A Euclidean perspective on the unfolding of azurin: spatial correlations

We investigate the stability to structural perturbation of Pseudomonas aeruginosa azurin using a previously developed geometric model. Our analysis considers Ru(2,2′,6′,2^″-terpyridine)(1,10-phenanthroline)(His83)-labelled wild-type azurin and five variants with mutations to Cu-ligating residues. We find that in the early stages of unfolding, the β-strands exhibit the most structural stability. The conserved residues comprising the hydrophobic core are dislocated only after nearly complete unfolding of the β-barrel. Attachment of the Ru-complex at His83 does not destabilize the protein fold, despite causing some degree of structural rearrangement. Replacing the Cys112 and/or Met121 Cu ligands does not affect the conformational integrity of the protein. Notably, these results are in accord with experimental evidence, as well as molecular dynamics simulations of the denaturation of azurin.     

Unfolding four-helix bundles

A geometrical model has been developed to describe the early stages of unfolding of cytochromes c′ and c-b₅₆₂ . Calculations are based on a step-wise extension of the polypeptide chain subject to the constraint that the spatial relationship among the residues of each triplet is fixed by the native-state crystallographic data. The response of each protein to these structural perturbations allows the evolution of each of the four helices in these two proteins to be differentiated. It is found that the two external helices in c′ unfold before its two internal helices, whereas exactly the opposite behaviour is demonstrated by c-b₅₆₂ . Each of these cytochromes has an extended, internal, non-helical (‘turning’) region that initially lags behind the most labile helix but then, at a certain stage (identified for each cytochrome), unravels before any of the four helices present in the native structure. It is believed that these predictions will be useful in guiding future experimental studies on the unfolding of these two cytochromes.     

Geometrical Analysis of Cytochrome c Unfolding

We have developed a geometrical model to study the unfolding of iso-1 cytochrome c. The model draws on the crystallographic data reported for this protein. These data were used to calculate the distance between specific residues in the folded state, and in a sequence of extended states defined by n= 3, 5, 7, 9, 11, 13, and 15 residue units. Exact calculations carried out for each of the 103 residues in the polypeptide chain demonstrate that different regions of the chain have different unfolding histories. Regions where there is a persistence of compact structures can be identified, and this geometrical characterization is fully consistent with analyses of time-resolved fluorescence energy-transfer (TrFET) data using dansyl-derivatized cysteine side-chain probes at positions 39, 50, 66, 85, and 99. Our calculations were carried out assuming that different regions of the polypeptide chain unfold synchronously. To test this assumption, we performed lattice Monte Carlo simulations to study systematically the possible importance of asynchronicity. Our calculations show that small departures from synchronous dynamics can arise if displacements of residues in the main body of the chain are much more sluggish than near-terminal residues.     

Geometrical analysis of cytochrome c unfolding

A geometrical model has been developed to study the unfolding of iso-1 cytochrome c. The model draws on the crystallographic data reported for this protein. These data were used to calculate the distance between specific residues in the folded state, and in a sequence of extended states defined by n?=?3, 5, 7, 9, 11, 13, and 15 residue units. Exact calculations carried out for each of the 103 residues in the polypeptide chain demonstrate that different regions of the chain have different unfolding histories. Regions where there is a persistence of compact structures can be identified, and this geometrical characterization is fully consistent with analyses of time-resolved fluorescence energy-transfer (TrFET) data using dansyl-derivatized cysteine side-chain probes at positions 39, 50, 66, 85, and 99. The calculations were carried out assuming that different regions of the polypeptide chain unfold synchronously. To test this assumption, lattice Monte Carlo simulations were performed to study systematically the possible importance of asynchronicity. Calculations show that small departures from synchronous dynamics can arise if displacements of residues in the main body of the chain are much more sluggish than near-terminal residues.     

Low-gravity liquid nonlinear sloshing analysis in a tank under pitching excitation

Under pitch excitation, the sloshing of liquid in circular cylindrical tank includes planar motion, rotary motion and rotary motion inside planar motion. The boundaries between stable motion and unstable motion depend on the radius of the tank, the liquid height, the gravitational intension, the surface tensor and the sloshing damping. In this article, the differential equations of nonlinear sloshing are built first. And by variational principle, the Lagrange function of liquid pressure is constructed in volume integration form. Then the velocity potential function is expanded in series by wave height function at the free surface. The nonlinear equations with kinematics and dynamics free surface boundary conditions through variation are derived. At last, these equations are solved by multiple-scales method. The influence of Bond number on the global stable response of nonlinear liquid sloshing in circular cylinder tank is analyzed in detail. The result indicates that the system's amplitude–frequency response changes from a ‘soft-spring’ to a ‘hard-spring’ in the planar motion with the decreasing of the Bond number, while it changes from a ‘hard-spring’ to a ‘soft-spring’ in the rotary motion. At the same time, jump, lag and other nonlinear phenomena of liquid sloshing are discovered.     

A computational error-assessment of central finite-volume discretizations in large-eddy simulation using a Smagorinsky model

We present a framework for the computational assessment and comparison of large-eddy simulation methods. We apply this to large-eddy simulation of homogeneous isotropic decaying turbulence using a Smagorinsky subgrid model and investigate the combined effect of discretization and model errors at coarse subgrid resolutions. We compare four different central finite-volume methods. These discretization methods arise from the four possible combinations that can be made with a second-order and a fourth-order central scheme for either the convective and the viscous fluxes. By systematically varying the simulation resolution and the Smagorinsky coefficient, we determine parameter regions for which a desired number of flow properties is simultaneously predicted with approximately minimal error. We include both physics-based and mathematics-based error definitions, leading to different error-measures designed to emphasize either errors in large- or in small-scale flow properties. It is shown that the evaluation of simulations based on a single physics-based error may lead to inaccurate perceptions on quality. We demonstrate however that evaluations based on a range of errors yields robust conclusions on accuracy, both for physics-based and mathematics-based errors. Parameter regions where all considered errors are simultaneously near-optimal are referred to as ‘multi-objective optimal’ parameter regions. The effects of discretization errors are particularly important at marginal spatial resolution. Such resolutions reflect local simulation conditions that may also be found in parts of more complex flow simulations. Under these circumstances, the asymptotic error-behavior as expressed by the order of the spatial discretization is no longer characteristic for the total dynamic consequences of discretization errors. We find that the level of overall simulation errors for a second-order central discretization of both the convective and viscous fluxes (the ‘2–2’ method), and the fully fourth-order (‘4–4’) method, is equivalent in their respective ‘multi-objective optimal’ regions. Mixed order methods, i.e. the ‘2–4’ and ‘4–2’ combinations, yield errors which are considerably higher.     

Relaxation phenomena of poly-γ-benzyl-L-glutamate,poly-γ-methyl-L-glutamate,and copoly(γ-methyl-L-glutamate, γ-benzyl-L-glutamate)

Relaxation phenomena of poly-α-amino acids in the solid state have been investigated using poly-γ-benzyl-L-glutamate (PBLG), poly-γ-methyl-L-glutamate (PMLG), and copoly (γ-methyl-L-glutamate, γ-benzyl-L-glutamate) (PMBG) by means of dielectric, dynamic mechanical, NMR, dilatometric, and X-ray diffraction measurements at temperatures between ?196 and 180°C.

Each of the samples exhibits two relaxation regions, one at room temperature (β-relaxation) and the other in the range from ?150 to ?100°C (γ-relaxation). The γ-relaxation is attributed to motion of the side chains with small amplitude. The β-relaxation is due to large-scale motion of the side chain. It has been found that the β-relaxation is well described by the WLF-equation.

The intensity of the X-ray diffraction peak at 2θ = 7° for PBLG increases with increasing temperature, which is similar to results obtained in small-angle X-ray scattering for polymer crystals consisting of two phases, amorphous and crystalline. A break point is observed at 18°C where the specific volumetemperature curve also shows a break point.

It is concluded that the side chains of these polymers are almost amorphous, and that they undergo a glass-like transition while the backbones keep an α-helical conformation.     

Bulk and boundary effects in a one-dimensional water-like fluid

Sites of a one-dimensional lattice may be either vacant or occupied by molecules with two orientational states, a ‘monomer’ state taking up one site and a ‘dimer’ state taking up two sites. There is a nearest-neighbour energy — ε for all molecules and an additional bonding energy — ω for adjacent dimers. Hence low temperatures and pressures favour an open structure with molecules predominantly in the dimer state. Bulk behaviour is investigated by both matrix and combinatorial methods and maxima in density isobars and minima in isothermal compressibility curves are found at certain parameter values. These are anomalous properties similar to those occurring in fluid water.

Boundary effects in a chain with end sites are calculated by matrix methods for several types of boundary condition. The effect on the open structure is measured by the change in the number of dimer-dimer bonds due to the presence of the boundary. For a ‘structure-breaking’ boundary, which forces the adjacent molecule into the monomer state, occupation probabilities near the boundary are compared with bulk values. It is concluded that boundary effects in the fluid are confined to the first few layers of molecules.     

On electromagnetic waves by an accelerated charged particle in medium

We have investigated the effects of acceleration of a charged particle on its Cerenkov emission and ionization-losses. We have considered the accelerated motion of a charged particle in an infinite medium with the acceleration parallel to the direction of its motion. We have used the method of Fourier transforms to solve the Maxwell's equations with appropriate current and charge-densities to find electromagnetic fields and hence the force experienced by the incident charge due to its interaction with the medium (dielectric or plasma). The results obtained are general and applicable to any acceleration. In the approximations of ‘small acceleration’ and ‘small interaction time’, we have solved the wave equations and determined electromagnetic potentials. It is found that the acceleration of the charged particle strongly changes both its ionization-loss and Cerenkov emission.     

Crystallization during polymerization with special reference to synthetic polypeptides

In order to pursue the possibilities of the extended chain crystals formed in the course of polymerization, kinetics of the heterogeneous polymerization of L-and DL-alanine NCA in acetonitrile and the morphologies of the resultant polymers were studied. Electron microscopy revealed that the fibers formed in the beginning of polymerization thickened as the polymerization proceeded and that the growth mechanism of the polypeptide crystals is quite similar to that of polyoxymethylene crystals during the polymerization of trioxane in cyclo-hexane. X-ray diffraction patterns and IR spectroscopy revealed that the growing chain molecules, when they attained a certain degree of polymerization (DP = -3 to 4) beyond which they lost solubility in the system, crystallized into the form of ribbon-like fibers in which molecules, with the β-conformation, were aligned perpendicularly to the fiber axis. As the growing chains attained a critical length by further polymerization, they began to take the α-helical conformation which seemed to be more stable than the β-conformation in the later stages. The crystals grew successively thereafter, taking the α-helical conformation through addition of the monomer molecules onto the reactive chain ends.

The grown polypeptide chains were loosely packed but extended α-helices in the crystals throughout the polymerization. Possible mechanisms are proposed for the nucleation and the subsequent growth of the crystals in the course of polymerization.

The polymerization of N-carboxy anhydrides of glycine and β-alanine has also been studied in acetonitrile with n-butylamine as initiator. As was expected from the similarity of the backbone chain structure to nylons, the polymer precipitated in the form of a spherulite consisting of ribbon-like crystalline units just as in the case of nylons previously reported. The molecules in the ribbon-like crystals were arranged antiparallel, forming a hydrogen-bond sheet.     

On rotational solutions for elliptically excited pendulum

The author considers the planar rotational motion of the mathematical pendulum with its pivot oscillating both vertically and horizontally, so the trajectory of the pivot is an ellipse close to a circle. The analysis is based on the exact rotational solutions in the case of circular pivot trajectory and zero gravity. The conditions for existence and stability of such solutions are derived. Assuming that the amplitudes of excitations are not small while the pivot trajectory has small ellipticity the approximate solutions are found both for high and small linear dampings. Comparison between approximate and numerical solutions is made for different values of the damping parameter.     

Kinematics of the forced and overdamped sine-Gordon soliton gas

Motion of a driven and heavily damped sine-Gordon chain with a low density of kinks and tight coupling between particles is controlled by the nucleation and subsequent annihilation of pairs of kinks and antikinks. We show that in the steady state there are no spatial correlations between kinks or between kinks and antikinks. For a given number of kinks and antikinks all geometrical distributions are equally alike, as in equilibrium. A master equation for the probability distribution for the number of kinks on a finite chain is solved, and substantiates the physical reasoning in previous work. The probability distribution characterizing the spread along the direction of particle motion of a finite chain in equilibrium as well as in the driven overdamped case is derived by simple combinatorial considerations. The spatial spread of a driven chain in the thermodynamic limit does not approach a steady state; a given particle followed in time deviates as t^1/2 from its average forced motion. This result follows from the hydrodynamic equations for the dilute kink gas. Comparison is made with other recent results.     

Aggregation and mesomorphic properties of ‘double-headed’ carbohydrate amphiphiles

Sugar-based amphiphiles, consisting of two sugar head groups and an alkylene chain within the molecules, are synthesized and their aggregation and mesomorphic properties are evaluated. The hydrophilic sugar head groups, constituted with β-D-glucopyranoside units, and the lyophilic alkylene units, are coupled to a glycerol backbone to afford the ‘double-headed’ sugar amphiphiles. Aggregation studies in aqueous solutions provided their critical micellar concentrations and the aggregation numbers. Mesophase characterizations by polarizing optical microscopy and differential scanning calorimetry (DSC) revealed the phase-transition behaviour of these new ‘double-headed’ glycolipids.     

The relation of chemical potentials and reactivity studied by a state path sum

In order to study the relation between chemical potentials and reactivity we divide the interaction region into physically decisive potential ‘boxes’. Each box is considered to be a small interaction region for a virtual chemical reaction with corresponding virtual transition probability amplitudes. These amplitudes are linked together and superimposed in a ‘state path sum’ which relates local potential properties with exact reaction probabilities. The state path sum is carried out by the supermatrix technique of the statistical theory of chain molecules.     

Nucleation of damage centres during ion implantation of silicon

Nucleation of damage centres in single crystal silicon held at room temperature and bombarded in a “random” direction with light ions is not at all times heterogeneous, as has sometimes been assumed. Homogeneous nucleation of interstitial clusters occurs at low ion fluences and this is characterized, for an extremely short period, by a linear dependence of the state of disorder on ion fluence, followed by a longer period during which disorder a (fluence)^1/2. During these periods of ‘nucleation’ and ‘primary growth’ small interstitial clusters behave as unsaturable traps. For higher fluences there is a smooth transfer to a form of damage increase which is not of displacement cascade origin. In this period of ‘secondary growth’ the state of disorder varies linearly with ion fluence, and interstitial clusters behave as nucleation traps.

It is shown how marked effects on the state of disorder due to changes in the mass of the bombarding ion, in the flux of the impinging beam, or in the temperature and impurity content of the bombarded crystal, can be simply traced to an early assistance for or a resistance to the onset of hetero- over homogeneous nucleation.     

高Q腔中原子内态布居对原子平移运动的影响

基于原子作双光子共振跃迁的原子－场缀饰态，讨论了驻波腔场中两能级原子的量子化平移运动与原子内态布居间的相互影响，结果表明原子平移运动敏感地依赖于原子的内态布居，特别当原子处于两内态等权重同相位叠加态时，平移运动呈现出很稳定的特征。     

Recent advances with association models for practical applications

ABSTRACT

Association models like Cubic Plus Association (CPA) equation of state and other Statistical Associating Fluid Theory variants have found widespread use, especially over the recent 30 or so years, and this is not limited anymore to universities and researchers. Industry is beginning slowly to adopt such models for some applications and a few of the association models are now provided by commercial simulators. Association models account explicitly for hydrogen bonding (and other complex) phenomena, and for this reason, they are potentially more useful and more successful than traditional models like cubic equations of state and activity coefficient models. Still, for practical applications, all models are judged by their results and these depend on the availability of experimental data, the number and type of adjustable parameters and the performance of the models for phase equilibria and occasionally also for other properties. We will consider four case studies in this work which, will illustrate some of the capabilities and limitations of these association models in different applications. We will offer a ‘model developer’s’ point of view showing in several cases all stages of model development in order to illustrate what worked, what did not and how it was corrected (when possible). The ‘physics’ and ‘application’ aspects of the models will be in all cases discussed. All results will be shown with the CPA equation of state, although we expect that the overall conclusions will be the same for a wide range of association models.     

Spatial bright–dark soliton steering through waveguide coupling

Analytical and numerical solutions that describe the coupling between bright and dark spatial solitons, located in separate planar waveguides are presented. The analytical theory rests upon a well-known variational approach and it is shown to be in good qualitative/semi-quantitative agreement with the exact numerical solutions of the coupled equations of the problem. By manipulating the soliton ‘masses’, through the input power, interesting trajectories for the solitons can be selected. Indeed, these trajectories are shown to possess behaviour patterns that qualify as the first steps in a design of an all-optical scanner. At all stages, the variational solutions are thoroughly checked by the numerical simulations and found to have excellent predictive qualities.     

Tryptophan Fluorescence Yields and Lifetimes as a Probe of Conformational Changes in Human Glucokinase

Five variants of glucokinase (ATP-D-hexose-6-phosphotransferase, EC 2.7.1.1) including wild type and single Trp mutants with the Trp residue at positions 65, 99, 167 and 257 were prepared. The fluorescence of Trp in all locations studied showed intensity changes when glucose bound, indicating that conformational change occurs globally over the entire protein. While the fluorescence quantum yield changes upon glucose binding, the enzyme’s absorption spectra, emission spectra and fluorescence lifetimes change very little. These results are consistent with the existence of a dark complex for excited state Trp. Addition of glycerol, L-glucose, sucrose, or trehalose increases the binding affinity of glucose to the enzyme and increases fluorescence intensity. The effect of these osmolytes is thought to shift the protein conformation to a condensed, high affinity form. Based upon these results, we consider the nature of quenching of the Trp excited state. Amide groups are known to quench indole fluorescence and amides of the polypeptide chain make interact with excited state Trp in the relatively unstructured, glucose-free enzyme. Also, removal of water around the aromatic ring by addition of glucose substrate or osmolyte may reduce the quenching.