gal=Galbeta(1-->4), G=Glcbeta(1-->4), and X=Xylalpha(1-->6)Glcbeta(1-->4)). Quantitation of ratios of protein and saccharide species at pseudo-equilibrium allowed us to estimate the free energy change (DeltaG(0)) for the formation of the covalent GalGXXXG-enzyme as 6.3-8.5 kJ/mol (1.5-2.0 kcal/mol). The data indicate that the free energy of the beta(1-->4) glucosidic bond in xyloglucans is preserved in the glycosyl-enzyme intermediate and harnessed for religation of the polysaccharide in vivo.     

Complete measurement of the pKa values of the carboxyl and imidazole groups in Bacillus circulans xylanase.

Electrostatic interactions in proteins can be dissected experimentally by determining the pKa values of their constituent ionizable amino acids. To complement previous studies of the glutamic acid and histidine residues in Bacillus circulans xylanase (BCX), we have used NMR methods to measure the pKa s of the seven aspartic acids and the C-terminus of this protein. The pKa s of these carboxyls are all less than the corresponding values observed with random coil polypeptides, indicating that their ionization contributes favorably to the stability of the folded enzyme. In general, the aspartic acids with the most reduced pKa s are those with limited exposure to the solvent and a high degree of conservation among homologous xylanases. Most dramatically, Asp 83 and Asp 101 have pKa s < 2 and thus remain deprotonated in native BCX under all conditions examined. Asp 83 is completely buried, forming a strong salt bridge with Arg 136. In contrast, Asp 101 is located on the surface of the protein, stabilized in the deprotonated form by an extensive network of hydrogen bonds involving an internal water molecule and the neutral side-chain and main-chain atoms of Ser 100 and Thr 145. These data provide a complete experimental database for theoretical studies of the ionization behavior of BCX under acidic conditions.     

The role of backbone conformational heat capacity in protein stability: temperature dependent dynamics of the B1 domain of Streptococcal protein G

The contributions of backbone NH group dynamics to the conformational heat capacity of the B1 domain of Streptococcal protein G have been estimated from the temperature dependence of 15N NMR-derived order parameters. Longitudinal (R1) and transverse (R2) relaxation rates, transverse cross-relaxation rates (eta(xy)), and steady state [1H]-15N nuclear Overhauser effects were measured at temperatures of 0, 10, 20, 30, 40, and 50 degrees C for 89-100% of the backbone secondary amide nitrogen nuclei in the B1 domain. The ratio R2/eta(xy) was used to identify nuclei for which conformational exchange makes a significant contribution to R2. Relaxation data were fit to the extended model-free dynamics formalism, incorporating an axially symmetric molecular rotational diffusion tensor. The temperature dependence of the order parameter (S2) was used to calculate the contribution of each NH group to conformational heat capacity (Cp) and a characteristic temperature (T*), representing the density of conformational energy states accessible to each NH group. The heat capacities of the secondary structure regions of the B1 domain are significantly higher than those of comparable regions of other proteins, whereas the heat capacities of less structured regions are similar to those in other proteins. The higher local heat capacities are estimated to contribute up to approximately 0.8 kJ/mol K to the total heat capacity of the B1 domain, without which the denaturation temperature would be approximately 9 degrees C lower (78 degrees C rather than 87 degrees C). Thus, variation of backbone conformational heat capacity of native proteins may be a novel mechanism that contributes to high temperature stabilization of proteins.     

Analysis of the internal motion of free and ligand-bound human lysozyme by use of 15N NMR relaxation measurement: a comparison with those of hen lysozyme

Human lysozyme has a structure similar to that of hen lysozyme and differs in amino acid sequence by 51 out of 129 residues with one insertion at the position between 47 and 48 in hen lysozyme. The backbone dynamics of free or (NAG)3-bound human lysozyme has been determined by measurements of 15N nuclear relaxation. The relaxation data were analyzed using the Lipari-Szabo formalism and were compared with those of hen lysozyme, which was already reported (Mine S et al.. 1999, J Mol Biol 286:1547-1565). In this paper, it was found that the backbone dynamics of free human and hen lysozymes showed very similar behavior except for some residues, indicating that the difference in amino acid sequence did not affect the behavior of entire backbone dynamics, but the folded pattern was the major determinant of the internal motion of lysozymes. On the other hand, it was also found that the number of residues in (NAG)3-bound human and hen lysozymes showed an increase or decrease in the order parameters at or near active sites on the binding of (NAG)3, indicating the increase in picosecond to nanosecond. These results suggested that the immobilization of residues upon binding (NAG)3 resulted in an entropy penalty and that this penalty was compensated by mobilizing other residues. However, compared with the internal motions between both ligand-bound human and hen lysozymes, differences in dynamic behavior between them were found at substrate binding sites, reflecting a subtle difference in the substrate-binding mode or efficiency of activity between them.     

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.     

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.     

Observing a late folding intermediate of Ubiquitin at atomic resolution by NMR

The study of intermediates in the protein folding pathway provides a wealth of information about the energy landscape. The intermediates also frequently initiate pathogenic fibril formations. While observing the intermediates is difficult due to their transient nature, extreme conditions can partially unfold the proteins and provide a glimpse of the intermediate states. Here, we observe the high resolution structure of a hydrophobic core mutant of Ubiquitin at an extreme acidic pH by nuclear magnetic resonance (NMR) spectroscopy. In the structure, the native secondary and tertiary structure is conserved for a major part of the protein. However, a long loop between the beta strands β3 and β5 is partially unfolded. The altered structure is supported by fluorescence data and the difference in free energies between the native state and the intermediate is reflected in the denaturant induced melting curves. The unfolded region includes amino acids that are critical for interaction with cofactors as well as for assembly of poly‐Ubiquitin chains. The structure at acidic pH resembles a late folding intermediate of Ubiquitin and indicates that upon stabilization of the protein's core, the long loop converges on the core in the final step of the folding process.     

Thermostabilization of Bacillus circulans xylanase: computational optimization of unstable residues based on thermal fluctuation analysis

Low thermostability often hampers the applications of xylanases in industrial processes operated at high temperature, such as degradation of biomass or pulp bleaching. Thermostability of enzymes can be improved by the optimization of unstable residues via protein engineering. In this study, computational modeling instead of random mutagenesis was used to optimize unstable residues of Bacillus circulans xylanase (Bcx). The thermal fluctuations of unstable residues known as important to the thermal unfolding of Bcx were investigated by the molecular dynamics (MD) simulations at 300 K and 330 K to identify promising residues. The N52 site in unstable regions showed the highest thermal fluctuations. Subsequently, computational design was conducted to predict the optimal sequences of unstable residues. Five optimal single mutants were predicted by the computational design, and the N52Y mutation showed the thermostabilization effect. The N52 residue is conserved in Bacillus species xylanases and the structure analysis revealed that the N52Y mutation introduced more hydrophobic clusters for thermostability, as well as a more favorable aromatic stacking environment for substrate binding. We confirm that flexible residues at high temperature in unstable regions can be promising targets to improve thermostability of enzymes.     

Crystal structure of the covalent intermediate of human cytosolic beta-glucosidase

Human cytosolic β-glucosidase, also known as klotho-related protein (KLrP, GBA3), is an enzyme that hydrolyzes various β-d-glucosides, including glucosylceramide. We recently reported the crystal structure of KLrP in complex with glucose [Y. Hayashi, N. Okino, Y. Kakuta, T. Shikanai, M. Tani, H. Narimatsu, M. Ito, Klotho-related protein is a novel cytosolic neutral beta-glycosylceramidase, J. Biol. Chem. 282 (2007) 30889-30900]. Here, we report the crystal structure of a covalent intermediate of the KLrP mutant E165Q, in which glucose was covalently bound to a nucleophile, Glu³⁷³. The structure confirms the double displacement mechanism of the retaining β-glucosidase. In addition, the structure suggests that a water molecule could be involved in the stabilization of transition states through a sugar, 2-hydroxyl.     

Foldon, the natural trimerization domain of T4 fibritin, dissociates into a monomeric A-state form containing a stable beta-hairpin: atomic details of trimer dissociation and local beta-hairpin stability from residual dipolar couplings

The C-terminal domain of T4 fibritin (foldon) is obligatory for the formation of the fibritin trimer structure and can be used as an artificial trimerization domain. Its native structure consists of a trimeric beta-hairpin propeller. At low pH, the foldon trimer disintegrates into a monomeric (A-state) form that has similar properties as that of an early intermediate of the trimer folding pathway. The formation of this A-state monomer from the trimer, its structure, thermodynamic stability, equilibrium association and folding dynamics have been characterized to atomic detail by modern high-resolution NMR techniques. The foldon A-state monomer forms a beta-hairpin with intact and stable H-bonds that is similar to the monomer in the foldon trimer, but lacks a defined structure in its N and C-terminal parts. Its thermodynamic stability in pure water is comparable to designed hairpins stabilized in alcohol/water mixtures. Details of the thermal unfolding of the foldon A-state have been characterized by chemical shifts and residual dipolar couplings (RDCs) detected in inert, mechanically stretched polyacrylamide gels. At the onset of the thermal transition, uniform relative changes in RDC values indicate a uniform decrease of local N-HN and Calpha-Halpha order parameters for the hairpin strand residues. In contrast, near-turn residues show particular thermal stability in RDC values and hence in local order parameters. This coincides with increased transition temperatures of the beta-turn residues observed by chemical shifts. At high temperatures, the RDCs converge to non-zero average values consistent with predictions from random chain polymer models. Residue-specific deviations above the unfolding transition reveal the persistence of residual order around proline residues, large hydrophobic residues and at the beta-turn.     

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.     

Mobility of NH bonds in DNA-binding protein HU of shape Bacillus stearothermophilus from reduced spectral density mapping analysis at multiple NMR fields

The dynamics of the backbone NH bonds of protein HU from Bacillus stearothermophilus (HUBst) have been characterized using measurements of cross-relaxation, longitudinal and transverse relaxation rates at 11.7, 14.1 and 17.6 T. Linear regression of the values with the squared Larmor frequency _N ² has revealed global exchange processes, which contributed on the order of 0.5–5.0 s^-1to the transverse relaxation rate. Subsequently, the experimental values were corrected for these exchange contributions. A reduced spectral density mapping procedure has been employed with the experimental relaxation rates and seven values of the spectral density function J() have been extracted. These spectral densities have been fitted within the framework of the model-free approach. The densities agree well with an axially symmetric rotational diffusion tensor with a diffusion anisotropy D_/D_ of 1.15, indicating that the flexible arms of HUBst do not significantly contribute to the rotational diffusion. The overall correlation time is 8.9 ± 0.6 ns/rad. The fast internal motions of most of the NH bonds in the core display order parameters ranging between 0.74 and 0.83 and internal correlation times between 1 and 20 ps. For the residues in the DNA-binding -arms, an extended version of the model function has been used. The slow internal motions show correlation times of 1–2 ns. The concomitant order parameters (0.3–0.6) are lower than those observed on the fast time scale, indicating that the flexibility of the -arms is mainly determined by the slower internal motions. A substantial decrease of the generalized order parameters in the -arms starting at residues Arg⁵⁵ and Ser⁷⁴, opposite on both strands of the -ribbon arms, has been explained as a hinge motion. A comparison of the order parameters for free and DNA-bound protein has demonstrated that the slow hinge motions largely disappear when HU binds DNA.     

Measurement of methyl 13C-1H cross-correlation in uniformly 13C-, 15N-, labeled proteins

An understanding of side chain motions in protein is of great interest since side chains often play an important role in protein folding and intermolecular interactions. A novel method for measuring the dynamics of methyl groups in uniformly ¹³C-, ¹⁵N-labeled proteins has been developed by our group. The method relies on the difference in peak intensities of ¹³C quartet components of methyl groups, in a spectrum recording the free evolution of ¹³C under proton coupling in a constant-time period. Cross-correlated relaxation rates between ¹³C-¹H dipoles can be easily measured from the intensities of the multiplet components. The degree of the methyl restrictions (S ²) can be estimated from the cross-correlated relaxation rate. The method is demonstrated on a sample of human fatty acid binding protein in the absence of fatty acid. We obtained relaxation data for 33 out of 46 residues having methyl groups in apo-IFABP. It has been found that the magnitude of the CSA tensor of spin ¹³C in a methyl group could be estimated from the intensities of the ¹³C multiplet components.     

NMR spectroscopic characterization of a beta-(1,4)-glycosidase along its reaction pathway: stabilization upon formation of the glycosyl-enzyme intermediate

NMR spectroscopy was used to search for mechanistically significant differences between the thermodynamic and dynamic properties of the 34 kDa (alpha/beta)8-barrel catalytic domain of beta-(1,4)-glycosidase Cex (or CfXyn10A) in its free (apo-CexCD) and trapped glycosyl-enzyme intermediate (2FCb-CexCD) states. The main chain chemical shift perturbations due to the covalent modification of CexCD with the mechanism-based inhibitor 2,4-dinitrophenyl 2-deoxy-2-fluoro-beta-cellobioside are limited to residues within its active site. Thus, consistent with previous crystallographic studies, formation of the glycosyl-enzyme intermediate leads to only localized structural changes. Furthermore, 15N relaxation methods demonstrated that the backbone amide and tryptophan side chains of apo-CexCD are very well ordered on both the nanosecond to picosecond and millisecond to microsecond time scales and that these dynamic features also do not change significantly upon formation of the trapped intermediate. However, covalent modification of CexCD led to the increased protection of many amides and indoles, clustered around the active site of the enzyme, against fluctuations leading to hydrogen exchange. Similarly, thermal denaturation studies demonstrated that 2FCb-CexCD has a significantly higher midpoint unfolding temperature than apo-CexCD. The covalently modified protein also exhibited markedly increased resistance to proteolytic degradation by thermolysin relative to apo-CexCD. Thus, the local and global stability of CexCD increase along its reaction pathway upon formation of the glycosyl-enzyme intermediate, while its structure and fast time scale dynamics remain relatively unperturbed. This may reflect thermodynamically favorable interactions with the relatively rigid active site of Cex necessary to bind, distort, and subsequently hydrolyze glycoside substrates.     

Production of a thermostable alkali-tolerant xylanase from Bacillus circulans AB 16 grown on wheat straw

Bacillus circulans AB 16 was able to produce 50 IU/ml of xylanase, with negligible cellulase activity when grown on untreated wheat straw. The pH optimum of the crude enzyme was 6–7 with a temperature optimum of 80 C. The enzyme showed high pH and thermal stability retaining 100% activity at 60 C, pH 8 and 9 after 2.5 h of incubation. The residual activity at 70 C after 2.5 h was 62% and 45% at pH 8 and 9, respectively. At 75 C only 22.2% activity remained at pH 8 after 1 h incubation. Since Kraft pulp is alkaline this enzyme could be used for prebleaching of pulp at temperatures up to 70 C without pH adjustment.     

Insights into the local residual entropy of proteins provided by NMR relaxation.

A simple model is used to illustrate the relationship between the dynamics measured by NMR relaxation methods and the local residual entropy of proteins. The expected local dynamic behavior of well-packed extended amino acid side chains are described by employing a one-dimensional vibrator that encapsulates both the spatial and temporal character of the motion. This model is then related to entropy and to the generalized order parameter of the popular "model-free" treatment often used in the analysis of NMR relaxation data. Simulations indicate that order parameters observed for the methyl symmetry axes in, for example, human ubiquitin correspond to significant local entropies. These observations have obvious significance for the issue of the physical basis of protein structure, dynamics, and stability.