A Gaussian network model study suggests that structural fluctuations are higher for inactive states than active states of protein kinases

We performed Gaussian network model based normal mode analysis of 3-dimensional structures of multiple active and inactive forms of protein kinases. In 14 different kinases, a more number of residues (1095) show higher structural fluctuations in inactive states than those in active states (525), suggesting that, in general, mobility of inactive states is higher than active states. This statistically significant difference is consistent with higher crystallographic B-factors and conformational energies for inactive than active states, suggesting lower stability of inactive forms. Only a small number of inactive conformations with the DFG motif in the ``in'' state were found to have fluctuation magnitudes comparable to the active conformation. Therefore our study reports for the first time, intrinsic higher structural fluctuation for almost all inactive conformations compared to the active forms. Regions with higher fluctuations in the inactive states are often localized to the aC-helix, aG-helix and activation loop which are involved in the regulation and/or in structural transitions between active and inactive states. Further analysis of 476 kinase structures involved in interactions with another domain/protein showed that many of the regions with higher inactive-state fluctuation correspond to contact interfaces. We also performed extensive GNM analysis of (i) insulin receptor kinase bound to another protein and (ii) holo and apo forms of active and inactive conformations followed by multi-factor analysis of variance. We conclude that binding of small molecules or other domains/proteins reduce the extent of fluctuation irrespective of active or inactive forms. Finally, we show that the perceived fluctuations serve as a useful input to predict the functional state of a kinase.

Dynamics of the chemical bond: inter- and intra-molecular hydrogen bond

In this discussion, we show that a static definition of a `bond' is not viable by looking at a few examples for both inter-and intra-molecular hydrogen bonding. This follows from our earlier work (Goswami and Arunan, Phys. Chem. Chem. Phys. 2009, 11, 8974) which showed a practical way to differentiate `hydrogen bonding' from `van der Waals interaction'. We report results from ab initio and atoms in molecules theoretical calculations for a series of Rg center dot center dot center dot HX complexes (Rg = He/Ne/Ar and X = F/Cl/Br) and ethane-1,2-diol. Results for the Rg center dot center dot center dot HX/DX complexes show that Rg center dot center dot center dot DX could have a `deuterium bond' even when Rg center dot center dot center dot HX is not `hydrogen bonded', according to the practical criterion given by Goswami and Arunan. Results for ethane-1,2-diol show that an `intra-molecular hydrogen bond' can appear during a normal mode vibration which is dominated by the O center dot center dot center dot O stretching, though a `bond' is not found in the equilibrium structure. This dynamical `bond' formation may nevertheless be important in ensuring the continuity of electron density across a molecule. In the former case, a vibration `breaks' an existing bond and in the later case, a vibration leads to `bond' formation. In both cases, the molecule/complex stays bound irrespective of what happens to this `hydrogen bond'. Both these cases push the borders on the recent IUPAC recommendation on hydrogen bonding (Arunan et al. Pure. Appl. Chem. 2011, 83 1637) and justify the inclusive nature of the definition.

Ляпунов方法在充液腔体旋转运动稳定问题中的应用

<正> 处理连续系统的运动稳定问题通常有二种办法:一种为简正模方法(Normal mode approuch);另一种为整体法(Global approuch),包括直接方法和能量法。前一方法要和后者等价必须假定本征模是完全的(个别情形能证明)。在最近三十年来,直接方法推广到连续系统已取得很大进展。在文献[3]中,我们应用简正模方法处理了充液腔体整体旋转运动的稳定问题。现有的

Tools for the study of dynamical spacetimes

This thesis covers a range of topics in numerical and analytical relativity, centered around introducing tools and methodologies for the study of dynamical spacetimes. The scope of the studies is limited to classical (as opposed to quantum) vacuum spacetimes described by Einstein's general theory of relativity. The numerical works presented here are carried out within the Spectral Einstein Code (SpEC) infrastructure, while analytical calculations extensively utilize Wolfram's Mathematica program.

We begin by examining highly dynamical spacetimes such as binary black hole mergers, which can be investigated using numerical simulations. However, there are difficulties in interpreting the output of such simulations. One difficulty stems from the lack of a canonical coordinate system (henceforth referred to as gauge freedom) and tetrad, against which quantities such as Newman-Penrose Psi_4 (usually interpreted as the gravitational wave part of curvature) should be measured. We tackle this problem in Chapter 2 by introducing a set of geometrically motivated coordinates that are independent of the simulation gauge choice, as well as a quasi-Kinnersley tetrad, also invariant under gauge changes in addition to being optimally suited to the task of gravitational wave extraction.

Another difficulty arises from the need to condense the overwhelming amount of data generated by the numerical simulations. In order to extract physical information in a succinct and transparent manner, one may define a version of gravitational field lines and field strength using spatial projections of the Weyl curvature tensor. Introduction, investigation and utilization of these quantities will constitute the main content in Chapters 3 through 6.

For the last two chapters, we turn to the analytical study of a simpler dynamical spacetime, namely a perturbed Kerr black hole. We will introduce in Chapter 7 a new analytical approximation to the quasi-normal mode (QNM) frequencies, and relate various properties of these modes to wave packets traveling on unstable photon orbits around the black hole. In Chapter 8, we study a bifurcation in the QNM spectrum as the spin of the black hole a approaches extremality.

Time-dependent monoenergetic neutron transport in two adjacent semi-infinite media

An exact solution to the monoenergetic Boltzmann equation is obtained for the case of a plane isotropic burst of neutrons introduced at the interface separating two adjacent, dissimilar, semi-infinite media. The method of solution used is to remove the time dependence by a Laplace transformation, solve the transformed equation by the normal mode expansion method, and then invert to recover the time dependence.

The general result is expressed as a sum of definite, multiple integrals, one of which contains the uncollided wave of neutrons originating at the source plane. It is possible to obtain a simplified form for the solution at the interface, and certain numerical calculations are made there.

The interface flux in two adjacent moderators is calculated and plotted as a function of time for several moderator materials. For each case it is found that the flux decay curve has an asymptotic slope given accurately by diffusion theory. Furthermore, the interface current is observed to change directions when the scattering and absorption cross sections of the two moderator materials are related in a certain manner. More specifically, the reflection process in two adjacent moderators appears to depend initially on the scattering properties and for long times on the absorption properties of the media.

This analysis contains both the single infinite and semi-infinite medium problems as special cases. The results in these two special cases provide a check on the accuracy of the general solution since they agree with solutions of these problems obtained by separate analyses.

Non-Linear Scale Interactions in a Forced Turbulent Boundary Layer

This thesis explores the dynamics of scale interactions in a turbulent boundary layer through a forcing-response type experimental study. An emphasis is placed on the analysis of triadic wavenumber interactions since the governing Navier-Stokes equations for the flow necessitate a direct coupling between triadically consist scales. Two sets of experiments were performed in which deterministic disturbances were introduced into the flow using a spatially-impulsive dynamic wall perturbation. Hotwire anemometry was employed to measure the downstream turbulent velocity and study the flow response to the external forcing. In the first set of experiments, which were based on a recent investigation of dynamic forcing effects in a turbulent boundary layer, a 2D (spanwise constant) spatio-temporal normal mode was excited in the flow; the streamwise length and time scales of the synthetic mode roughly correspond to the very-large-scale-motions (VLSM) found naturally in canonical flows. Correlation studies between the large- and small-scale velocity signals reveal an alteration of the natural phase relations between scales by the synthetic mode. In particular, a strong phase-locking or organizing effect is seen on directly coupled small-scales through triadic interactions. Having characterized the bulk influence of a single energetic mode on the flow dynamics, a second set of experiments aimed at isolating specific triadic interactions was performed. Two distinct 2D large-scale normal modes were excited in the flow, and the response at the corresponding sum and difference wavenumbers was isolated from the turbulent signals. Results from this experiment serve as an unique demonstration of direct non-linear interactions in a fully turbulent wall-bounded flow, and allow for examination of phase relationships involving specific interacting scales. A direct connection is also made to the Navier-Stokes resolvent operator framework developed in recent literature. Results and analysis from the present work offer insights into the dynamical structure of wall turbulence, and have interesting implications for design of practical turbulence manipulation or control strategies.

Insights into mechanism kinematics for protein motion simulation

Background: The high demanding computational requirements necessary to carry out protein motion simulations make it difficult to obtain information related to protein motion. On the one hand, molecular dynamics simulation requires huge computational resources to achieve satisfactory motion simulations. On the other hand, less accurate procedures such as interpolation methods, do not generate realistic morphs from the kinematic point of view. Analyzing a protein's movement is very similar to serial robots; thus, it is possible to treat the protein chain as a serial mechanism composed of rotational degrees of freedom. Recently, based on this hypothesis, new methodologies have arisen, based on mechanism and robot kinematics, to simulate protein motion. Probabilistic roadmap method, which discretizes the protein configurational space against a scoring function, or the kinetostatic compliance method that minimizes the torques that appear in bonds, aim to simulate protein motion with a reduced computational cost. Results: In this paper a new viewpoint for protein motion simulation, based on mechanism kinematics is presented. The paper describes a set of methodologies, combining different techniques such as structure normalization normalization processes, simulation algorithms and secondary structure detection procedures. The combination of all these procedures allows to obtain kinematic morphs of proteins achieving a very good computational cost-error rate, while maintaining the biological meaning of the obtained structures and the kinematic viability of the obtained motion. Conclusions: The procedure presented in this paper, implements different modules to perform the simulation of the conformational change suffered by a protein when exerting its function. The combination of a main simulation procedure assisted by a secondary structure process, and a side chain orientation strategy, allows to obtain a fast and reliable simulations of protein motion.

Non-modal instabilities of two-dimensional disturbances in plane Couette flow of a power-law fluid

Instabilities of fluid flows have traditionally been investigated by normal mode analysis, i.e. by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In this paper we study the instabilities of two-dimensional Couette flow of a polymeric fluid in the framework of non-modal stability theory rather than normal mode analysis. A power-law model is used to describe the polymeric liquid. We focus on the response to external excitations and initial conditions by examining the pseudospectra structures and the transient energy growths. For both Newtonian and non-Newtonian flows, the results show that there can be a rather large transient growth even though the linear operator of Couette flow has no unstable eigenvalue. The effects of non-Newtonian viscosity on the transient behaviors are examined in this study. The results show that the "shear-thinning/shear-thickening" effect increases/decreases the amplitude of responses to external excitations and initial conditions. (C) 2010 Elsevier B.V. All rights reserved.

Instabilities and transient behaviors of a liquid film flowing down a porous inclined plane

The nonmodal linear stability of a falling film over a porous inclined plane has been investigated. The base flow is driven by gravity. We use Darcy's law to describe the flow in the porous medium. A simplified one-sided model is used to describe the fluid flow. In this model, the influence of the porous layer on the flow in the film can be identified by a parameter beta. The instabilities of a falling film have traditionally been investigated by linearizing the governing equations and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In the present paper, we have studied the linear stability of three-dimensional disturbances using the nonmodal stability theory. Particular attentions are paid to the transient behavior rather than the long time behavior of eigenmodes predicted by traditional normal mode analysis. The transient behaviors of the response to external excitations and the response to initial conditions are studied by examining the pseudospectral structures and the energy growth function G(t) Before we study the nonmodal stability of the system, we extend the results of long-wave analysis in previous works by examining the linear stabilities for streamwise and spanwise disturbances. Results show that the critical conditions of both the surface mode and the shear mode instabilities are dependent on beta for streamwise disturbances. However, the spanwise disturbances have no unstable eigenvalue. 2010 American Institute of Physics. [doi:10.1063/1.3455503]

Sequential deprotonation of meso-(p-hydroxyphenyl)porphyrins in DMF: From hyperporphyrins to sodium porphyrin complexes

Sequential deprotonations of meso-(p-hydroxyphenyl)porphyrins (p-OHTPPH2) in DMF + H2O (V/V = 1:1) mixture have been verified to result in the appearance of hyperporphyrin spectra. However, when the deprotonations of these p-OHTPPH2 are carried out in DMF, the spectral changes differ considerably from those in the mixture mentioned above. At low [OH-], the optical spectra in the visible region are still considered to have characteristics of hyperporphyrin spectra. Further deprotonation at much higher basicity makes the optical spectra form three-banded spectra similar to those in the acidic solution. To clarify the molecular origins of these changes, UV-vis, resonance Raman (RR), proton nuclear magnetic resonance (H-1 NMR) experiments are carried out. Our data give evidence that p-OHTPPH2 in DMF can be further deprotonated of pyrrolic-H by higher concentrated NaOH, due to an aprotic medium like DMF effectively weakening the basicity of the porphyrin relative to that of the NaOH, and coordinates with two sodium ions (except the sodium ions that interact with the peripherial phenoxide anions) to form the sodium complexes of p-OHTPPH2 (Na2P, to lay a strong emphasis on the sodium ions that coordinate with the central nitrogen atom), which can be regarded as the porphyrin anions being perturbed by the sodium cations due to their highly ionic character.

Vibronic transitions and site substitution of Eu2+ and codoped ions in KMgF3 : Eu-X (X=Ce, Cr, Gd, Cu) system

The high-resolution emission spectra of KMgF3 : Eu and KMgF3 : Eu-X(X = Ce, Cr, Gd, Cu) single crystals were measured at 300 and 77 K. The vibronic side bands of Eu2+ were characterized and an assignment of the normal mode frequencies to particular vibrations has been made. The correlation between the vibronic frequencies of Eu2+ and the site substitution of other co-dopcd ions was first found. The relationship between vibronic intensity of Eu2+ and other doped ions concentration showed that Cr3+, Gd3+ ions competed K+ sites with Eu2+ ions. Ce3+ and Eu3+ occurred the electron transference. The introduction of Cu+ made for Eu2+ substuting for K+ sites.

Effect of low-frequency Rossby wave on thermal structure of the upper southwestern tropical Indian Ocean

We investigate the influence of low-frequency Rossby waves on the thermal structure of the upper southwestern tropical Indian Ocean (SWTIO) using Argo profiles, satellite altimetric data, sea surface temperature, wind field data and the theory of linear vertical normal mode decomposition. Our results show that the SWTIO is generally dominated by the first baroclinic mode motion. As strong downwelling Rossby waves reach the SWTIO, the contribution of the second baroclinic mode motion in this region can be increased mainly because of the reduction in the vertical stratification of the upper layer above thermocline, and the enhancement in the vertical stratification of the lower layer under thermocline also contributes to it. The vertical displacement of each isothermal is enlarged and the thermal structure of the upper level is modulated, which is indicative of strong vertical mixing. However, the cold Rossby waves increase the vertical stratification of the upper level, restricting the variability related to the second baroclinic mode. On the other hand, during decaying phase of warm Rossby waves, Ekman upwelling and advection processes associated with the surface cyclonic wind circulation can restrain the downwelling processes, carrying the relatively colder water to the near-surface, which results in an out-of-phase phenomenon between sea surface temperature anomaly (SSTA) and sea surface height anomaly (SSHA) in the SWTIO.

A vibrational spectroscopic investigation of rhodanine and its derivatives in the solid state

Raman and infrared spectra are reported for rhodanine, 3-aminorhodanine and 3-methylrhodanine in the solid state. Comparisons of the spectra of non-deuterated/deuterated species facilitate discrimination of the bands associated with N-H, NH2, CH2 and CH3 vibrations. DFT calculations of structures and vibrational spectra of isolated gas-phase molecules, at the B3-LYP/cc-pVTZ and B3-PW91/cc-pVTZ level, enable normal coordinate analyses in terms of potential energy distributions for each vibrational normal mode. The cis amide I mode of rhodanine is associated with bands at ~ 1713 and 1779 cm-1, whereas a Raman and IR band at ~ 1457 cm-1 is assigned to the amide II mode. The thioamide II and III modes of rhodanine, 3-aminorhodanine and 3-methylrhodanine are observed at 1176 and 1066/1078; 1158 and 1044; 1107 and 984 cm-1 in the Raman and at 1187 and 1083; 1179 and 1074; 1116 and 983 cm-1 in the IR spectra, respectively.

On how structural model variability influence transonic aeroelasticity stability.

This paper considers the ways in which structural model parameter variability can in?uence aeroelastic stability. Previous work on formulating the stability calculation (with the Euler equations providing the aerodynamic predictions) is exploited to use Monte Carlo, Interval and Perturbation calculations to allow this question to be investigated. Three routes are identi?ed. The ?rst involves variable normal mode frequencies only. The second involves normal mode frequencies and mode shapes. Finally, the third, in addition to normal mode frequencies and mode shapes, also includes their in?uence on the static equilibrium. Previous work has suggested only considering route 1, which allows signi?cant gains in computational e?ciency if reduced order models can be built for the aerodynamics. However, results in the current paper show that neglecting route 2 can give misleading results for the ?utter onset prediction.

How Structural Model Variability Influences Transonic Aeroelastic Stability

This paper considers the ways in which structural model parameter variability can influence aeroelastic stability. Previous work on formulating the stability calculation (with the Euler equations providing the aerodynamic predictions) is exploited to use Monte Carlo, interval, and perturbation calculations to allow this question to be investigated. Three routes are identified. The first involves variable normal-mode frequencies only. The second involves normal-mode frequencies and shapes. Finally, the third, in addition to normal-mode frequencies and shapes, also includes their influence on the static equilibrium. Previous work has suggested only considering the first route, which allows significant gains in computational efficiency if reduced-order models can be built for the aerodynamics. However, results in the current paper show that neglecting the mode-shape variation can give misleading results for the flutter-onset prediction, complicating the development of reduced aerodynamic models for variability analysis.