Dynamics of the three methionyl side chains of Streptomyces subtilisin inhibitor. Deuterium NMR studies in solution and in the solid state

Flexibility and Solvation of Amyloid-β Hydrophobic Core

Amyloid fibril deposits found in Alzheimer disease patients are composed of amyloid-β (Aβ) protein forming a number of hydrophobic interfaces that are believed to be mostly rigid. We have investigated the μs-ms time-scale dynamics of the intra-strand hydrophobic core and interfaces of the fibrils composed of Aβ1-40 protein. Using solid-state (2)H NMR line shape experiments performed on selectively deuterated methyl groups, we probed the 3-fold symmetric and 2-fold symmetric polymorphs of native Aβ as well as the protofibrils of D23N Iowa mutant, associated with an early onset of Alzheimer disease. The dynamics of the hydrophobic regions probed at Leu-17, Leu-34, Val-36, and Met-35 side chains were found to be very pronounced at all sites and in all polymorphs of Aβ, with methyl axis motions persisting down to 230-200 K for most of the sites. The dominant mode of motions is the rotameric side chain jumps, with the Met-35 displaying the most complex multi-modal behavior. There are distinct differences in the dynamics among the three protein variants, with the Val-36 site displaying the most variability. Solvation of the fibrils does not affect methyl group motions within the hydrophobic core of individual cross-β subunits but has a clear effect on the motions at the hydrophobic interface between the cross-β subunits, which is defined by Met-35 contacts. In particular, hydration activates transitions between additional rotameric states that are not sampled in the dry protein. Thus, these results support the existence of water-accessible cavity recently predicted by molecular dynamics simulations and suggested by cryo-EM studies.

Quasielastic neutron scattering in biology: Theory and applications

Neutrons scatter quasielastically from stochastic, diffusive processes, such as overdamped vibrations, localized diffusion and transitions between energy minima. In biological systems, such as proteins and membranes, these relaxation processes are of considerable physical interest. We review here recent methodological advances and applications of quasielastic neutron scattering (QENS) in biology, concentrating on the role of molecular dynamics simulation in generating data with which neutron profiles can be unambiguously interpreted. We examine the use of massively-parallel computers in calculating scattering functions, and the application of Markov state modeling. The decomposition of MD-derived neutron dynamic susceptibilities is described, and the use of this in combination with NMR spectroscopy. We discuss dynamics at very long times, including approximations to the infinite time mean-square displacement and nonequilibrium aspects of single-protein dynamics. Finally, we examine how neutron scattering and MD can be combined to provide information on lipid nanodomains. This article is part of a Special Issue entitled "Science for Life" Guest Editor: Dr. Austen Angell, Dr. Salvatore Magazù and Dr. Federica Migliardo.

Protein Dynamics in the Solid State from (2)H NMR Line Shape Analysis. II. MOMD Applied to C-D and C-CD3 Probes

Deuterium line shape analysis from mobile C–D and C–CD₃ groups has emerged as a particularly useful tool for studying dynamics in the solid state. The theoretical models devised so far consist typically of sets of independent dynamic modes. Each such mode is simple and usually case-specific. In this scenario, model improvement entails adding yet another mode (thereby changing the overall model), comparison of different cases is difficult, and ambiguity is unavoidable. We recently developed the microscopic order macroscopic disorder (MOMD) approach as a single-mode alternative. In MOMD, the local spatial restrictions are expressed by an anisotropic potential, the local motion by a diffusion tensor, and the local molecular geometry by relative (magnetic and model-related) tensor orientations, all of adjustable symmetry. This approach provides a consistent method of analysis, thus resolving the issues above. In this study, we apply MOMD to PS-adsorbed LKα14 peptide and dimethylammonium tetraphenylborate (C–CD₃ and N–CD₃ dynamics, respectively), as well as HhaI methyltransferase target DNA and phase III of benzene-6-hexanoate (C–D dynamics). The success with fitting these four disparate cases, as well as the two cases in the previous report, demonstrates the generality of this MOMD-based approach. In this study, C–D and C–CD₃ are both found to execute axial diffusion (rates R_⊥ and R_∥) in the presence of a rhombic potential given by the L = 2 spherical harmonics (coefficients c₀² and c₂²). R_⊥ (R_∥) is in the 10²–10³ (10⁴–10⁵) s^–1 range, and c₀² and c₂² are on the order of 2–3 k_BT. Specific parameter values are determined for each mobile site. The diffusion and quadrupolar tensors are tilted at either 120° (consistent with trans–gauche isomerization) or nearly 110.5° (consistent with methyl exchange). Future prospects include extension of the MOMD formalism to include MAS, and application to ¹⁵N and ¹³C nuclei.

Unraveling the complexity of protein backbone dynamics with combined (13)C and (15)N solid-state NMR relaxation measurements

Typically, protein dynamics involve a complex hierarchy of motions occurring on different time scales between conformations separated by a range of different energy barriers. NMR relaxation can in principle provide a site-specific picture of both the time scales and amplitudes of these motions, but independent relaxation rates sensitive to fluctuations in different time scale ranges are required to obtain a faithful representation of the underlying dynamic complexity. This is especially pertinent for relaxation measurements in the solid state, which report on dynamics in a broader window of time scales by more than 3 orders of magnitudes compared to solution NMR relaxation. To aid in unraveling the intricacies of biomolecular dynamics we introduce (13)C spin-lattice relaxation in the rotating frame (R1ρ) as a probe of backbone nanosecond-microsecond motions in proteins in the solid state. We present measurements of (13)C'R1ρ rates in fully protonated crystalline protein GB1 at 600 and 850 MHz (1)H Larmor frequencies and compare them to (13)C'R1, (15)N R1 and R1ρ measured under the same conditions. The addition of carbon relaxation data to the model free analysis of nitrogen relaxation data leads to greatly improved characterization of time scales of protein backbone motions, minimizing the occurrence of fitting artifacts that may be present when (15)N data is used alone. We also discuss how internal motions characterized by different time scales contribute to (15)N and (13)C relaxation rates in the solid state and solution state, leading to fundamental differences between them, as well as phenomena such as underestimation of picosecond-range motions in the solid state and nanosecond-range motions in solution.

Protein dynamics in the solid state from 2H NMR line shape analysis: a consistent perspective

Deuterium line shape analysis of CD3 groups has emerged as a particularly useful tool for studying microsecond-millisecond protein motions in the solid state. The models devised so far consist of several independently conceived simple jump-type motions. They are comprised of physical quantities encoded in their simplest form; improvements are only possible by adding yet another simple motion, thereby changing the model. The various treatments developed are case-specific; hence comparison among the different systems is not possible. Here we develop a new methodology for (2)H NMR line shape analysis free of these limitations. It is based on the microscopic-order-macroscopic-disorder (MOMD) approach. In MOMD motions are described by diffusion tensors, spatial restrictions by potentials/ordering tensors, and geometric features by relative tensor orientations. Jump-type motions are recovered in the limit of large orientational potentials. Model improvement is accomplished by monitoring the magnitude, symmetry, and orientation of the various tensors. The generality of MOMD makes possible comparison among different scenarios. CD3 line shapes from the Chicken Villin Headpiece Subdomain and the Streptomyces Subtilisin Inhibitor are used as experimental examples. All of these spectra are reproduced by using rhombic local potentials constrained for simplicity to be given by the L = 2 spherical harmonics, and by axial diffusion tensors. Potential strength and rhombicity are found to be ca. 2-3 k(B)T. The diffusion tensor is tilted at 120° from the C-CD3 axis. The perpendicular (parallel) correlation times for local motion are 0.1-1.0 ms (3.3-30 μs). Activation energies in the 1.1-8.0 kcal/mol range are estimated. Future prospects include extension to the (2)H relaxation limit, application to the (15)N and (13)C NMR nuclei, and accounting for collective motions and anisotropic media.

Vanishing amplitude of backbone dynamics causes a true protein dynamical transition: 2H NMR studies on perdeuterated C-phycocyanin

Using a combination of H2 nuclear magnetic resonance (NMR) methods, we study internal rotational dynamics of the perdeuterated protein C-phycocyanin (CPC) in dry and hydrated states over broad temperature and dynamic ranges with high angular resolution. Separating H2 NMR signals from methyl deuterons, we show that basically all backbone deuterons exhibit highly restricted motion occurring on time scales faster than microseconds. The amplitude of this motion increases when a hydration shell exists, while it decreases upon cooling and vanishes near 175 K. We conclude that the vanishing of the highly restricted motion marks a dynamical transition, which is independent of the time window and of a fundamental importance. This conclusion is supported by results from experimental and computational studies of the proteins myoglobin and elastin. In particular, we argue based on findings in molecular dynamics simulations that the behavior of the highly restricted motion of proteins at the dynamical transition resembles that of a characteristic secondary relaxation of liquids at the glass transition, namely the nearly constant loss. Furthermore, H2 NMR studies on perdeuterated CPC reveal that, in addition to highly restricted motion, small fractions of backbone segments exhibit weakly restricted dynamics when temperature and hydration are sufficiently high.

Effect of subdomain interactions on methyl group dynamics in the hydrophobic core of villin headpiece protein

Thermostable villin headpiece protein (HP67) consists of the N-terminal subdomain (residues 10-41) and the autonomously folding C-terminal subdomain (residues 42-76) which pack against each other to form a structure with a unified hydrophobic core. The X-ray structures of the isolated C-terminal subdomain (HP36) and its counterpart in HP67 are very similar for the hydrophobic core residues. However, fine rearrangements of the free energy landscape are expected to occur because of the interactions between the two subdomains. We detect and characterize these changes by comparing the µs-ms time scale dynamics of the methyl-bearing side chains in isolated HP36 and in HP67. Specifically, we probe three hydrophobic side chains at the interface of the two subdomains (L42, V50, and L75) as well as at two residues far from the interface (L61 and L69). Solid-state deuteron NMR techniques are combined with computational modeling for the detailed characterization of motional modes in terms of their kinetic and thermodynamic parameters. The effect of interdomain interactions on side chain dynamics is seen for all residues but L75. Thus, changes in dynamics because of subdomain interactions are not confined to the site of perturbation. One of the main results is a two- to threefold increase in the value of the activation energies for the rotameric mode of motions in HP67 compared with HP36. Detailed analysis of configurational entropies and heat capacities complement the kinetic view of the degree of the disorder in the folded state.

Surface hydration amplifies single-well protein atom diffusion propagating into the macromolecular core

The effect of surface hydration water on internal protein motion is of fundamental interest in molecular biophysics. Here, by decomposing the picosecond to nanosecond atomic motion in molecular dynamics simulations of lysozyme at different hydration levels into three components--localized single-well diffusion, methyl group rotation, and nonmethyl jumps--we show that the effect of surface hydration is mainly to increase the volume of the localized single-well diffusion. These diffusive motions are coupled in such a way that the hydration effect propagates from the protein surface into the dry core.

Methyl dynamics of a Ca2+-calmodulin-peptide complex from NMR/SRLS

We developed the slowly relaxing local structure (SRLS) approach for analyzing NMR spin relaxation in proteins. SRLS accounts for dynamical coupling between the tumbling of the protein and the local motion of the probe and for general tensorial properties. It is the generalization of the traditional model-free (MF) method, which does not account for mode-coupling and treats only simple tensorial properties. SRLS is applied herein to ²H relaxation of ¹³CDH₂ groups in the complex of Ca(2+)-calmodulin with the peptide smMLCKp. Literature data comprising ²H T₁ and T₂ acquired at 14.1 and 17.6 T, and 288, 295, 308, and 320 K, are used. We find that mode-coupling is a small effect for methyl dynamics. On the other hand, general tensorial properties are important. In particular, it is important to allow for the asymmetry of the local spatial restrictions, which can be represented in SRLS by a rhombic local ordering tensor with components S(0)(2) and S(2)(2). The principal axes frame of this tensor is obviously different from the axial frames of the magnetic tensors. Here, we find that -0.2 ≤ S(0)(2) ≤ 0.5 and -0.4 ≤ S(2)(2) ≤ 0. MF features a single "generalized" order parameter, S, confined to the 0-0.316 range; the local geometry is inherently simple. The parameter S is inaccurate, having absorbed unaccounted for effects, notably S(2)(2) ≠ 0. We find that the methionine methyls (the other methyl types) reorient with rates of 8.6 × 10⁹ to 21.4 × 10⁹ (0.67 × 10⁹ to 6.5 × 10⁹) 1/s. The corresponding activation energies are 10 (10-27) kJ/mol. By contrast, MF yields inaccurate effective local motional correlation times, τ(e), with nonphysical temperature dependence. Thus, the problematic S- and τ(e)-based MF picture of methyl dynamics has been replaced with an insightful physical picture based on a local ordering tensor related to structural features, and a local diffusion tensor that yields accurate activation energies.

Comparative dynamics of leucine methyl groups in FMOC-leucine and in a protein hydrophobic core probed by solid-state deuteron nuclear magnetic resonance over 7-324 K temperature range

Quantitative dynamics of methyl groups in 9-fluorenylmethyloxycarbonyl-leucine (FMOC-leu) have been analyzed and compared with earlier studies of methyl dynamics in chicken villin headpiece subdomain protein (HP36) labeled at L69, a key hydrophobic core position. A combination of deuteron solid-state nuclear magnetic resonance experiments over the temperature range of 7-324 K and computational modeling indicated that while the two compounds show the same modes of motions, there are marked differences in the best-fit parameters of these motions. One of the main results is that the crossover observed in the dynamics of the methyl groups in the HP36 sample at 170 K is absent in FMOC-leu. A second crossover at around 95-88 K is present in both samples. The differences in the behavior of the two compounds suggest that some of the features of methyl dynamics reflect the complexity of the protein hydrophobic core and are not determined solely by local interactions.

Probing the dynamics of a protein hydrophobic core by deuteron solid-state nuclear magnetic resonance spectroscopy

With the goal of investigating dynamical features of hydrophobic cores of proteins over a wide range of temperatures, the chicken villin headpiece subdomain protein (HP36) was labeled at a "single" site corresponding to any one of the two C(delta)D(3) groups of leucine-69, which is located in a key position of the core. The main techniques employed are deuteron NMR quadrupolar echo line shape analysis, and T(1Z) (Zeeman) and T(1Q) (quadrupolar order) relaxation experiments performed at 11.7 and 17.6 T over the temperature range of 112 to 298 K. The experimental data are compared with computer simulations. The deuteron line shapes give an excellent fit to a three-mode motional model that consists of (a) fast three-site rotational jumps about the pseudo C(3) methyl spinning axis, (b) slower reorientation of the spinning axis, described by diffusion along a restricted arc, and (c) large angle jumps between traces of rotameric conformers. Relaxation behavior is described by a phenomenological distribution of activation energies for three-site hops at high temperatures that collapses to a single, distinctly smaller value for lower temperatures.

13C and 15N NMR study of the hydration response of T4 lysozyme and alphaB-crystallin internal dynamics

The response to hydration of the internal protein dynamics was studied by the means of solid state NMR relaxation and magic angle spinning exchange techniques. Two proteins, lysozyme from bacteriophage T4 and human alphaB-crystallin were used as exemplars. The relaxation rates R1 and R1rho of 13C and 15N nuclei were measured as a function of a hydration level of the proteins in the range 0-0.6 g of water/g of protein. Both proteins were totally 15N-enriched with natural 13C abundance. The relaxation rates were measured for different spectral bands (peaks) that enabled the characterization of the dynamics separately for the backbone, side chains, and CH3 and NH3+ groups. The data obtained allowed a comparative analysis of the hydration response of the protein dynamics in different frequency ranges and different sites in the protein for two different proteins and two magnetic nuclei. The most important result is a demonstration of a qualitatively different response to hydration of the internal dynamics in different frequency ranges. The amplitude of the fast (nanosecond time scale) motion gradually increases with increasing hydration, whereas that of the slow (microsecond time scale) motion increases only until the hydration level 0.2-0.3 g of water/g of protein and then shows almost no hydration dependence. The reason for such a difference is discussed in terms of the different physical natures of these two dynamic processes. Backbone and side chain nuclei show the same features of the response of dynamics with hydration despite the fact that the backbone motional amplitudes are much smaller than those of side chains. Although T4 lysozyme and alphaB-crystallin possess rather different structural and biochemical properties, both proteins show qualitatively very similar hydration responses. In addition to the internal motions, exchange NMR data enabled the identification of one more type of motion in the millisecond to second time scale that appears only at high hydration levels. This motion was attributed to the restricted librations of the protein as a whole.

Comparison of the internal dynamics of globular proteins in the microcrystalline and rehydrated lyophilized states

Natural abundance solid-state 13C-NMR spin-lattice relaxation experiments in the laboratory (T1) and off-resonance rotating (T(1rho)) frames were applied for qualitative comparison of the internal molecular dynamics of barstar, hen egg white lysozyme and bacteriophage T4 lysozyme in both the microcrystalline and the rehydrated (water content is 50% of the protein mass) lyophilized states. The microcrystalline state of proteins provides a better spectral resolution; however, less is known about the local structure and dynamics in the different states. We found by visual comparison of both T1 and T(1rho) relaxation decays of various resonance bands of the CPMAS spectra that within the ns-mus range of correlation times there is no appreciable difference in the internal dynamics between rehydrated lyophilized and crystalline states for all three proteins tested. This suggests that the internal conformational dynamics depends weakly if at all on inter-protein interactions in the solid state. Hence, physical properties of globular proteins in a fully hydrated solid state seem to be similar to those in solution. This result at least partly removes concerns about biological relevance of studies of globular proteins in the solid state.

Protein Side-Chain Dynamics Observed by Solution- and Solid-State NMR: Comparative Analysis of Methyl 2H Relaxation Data

Rapid advances in solid-state MAS NMR made it possible to probe protein dynamics on a per-residue basis, similar to solution experiments. In this work we compare methyl 2H relaxation rates measured in the solid and liquid samples of alpha-spectrin SH3 domain. The solution data are treated using a model-free approach to separate the contributions from the overall molecular tumbling and fast internal motion. The latter part forms the basis for comparison with the solid-state data. Although the accuracy of solid-state measurements is limited by deuterium spin diffusion, the results suggest a significant similarity between methyl dynamics in the two samples. This is a potentially important observation, preparing the ground for combined analysis of the dynamics data by solid- and solution-state NMR.

Deuterium spin probes of side-chain dynamics in proteins. 2. Spectral density mapping and identification of nanosecond time-scale side-chain motions

In the previous paper in this issue we have demonstrated that it is possible to measure the five different relaxation rates of a deuteron in (13)CH(2)D methyl groups of (13)C-labeled, fractionally deuterated proteins. The extensive set of data acquired in these experiments provides an opportunity to investigate side-chain dynamics in proteins at a level of detail that heretofore was not possible. The data, acquired on the B1 domain of peptostreptococcal protein L, include 16 (9) relaxation measurements at 4 (2) different magnetic field strengths, 25 degrees C (5 degrees C). These data are shown to be self-consistent and are analyzed using a spectral density mapping procedure which allows extraction of values of the spectral density function at a number of frequencies with no assumptions about the underlying dynamics. Dynamics data from 31 of 35 methyls in the protein for which data could be obtained were well-fitted using the two-parameter Lipari-Szabo model (Lipari, G.; Szabo, A. J. Am. Chem. Soc. 1982, 104, 4546). The data from the remaining 4 methyls can be fitted using a three-parameter version of the Lipari-Szabo model that takes into account, in a simple manner, additional nanosecond time-scale local dynamics. This interpretation is supported by analysis of a molecular dynamics trajectory where spectral density profiles calculated for side-chain methyl sites reflect the influence of slower (nanosecond) time-scale motions involving jumps between rotameric wells. A discussion of the minimum number of relaxation measurements that are necessary to extract the full complement of dynamics information is presented along with an interpretation of the extracted dynamics parameters.

A new approach to visualizing spectral density functions and deriving motional correlation time distributions: applications to an alpha-helix-forming peptide and to a well-folded protein

A new approach to visualizing spectral densities and analyzing NMR relaxation data has been developed. By plotting the spectral density function, J(omega), as F(omega)=2 omega J(omega) on the log-log scale, the distribution of motional correlation times can be easily visualized. F(omega) is calculated from experimental data using a multi-Lorentzian expansion that is insensitive to the number of Lorentzians used and allows contributions from overall tumbling and internal motions to be separated without explicitly determining values for correlation times and their weighting coefficients. To demonstrate the approach, (15)N and (13)C NMR relaxation data have been analyzed for backbone NH and C(alpha)H groups in an alpha-helix-forming peptide 17mer and in a well-folded 138-residue protein, and the functions F(omega) have been calculated and deconvoluted for contributions from overall tumbling and internal motions. Overall tumbling correlation time distribution maxima yield essentially the same overall correlation times obtained using the Lipari-Szabo model and other standard NMR relaxation data analyses. Internal motional correlational times for NH and C(alpha)H bond motions fall in the range from 100 ps to about 1 ns. Slower overall molecular tumbling leads to better separation of internal motional correlation time distributions from those of overall tumbling. The usefulness of the approach rests in its ability to visualize spectral densities and to define and separate frequency distributions for molecular motions.

Peptide internal motions on nanosecond time scale derived from direct fitting of (13)C and (15)N NMR spectral density functions

NMR relaxation-derived spectral densities provide information on molecular and internal motions occurring on the picosecond to nanosecond time scales. Using (13)C and (15)N NMR relaxation parameters [T(1), T(2), and NOE] acquired at four Larmor frequencies (for (13)C: 62.5, 125, 150, and 200 MHz), spectral densities J(0), J(omega(C)), J(omega(H)), J(omega(H) + omega(C)), J(omega(H) - omega(C)), J(omega(N)), J(omega(H) + omega(N)), and J(omega(H) - omega(N)) were derived as a function of frequency for (15)NH, (13)C(alpha)H, and (13)C(beta)H(3) groups of an alanine residue in an alpha-helix-forming peptide. This extensive relaxation data set has allowed derivation of highly defined (13)C and (15)N spectral density maps. Using Monte Carlo minimization, these maps were fit to a spectral density function of three Lorentzian terms having six motional parameters: tau(0), tau(1), tau(2), c(0), c(1), and c(2), where tau(0), tau(1) and tau(2) are correlation times for overall tumbling and for slower and faster internal motions, and c(0), c(1), and c(2) are their weighting coefficients. Analysis of the high-frequency portion of these maps was particularly informative, especially when deriving motional parameters of the side-chain methyl group for which the order parameter is very small and overall tumbling motions do not dominate the spectral density function. Overall correlation times, tau(0), are found to be in nanosecond range, consistent with values determined using the Lipari-Szabo model-free approach. Internal motional correlation times range from picoseconds for methyl group rotation to nanoseconds for backbone N-H, C(alpha)-H, and C(alpha)-C(beta) bond motions. General application of this approach will allow greater insight into the internal motions in peptides and proteins.

Superslow backbone protein dynamics as studied by 1D solid-state MAS exchange NMR spectroscopy

Superslow backbone dynamics of the protein barstar and the polypeptide polyglycine was studied by means of a solid-state MAS 1D exchange NMR method (time-reverse ODESSA) that can detect reorientation of nuclei carrying anisotropic chemical shift tensors. Experiments were performed on carbonyl 13C in polyglycine (natural abundance) and backbone 15N nuclei in uniformly 15N-enriched barstar within a wide range of temperatures in dry and wet powders for both samples. Two exchange processes were observed in the experiments: molecular reorientation and spin diffusion. Experimental conditions that are necessary to separate these two processes are discussed on a quantitative level. It was revealed that the wet protein undergoes molecular motion in the millisecond range of correlation times, whereas in dry protein and polyglycine molecular reorientations could not be detected. The correlation time of the motion in the wet barstar at room temperature is 50-100 ms; the activation energy is about 80 kJ/mol. Previously, protein motions with such a long correlation time could be observed only by methods detecting chemical exchange in solution (e.g., hydrogen exchange). The application of solid-state MAS exchange spectroscopy provides new opportunities in studying slow biomolecular dynamics that is important for the biological function of proteins.

Correlation between binding and dynamics at SH2 domain interfaces

Protein recognition is a key determinant in regulating biological processes. Structures of complexes of interacting proteins provide significant insights into the mechanism of specific recognition. However, studies performed by modifying residues within a protein interface demonstrate that binding is not fully explained by these static pictures. Thus, structural data alone was not predictive of affinities in binding studies of phospholipase Cgamma1 and Syp phosphatase SH2 domains with phosphopeptides. NMR relaxation experiments probing dynamics of methyl groups of these complexes indicate a correlation between binding energy and restriction of motion at the interfacial region responsible for specific binding.

Binding of amino acid side-chains to S1 cavities of serine proteinases

The P1 or primary specificity residue of standard mechanism canonical protein inhibitors of serine proteinases, inserts into the S1 primary specificity cavity of the cognate enzyme upon enzyme-inhibitor complex formation. Both natural evolution and protein engineering often change the P1 residue to greatly alter the specificity and the binding strength. To systematize such results we have obtained all 20 coded P1 variants of one such inhibitor, turkey ovomucoid third domain, by recombinant DNA technology. The variants were extensively characterized. The association equilibrium constants were measured at pH 8.30, 21 (+/-2) degrees C, for interaction of these variants with six well characterized serine proteinases with hydrophobic S1, cavities. The enzyme names are followed by the best, worst and most specific coded residue for each. Bovine chymotrypsin A alpha (Tyr, Pro, Trp), porcine pancreatic elastase (Leu/Ala, Arg, Ala), subtilisin Carlsberg (Cys, Pro, Glu), Streptomyces griseus proteinase A (Cys, Pro, Leu) and B (Cys, Pro, Lys) and human leukocyte elastase (Ile, Asp, Ile). The data set was merged with Ka values for five non-coded variants at P1 of turkey ovomucoid third domain obtained in our laboratory by enzymatic semisynthesis. The ratios of the highest to the lowest Ka for each of the six enzymes range from 10(6) to 10(8). The dominant force for binding to these pockets is the hydrophobic interaction. Excess steric bulk (too large for the pocket), awkward shape (Pro, Val and Ile), polarity (Ser) oppose interaction. Ionic charges, especially negative charges on Glu- and Asp- are strongly unfavorable. The Pearson pro duct moment correlations for all the 15 enzyme pairs were calculated. We suggest that these may serve as a quantitative description of the specificity of the enzymes at P1. The sets of Streptomyces griseus proteinases A and B and of the two elastases are strongly positively correlated. Strikingly, chymotrypsin and pancreatic elastase are negatively correlated (-0.10). Such correlations can be usefully extended to many other enzymes and to many other binding pockets to provide a general measure of pocket binding specificity.

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.

Dynamic structure of proteins in solid state. 1H and 13C NMR relaxation study

Temperature dependencies of 1H non-selective NMR T1 and T2 relaxation times measured at two resonance frequencies and natural abundance 13C NMR relaxation times T1 and T1r measured at room temperature have been studied in a set of dry and wet solid proteins - Bacterial RNase, lysozyme and Bovine serum albumin (BSA). The proton and carbon data were interpreted in terms of a model supposing three kinds of internal motions in a protein. These are rotation of the methyl protons around the axis of symmetry of the methyl group, and fast and slow oscillations of all atoms. The correlation times of these motions in solid state are found around 10(-11), 10(-9) and 10(-6)s, respectively. All kinds of motion are characterized by the inhomogeneous distribution of the correlation times. The protein dehydration affects only the slow internal motion. The amplitude of the slow motion obtained from the carbon data is substantially less than that obtained from the proton data. This difference can be explained by taking into account different relative inter- and intra- chemical group contributions to the proton and carbon second moments. The comparison of the solid state and solution proton relaxation data showed that the internal protein dynamics in these states is different: the slow motion seems to be few orders of magnitude faster in solution.