Local Structural Fluctuations Research Articles

Characterization of a buried neutral histidine in Bacillus circulans xylanase: internal dynamics and interaction with a bound water molecule.

NMR spectroscopy was used to characterize the dynamic behavior of His149 in Bacillus circulans xylanase (BCX) and its interaction with an internal water molecule. Rate constants for the specific acid- and base-catalyzed exchange following bimolecular kinetics (EX2) of the nitrogen-bonded H epsilon 2 of this buried, neutral histidine were determined. At pDmin 7.0 and 30 degrees C, the lifetime for this proton is 9.9 h, corresponding to a protection factor of approximately 10(7) relative to that predicted for an exposed histidine. The apparent activation energies measured for specific acid and base catalysis (7.0 and 17.4 kcal/mol) indicate that exchange occurs via local structural fluctuations. Consistent with its buried environment, the N epsilon 2-H bond vector of His149 shows restricted mobility, as evidenced by an order parameter S2 = 0.83 determined from 15N relaxation measurements. The crystal structure of BCX reveals that a conserved, buried water hydrogen-bonds to the H epsilon 2 of His149. Strong support for this interaction in solution is provided by the observation of a negative nuclear Overhauser effect (NOE) and positive rotating-frame Overhauser effect (ROE) between His149 H epsilon 2 and a water molecule with the same chemical shift as the bulk solvent. However, the chemical shift of H epsilon 2 (12.2 ppm) and a D/H fractionation factor close to unity (0.89 +/- 0.02) indicate that this is not a so-called low-barrier hydrogen bond. Lower and upper bounds on the lifetime of the internal water are estimated to be 10(-8) and 10(-3) s. Therefore the chemical exchange of solvent protons with those of His149 H epsilon 2 and the diffusion or physical exchange of the internal water to which the histidine is hydrogen-bonded differ in rate by over 7 orders of magnitude.

Conformational stability of ribonuclease T1 determined by hydrogen-deuterium exchange.

The hydrogen-deuterium exchange kinetics of 37 backbone amide residues in RNase T1 have been monitored at 25, 40, 45, and 50 degrees C at pD 5.6 and at 40 and 45 degrees C at pD 6.6. The hydrogen exchange rate constants of the hydrogen-bonded residues varied over eight orders of magnitude at 25 degrees C with 13 residues showing exchange rates consistent with exchange occurring as a result of global unfolding. These residues are located in strands 2-4 of the central beta-pleated sheet. The residues located in the alpha-helix and the remaining strands of the beta-sheet exhibited exchange behaviors consistent with exchange occurring due to local structural fluctuations. For several residues at 25 degrees C, the global free energy change calculated from the hydrogen exchange data was over 2 kcal/mol greater than the free energy of unfolding determined from urea denaturation experiments. The number of residues showing this unexpected behavior was found to increase with temperature. This apparent inconsistency can be explained quantitatively if the cis-trans isomerization of the two cis prolines, Pro-39 and Pro-55, is taken into account. The cis-trans isomerization equilibrium calculated from kinetic data indicates the free energy of the unfolded state will be 2.6 kcal/mol higher at 25 degrees C when the two prolines are cis rather than trans (Mayr LM, Odefey CO, Schutkowski M, Schmid FX. 1996. Kinetic analysis of the unfolding and refolding of ribonuclease T1 by a stopped-flow double-mixing technique. Biochemistry 35: 5550-5561). The hydrogen exchange results are consistent with the most slowly exchanging hydrogens exchanging from a globally higher free energy unfolded state in which Pro-55 and Pro-39 are still predominantly in the cis conformation. When the conformational stabilities determined by hydrogen exchange are corrected for the proline isomerization equilibrium, the results are in excellent agreement with those from an analysis of urea denaturation curves.

Vitrification and structural differences between metal glass, quasicrystal, and Frank-Kasper phases

The concept of icosahedral short-range order is extended to metallic glass, quasicrystal, and Frank-Kasper phases. The cluster model, together with the theory of local structural fluctuations, explains the static elasticity of glass, which distinguishes glass from liquid. An elastic peak of the dynamic structural factor indicates the possibility of transverse mode propagation in glass. As opposed to dislocations and disclinations in crystals, those in glass are artificially introduced defects, which serve as easily perceptible structural models. Thermodynamic relaxation theory may only be used for limited groups of vitrifying compounds the same applies to representation of vitrification as the second-order phase transition. The structure of real quasicrystals may not be adequately represented by Penrose tiling even after its decoration. This is associated with packing defects, inclusions of other phases, and chemical inhomogeneities. Quasicrystals have specific defects in an icosahedrally coordinated network of bonds, which distinguish them from Frank-Kasper phases. Criteria for isolating physically realizable Penrose tiling from all possible mosaics of this type are suggested. Structural distortions that transfer the diffraction rings of quasicrystalline samples into ellipses are explicable even in a linear approximation for the stress field created by a phason. The term “long-range order” seems to be wrong even for ordinary crystals. For quasicrystals, the notion of “rotational” order is more pertinent.

A Continuum Model for Protein–Protein Interactions: Application to the Docking Problem

The prediction of protein–protein interactions in solution is a major goal of theoretical structural biology. Here, we implement a continuum description of the thermodynamic processes involved. The model differs considerably from previous models in its use of ‘ molecular surface’' area to describe the hydrophobic component to the free energy of conformational change in solution. We have applied this model to a data set of alternative docked conformations of protein–protein complexes which were generated independently of this work. It was found previously that commonly used energy evaluation techniques fail to distinguish between near-native and certain non-native complexes in this data set. Here, we found that an energy function that takes into account (1) total electrostatic free energy, (2) hydrophobic free energy and (3) loss in side-chain conformational energy was able to reliably discriminate between near-native and non-native configurations but only when molecular surface is used as a descriptor of the hydrophobic effect. It is shown that the molecular surface and the more conventional surface descriptor ‘ solvent accessible surface’' give very different quantitative measures of hydrophobicity. In terms of the contribution of different energy components to the free energy of complex formation it was found that loss in side-chain conformational entropy is a second order effect. Electrostatic interaction energy (which is commonly used to score docked conformations) was a poor indicator of complementarity when starting from unbound conformations. It was found that electrostatic desolvation energy and the hydrophobic contribution (based on a molecular surface area descriptor) are much less sensitive to local fluctuations in atomic structure than point-to-point interaction energies and thus may be more suited for use as a scoring function when docking unbound conformations, where atomic complementarity is much less apparent. Whilst a combined energy function was able to distinguish near-native from non-native energy function was able to distinguish near-native from non-native conformations in the six systems studied here, it remains to be determined to what extent more sizeable conformational changes would influence the results. f2 f2 Abbreviations used: vdW, van der Waals; MS, molecular surface; SAS, solvent accessible surface; r.m.s.d., root-mean-square deviation; BPTI, bovine pancreatic trypsin inhibitor.

Computer Simulation of Protein-induced Structural Changes in Closed Circular DNA

The effect of protein-induced wrapping on overall DNA folding is studied using Monte Carlo computer simulation techniques. A new modeling scheme is devised to represent configurations of closed circular DNA containing fragments of the double helix partially wrapped around a core of proteins. The DNA consists of two regions, a fragment wrapped in a left-handed superhelical path around a `phantom' protein core and a free connecting loop. The loop has at least one single-stranded scission so that it can assume a torsionally relaxed state. The configuration of the loop is varied during the course of the computer simulations and the three-dimensional spatial arrangements of lowest total energy are identified. The axis of the DNA loop is represented by a finite three-dimensional Fourier series perturbation of an initial Bezier curve, making it possible to fix the position and orientation of the chain ends as well as the contour length of the free loop. The energy is approximated by elastic terms for the bending and twisting of the DNA and an excluded volume contribution that prevents the self-intersection of sequential distant chain segments. The proportions of the protein-DNA complex, the number of superhelical turns, the chain length and the imposed linking number difference of the closed DNA are varied in the calculations. The resulting minimum energy structures are consistent with physical models and suggest new ways to think about how proteins add and remove supercoils from DNA. Of special note in this regard is the sudden collapse of three-dimensional structure that accompanies small incremental wrapping of the DNA around the idealized protein core. These observations offer new structural insight into the mechanisms of action of proteins which add or remove supercoils from DNA and provide a first step in thinking about the activity of such systems at the chemical level whereby small fluctuations in local molecular structure are translated into large-scale macromolecular changes. The configurations identified in the simulations can also be examined in the context of the well known "linking number paradox" associated with nucleosome formation on closed circular plasmids. The findings bear relevance to DNA with natural curvature as well as to protein-induced bending and deformations of the double helix.

Spatial translational motions of base pairs in DNA molecules: application of the extended matrix generator method.

We have used the elementary generator matrices outlined in the preceding paper to examine the conformational plasticity of the nucleic acid double helix. Here we investigate kinked DNA structures made up of alternating B- and A-type helices and intrinsically curved duplexes perturbed by the intercalation of ligands. We model the B-to-A transition by the lateral translation of adjacent base pairs, and the intercalation of ligands by the vertical displacement of neighboring residues. We report a complete set of average configuration-dependent parameters, ranging from scalars (i.e., persistence lengths) to first- and second-order tensor parameters (i.e., average second moments of inertia), as well as approximations of the associated spatial distributions of the DNA and their angular correlations. The average structures of short chains (of lengths less than 100 base pairs) with local kinks or intrinsically curved sequences are essentially rigid rods. At the smallest chain lengths (10 base pairs), the kinked and curved chains exhibit similar average properties, although they are structurally perturbed compared to the standard B-DNA duplex. In contrast, at lengths of 200 base pairs, the curved and kinked chains are more compact on average and are located in a different space from the standard B- or A-DNA helix. While A-DNA is shorter and thicker than B-DNA in x-ray models, the long flexible A-DNA helix is thinner and more extended on average than its B-DNA counterpart because of more limited fluctuations in local structure. Curved polymers of 50 base pairs or longer also show significantly greater asymmetry than other DNAs (in terms of the distribution of base pairs with respect to the center of gravity of the chain). The intercalation of drugs in the curved DNA straightens and extends the smoothly deformed template. The dimensions of the average ellipsoidal boundaries defining the configurations of the intercalated polymers are roughly double those of the intrinsically curved chain. The altered proportions and orientations of these density functions reflect the changing shape and flexibility of the double helix. The calculations shed new light on the possible structural role of short A-DNA fragments in long B-type duplexes and also offer a model for understanding how GC-specific intercalative ligands can straighten naturally curved DNA. The mechanism is not immediately obvious from current models of DNA curvature, which attribute the bending of the chain to a perturbed structure in repeating tracts of A.T base pairs.

Cysteinyl peptides labeled by dibromobutanedione in reaction with rabbit muscle pyruvate kinase.

The bifunctional reagent 1,4-dibromobutanedione (DBBD) reacts covalently with pyruvate kinase from rabbit muscle to cause inactivation of the enzyme at a rate that is linearly dependent on the reagent concentration, giving a second order rate constant of 444 min-1 M-1. The individual substrates phosphoenolpyruvate (with KCl), ADP, or ATP in the presence of divalent metal cation provide marked protection against inactivation suggesting that reaction occurs in the region of the active site. The limited incorporation of DBBD into pyruvate kinase was measured by reduction of the carbonyl groups of the enzyme-bound reagent using [3H]NaBH4. When pyruvate kinase was reacted with 120 microM DBBD at pH 7.0 for 50 min in the absence of protectants, 1.8 mol of tritium/mol of subunit was incorporated, whereas in the presence of phosphoenolpyruvate with KCl, only 1.0 mol of tritium was incorporated per mole of subunit. Modified peptides were isolated from tryptic digests of pyruvate kinase. Reaction of enzyme in the presence of substrate (showing no activity loss) yielded a single peptide, Asn-Ile-X1-Lys, where X1 corresponds to Cys164 of the known amino acid sequence of muscle pyruvate kinase. In the absence of protectants, reaction for 10 min (when the enzyme retained substantial activity) yielded Asn-Ile-X1-Lys as the major labeled peptide, whereas reaction for 50 min (when the enzyme was 88% inactivated) yielded predominantly Asn-Ile-X1-Lys cross-linked to X2-Asp-Glu-Asn-Ile-Leu-Trp-Leu-Asp-Tyr-Lys, where X2 corresponds to Cys151. Because activity loss correlates with the appearance of the cross-linked peptides but not with formation of Asn-Ile-X1-Lys, inactivation is likely caused by the reaction leading to the cross-link between Cys151 and Cys164. The distance between the alpha-carbons of these residues in the crystal structure is 15.5 A, whereas only 12.0 A can be spanned by the two side chains linked by a dioxobutyl group, suggesting either that pyruvate kinase undergoes a conformational change in forming the cross-link or that local rapid fluctuations in structure occur in solution to the extent of 3.5 A in this region of pyruvate kinase.

13C and1H NMR Relaxation of Chloroform in a Nematic Liquid Crystal. II. Dynamical Behavior of the Small Probe Molecule

Longitudinal relaxation of 13 C and 1 H in chloroform dissolved in a nematic liquid crystal has been observed between 25 and 34°C at 89.6 and 400.1 MHz (for 1 H) by the selective and nonselective inversion recovery method. The data can be satisfactorily explained by a combination of fast reorientation of the solute and slow fluctuations in the nematic phase, under consideration of the intramolecular dipole-dipole and external random field interactions together with cross correlations between the two. Local structure fluctuations in the nematic phase have played a substantial role in the spin relaxations. The external random field interaction on the proton and the cross correlation relating this interaction have considerably been dependent on the observing frequency.

Computer Simulations of ESR Spectra of Amorphous Thiomolybdates

AbstractESR spectra of amorphous chalcogenides MoS2+x (1 ≧ x ≧ 0) at 9.5 and 35 GHz reveal three different signals whose parameters are determined by computer simulation. The corresponding paramagnetic centers are: a) an electron hole center, with three principal values of the g‐tensor, localized on a sulfur atom, b) a Mo(V) center surrounded by sulfur atoms and characterized by an axial g‐tensor, c) a Mo(V) center surrounded by oxygen atoms, with also an axial g‐tensor, which results from a contamination by oxide traces. An anisotropic linewidth is taken into account to obtain an acceptable fitting for the different signals, it means distributions of g‐values originating from random local structural fluctuations in the amorphous compounds. Amorphous Li2MoS3 is also examined by ESR for comparison.

Self-diffusion in fluids: A molecular model

A molecular model of self-diffusion in an atomic fluid is developed and tested against hard sphere simulation results. The model is based on a variation of Kirkwood’s theory of friction and a theory of binary encounters of Sceats. The model uses characteristics of the potential of mean force to characterize the deviation of D from Enskog theory DE as the density increases. At intermediate density D/DE exceeds unity because of the reduction of flux of binary encounters caused by third body collisions and at high density this effect is overwhelmed by the enhancement of the zero frequency value of the force power spectrum due to three center force correlations. Fluctuations in local structure are important at densities where caging becomes important.

Optical phonons in disordered materials

A quantized Hamiltonian, including both the short- and long-range forces, for optical phonons in disordered materials is presented in this paper. The spectra of the optical phonons and the LOTO splitting are calculated under the coherent potential approximation. The competed effects of the long-range correlation and the local structural fluctuation on the optical phonons are also discussed.

Amide proton exchange in proteins by EX1 kinetics: studies of the basic pancreatic trypsin inhibitor at variable p2H and temperature

With the use of one-dimensional 1H nuclear magnetic resonance, two-dimensional correlated spectroscopy, and two-dimensional nuclear Overhauser enhancement spectroscopy, the exchange mechanisms for numerous individual amide protons in the basic pancreatic trypsin inhibitor (BPTI) were investigated over a wide range of p2H and temperature. Correlated exchange under an EX1 regime was observed only for the most slowly exchanging protons in the central hydrogen bonds of the antiparallel beta-sheet and only over a narrow range of temperature and p2H, i.e., above ca. 55 degrees C and between p2H 7 and 9, where the opening rates of the structure fluctuations which promote the exchange of these protons are of the order 0.1 min-1. At p2H below 7, the exchange of this most stable group of protons is uncorrelated and is governed by an EX2 mechanism. At p2H above 9, the exchange is also uncorrelated and occurs via either EX2 or EX1 processes promoted by strictly local structure fluctuations. For all other backbone amide protons in BPTI, the exchange was found to be uncorrelated and by an EX2 mechanism under all conditions of p2H and temperature where quantitative measurements could be obtained with the methods used, i.e., for kex approximately less than 5 min-1. From these observations with BPTI it can be concluded that the amide proton exchange in globular proteins is quite generally via EX2 processes, with rare exceptions for measurements with extremely stable protons at high temperature and basic p2H. This emphasizes the need for further development of suitable concepts for the structural interpretation of EX2 amide proton exchange [Wagner, G. (1983) Q. Rev. Biophys. 16, 1-57; Wagner, G., Stassinopoulou, C. I., & Wüthrich, K. (1984) Eur. J. Biochem. 145, 431-436] and for more detailed investigations of the intrinsic exchange rates for solvent-exposed amide protons in the "open" states of a protein [Roder, H., Wagner, G., & Wüthrich, K. (1985) Biochemistry (following paper in this issue)].

Amide‐proton exchange studies by two‐dimensional correlated 1H NMR in two chemically modified analogs of the basic pancreatic trypsin inhibitor

The backbone amide proton exchange with the solvent was investigated in 2H2O solutions of the basic pancreatic trypsin inhibitor and two chemical modifications thereof, which were obtained by transamination of the N-terminus and by cleavage of the disulfide bond 14-38, respectively. The three proteins have nearly identical conformations, but the stability with respect to thermal denaturation is markedly different. Exchange rates for a large number of individually assigned amide protons located both in central and peripheral parts of the protein structures were measured by two-dimensional correlated spectroscopy (COSY). From analysis of the individual proton exchange rates in the three proteins at different temperatures, an interplay of global and local structure fluctuations was characterized, which promote hydrogen exchange in distinct regions of the molecules. The exchange of particular amide protons may be governed by different motional processes at different temperatures. As a general trend, global fluctuations involving breakage of numerous hydrophilic secondary bonds appear to be dominant at higher temperatures, whereas at lower temperatures the influence of local fluctuations in hydrophobic regions of the protein structures is also clearly noticeable.

Reversibility of the structural relaxation in amorphous alloys

Changes in volume, Curie temperature, field induced anisotropy, and elastic constant due to the structural relaxation induced by annealing are compared for metal-metalloid glasses. It is shown that the volume relaxation and other relaxation phenomena have different kinetics, therefore at least two parameters are necessary to describe the internal state of the metallic glasses. The results are discussed in terms of the recently proposed theory of local structural fluctuations.

Local structural fluctuations and defects in metallic glasses

The atomic short range order in liquid and amorphous metals is most often described by the atomic pair distribution function. However, the local variation in properties and the structural defects are better described in terms of more collective structural parameters. It is suggested that the concept of the local structure including all the nearest neighbors provides the most useful description of the local short range order. In particular the method based upon the atomic-level stresses is able to describe satisfactorily the glass transition, structural relaxation and defects. The theory incorporates the free volume as one of the thermal defects, while other types of thermal defects also exist. Furthermore the feasibility of the existence of extended athermal defects is discussed.

Local structural fluctuations in amorphous and liquid metals: a simple theory of the glass transition

Local structural fluctuations in amorphous and liquid metals: a simple theory of the glass transition

Local structural fluctuations in amorphous and liquid metals: a simple theory of the glass transition

A method of describing the thermal fluctuations in the local atomic structure of liquid and amorphous metals in terms of the fluctuations in the atomic level stresses is proposed. The energy of the system is expressed in terms of these stresses in the elastic approximation. The temperature dependence of the second moments of the stresses is then calculated and shown to be linear with temperature. The glass transition is assumed to take place when the second moments freeze to certain values determined by computer simulation. It is shown that the pressure fluctuations and the shear fluctuations freeze at different temperatures. The glass transition, in the normal sense, is described by the freezing of the pressure fluctuation. This method provides a reasonable estimate of the glass transition temperature, and predicts it to be proportional to the product of atomic volume and bulk modulus. It furthermore provides an explanation of the different relaxation behaviours between the pressure and shear fluctuations.

Causes for the variable superconducting transition temperature in uranium metal

The variable superconducting transition temperature of uranium metal appears to depend upon the variability of a low-temperature martensitic transformation. Local structural fluctuations and phase instabilities are suggested as resulting when the transformation is incomplete. The thermodynamic stability of a two-phase modulated structure involving domain formation is discussed along with possible consequences of a domain configuration. Factors affecting T c are used to explain the anamalous thermal property behavior of α-phase uranium.

Mechanisms of hydrogen exchange in proteins from nuclear magnetic resonance studies of individual tryptophan indole NH hydrogens in lysozyme.

The individual rates of solvent exchange of the six tryptophan indole NH hydrogens of lysozyme in 2H2O have been measured over a wide range of temperatures by using 1H NMR. Two distinct mechanisms for exchange have been identified, one characterized by a high activation energy and the other by a much lower activation energy. The high-energy process has been shown to be associated directly with the cooperative thermal unfolding of the protein and is the dominant mechanism for exchange of the most slowly exchanging hydrogen even 15 degrees C below the denaturation temperature. Rate constants and activation for the folding and unfolding reactions were obtained from the experimental exchange rates. At low temperatures, a lower activation energy mechanism is dominant for all hydrogens, and this can be associated with local fluctuations in the protein structure which allows access of solvent. The relative exchange rates and activation energies can only qualitatively be related to the different environments of the residues in the crystal structure. There is provisional evidence that a mechanism intermediate between these two extremes may be significant for some hydrogens under restricted conditions.

Evolution of responses to relative homozygosity.

ACCORDING to the theory of kin selection first elaborated by Hamilton1,2, all individual behaviour is selected to maximise the increment to inclusive fitness ΔWi + ΣΔWjrij, where ΔWi is the effect of an act on the fitness of the actor, ΔWj is the effect of the same act on the fitness of a conspecific, and rij is the coefficient of relationship between the actor and the conspecific. Acts that lower an individual's direct fitness can thus be favoured by natural selection if, by conferring benefits on relatives of the actor, they cause a positive increment to the actor's inclusive fitness3,4. Since the average rij between an individual and the targets of its behaviour varies because of fluctuations in local population structure, an individual is most likely to secure a positive increment if its behaviour is conditioned on as accurate an estimate as possible of the particular local distribution of rij. I describe here a mechanism by which this estimate could be improved on the basis of information derived from the relative homozygosity of the individual's own genotype, in species with certain kinds of life histories.