Influence of the hydrogen bond on the N-H stretching frequencies in amino-acids

The spectra of glycine, its addition compounds and other amino-acids exhibit Raman lines in the region from 3250 cm.−1 to 2500 cm.−1 It has been shown that these lines cannot be assigned to N-H...O stretching vibrations, where the N atom has the covalency of three, but to N+-H...O stretching vibration where the N atom has the covalency of four. Using the data obtained with triglycine sulphate which has the largest number of N+-H...O bonds and whose H bond lengths are known, the correlation curve giving the relation between the N+-H...O stretching frequencies and the corresponding H bond lengths has been drawn. Using this correlation curve, the N+-H...O stretching frequencies appearing inα-glycine,γ-glycine, diglycine hydrochloride, diglycine hydrobromide,l-asparagine monohydrate anddl-alanine have been satisfactorily accounted for on the basis of the known hydrogen bond lengths in these substances.

The C=S stretching frequency and the “-N-C=S bands” in the infrared

A correlation of the infrared spectra of thiocarbonyl derivatives based on the literature data has been carried out. Assignments have also been made in some new systems. Since simple alkyl thioketones are unstable, we have prepared thiofenchone in order to obtain a reference C=S stretching frequency. The C=S stretching frequency in thiofenchone has been found around 1180 cm−1 which is in fair agreement with the value calculated for thioformaldehyde. In the case of the thiocarbonyl derivatives where the C=S group is linked to elements other than nitrogen, the stretching frequency is generally found in the region 1025–1225 cm−1. Strong vibrational coupling is operative in the case of the nitrogen containing thiocarbonyl derivatives and three bands seem to consistently appear in the regions 1395–1570 cm−1, 1260–1420 cm−1, 940–1140 cm−1 due to the mixed vibrations. These bands, which may be tentatively designated as the “-N-C=S I, II and III bands”, could be useful in qualitative analysis.

Natural frequencies and modes of tapered skew plates

The vibration of simply supported skew plates having a linear variation in thickness in one direction is considered. Approximate analysis is made by using Lagrange's equations employing the double Fourier sine series in oblique co-ordinates to represent the deflected surface. Natural frequencies are obtained for rhombic plates for several ranges of thickness variation and skew angle. The nodal patterns plotted for a few typical configurations show interesting metamorphoses with variation in thickness and skew angle.

Natural modes of a coupled non-linear system

The natural modes of a non-linear system with two degrees of freedom are investigated. The system, which may contain either hard or soft springs, is shown to possess three modes of vibration one of which does not have any counterpart in the linear theory. The stability analysis indicates the existence of seven different modal stability patterns depending on the values of two parameters of non-linearity.

Anomalous behavior of hydrodynamic modes in the two dimensional shear flow of a granular material

The growth rates of the hydrodynamic modes in the homogeneous sheared state of a granular material are determined by solving the Boltzmann equation. The steady velocity distribution is considered to be the product of the Maxwell Boltzmann distribution and a Hermite polynomial expansion in the velocity components; this form is inserted into them Boltzmann equation and solved to obtain the coeificients of the terms in the expansion. The solution is obtained using an expansion in the parameter epsilon =(1 - e)(1/2), and terms correct to epsilon(4) are retained to obtain an approximate solution; the error due to the neglect of higher terms is estimated at about 5% for e = 0.7. A small perturbation is placed on the distribution function in the form of a Hermite polynomial expansion for the velocity variations and a Fourier expansion in the spatial coordinates: this is inserted into the Boltzmann equation and the growth rate of the Fourier modes is determined. It is found that in the hydrodynamic limit, the growth rates of the hydrodynamic modes in the flow direction have unusual characteristics. The growth rate of the momentum diffusion mode is positive, indicating that density variations are unstable in the limit k--> 0, and the growth rate increases proportional to kslash} k kslash}(2/3) in the limit k --> 0 (in contrast to the k(2) increase in elastic systems), where k is the wave vector in the flow direction. The real and imaginary parts of the growth rate corresponding to the propagating also increase proportional to kslash k kslash(2/3) (in contrast to the k(2) and k increase in elastic systems). The energy mode is damped due to inelastic collisions between particles. The scaling of the growth rates of the hydrodynamic modes with the wave vector I in the gradient direction is similar to that in elastic systems. (C) 2000 Elsevier Science B.V. All rights reserved.

Computer modelling approach to study the modes of binding of alpha- and beta-anomers of D-galactose, D-fucose and D-glucose to L-arabinose-binding protein

The modes of binding of alpha- and beta-anomers of D-galactose, D-fucose and D-glucose to L-arabinose-binding protein (ABP) have been studied by energy minimization using the low resolution (2.4 A) X-ray data of the protein. These studies suggest that these sugars preferentially bind in the alpha-form to ABP, unlike L-arabinose where both alpha- and beta-anomers bind almost equally. The best modes of binding of alpha- and beta-anomers of D-galactose and D-fucose differ slightly in the nature of the possible hydrogen bonds with the protein. The residues Arg 151 and Asn 232 of ABP from bidentate hydrogen bonds with both L-arabinose and D-galactose, but not with D-fucose or D-glucose. However in the case of L-arabinose, Arg 151 forms hydrogen bonds with the hydroxyl group at the C-4 atom and the ring oxygen, whereas in case of D-galactose it forms bonds with the hydroxyl groups at the C-4 and C-6 atoms of the pyranose ring. The calculated conformational energies also predict that D-galactose is a better inhibitor than D-fucose and D-glucose, in agreement with kinetic studies. The weak inhibitor D-glucose binds preferentially to one domain of ABP leading to the formation of a weaker complex. Thus these studies provide information about the most probable binding modes of these sugars and also provide a theoretical explanation for the observed differences in their binding affinities.

Coupled ocean-atmosphere inter-decadal modes in the tropics

Homogencous upper air data for 50 years (1949-1998) from the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis project, sea surface temperatures and sea level pressure are used to bring out the three dimensional structure of two dominant decadal/multi-decadal variations in the tropics. The global three dimensional modes represent generalized forms of inter-decadal modes studied earlier only with surface data. In the vertical, both modes show approximate first baroclinic structures over the tropics. The Walker circulation associated with the multidecadal mode has a wavenumber two structure in the zonal direction. It is shown that the magnitude of major ascending and descending motions associated with the multi-decadal Hadley and Walker circulations, are comparable to those associated with the dominant inter-annual mode. Implications of these large scale global circulations associated with the low frequency oscillations in modulating regional climate on a inter-annual time scale are discussed.

Three-Dimensional Unsteady Flow With Heat and Mass Transfer Over a Continuous Stretching Surface

A numerical solution of the unsteady boundary layer equations under similarity assumptions is obtained. The solution represents the three-dimensional unsteady fluid motion caused by the time-dependent stretching of a flat boundary. It has been shown that a self-similar solution exists when either the rate of stretching is decreasing with time or it is constant. Three different numerical techniques are applied and a comparison is made among them as well as with earlier results. Analysis is made for various situations like deceleration in stretching of the boundary, mass transfer at the surface, saddle and nodal point flows, and the effect of a magnetic field. Both the constant temperature and constant heat flux conditions at the wall have been studied.

Sliding Modes for the Simulation of Mechanical and Electrical Systems Defined by Differential-Algebraic Equations

We offer a technique, motivated by feedback control and specifically sliding mode control, for the simulation of differential-algebraic equations (DAEs) that describe common engineering systems such as constrained multibody mechanical structures and electric networks. Our algorithm exploits the basic results from sliding mode control theory to establish a simulation environment that then requires only the most primitive of numerical solvers. We circumvent the most important requisite for the conventionalsimulation of DAEs: the calculation of a set of consistent initial conditions. Our algorithm, which relies on the enforcement and occurrence of sliding mode, will ensure that the algebraic equation is satisfied by the dynamic system even for inconsistent initial conditions and for all time thereafter. [DOI:10.1115/1.4001904]

Correlations between frequency of infra-red active vibrational modes and copper-oxygen distance in copper oxides. Application to superconductors

The infra-red spectra of a large number of ternary Cu(II) oxides with at least a quasi square-planar coordination of oxygen around the copper ions have been studied. The frequency of the bands with the highest frequency,v max, is found to correlate extremely well with the shortest Cu–O distance.v max increases at an impressive rate of sim20 cm–1 per 0.01 Å when the Cu–O distance becomes less than 1.97 Å, which is the Cu2+–O2– distance in square-planar CuO4 complexes as obtained from empirical ionic radii considerations. The marked sensitivity may be used as a ldquotitrationrdquo procedure not only to assign bands but also to obtain diagnostic information about local coordination in compounds derived, for example, from the YBa2Cu3O7–d structure such as LaCaBaCu3O7–d . The only example where this correlation fails is in the two-layer non-superconducting oxides derived from La2(Ca, Sr)Cu2O6. The significance of this result is discussed. The marked dependence of frequency on the bond-distance is qualitatively examined in terms of an increased electron-phonon coupling to account for the observed tendency of the superconducting transition temperature to go through a maximum as the average basal plane Cu–O distance is decreased.

Modes of binding of guanosine monophosphates to ribonuclease T1 - A computer modelling study

Computer-modelling studies on the modes of binding of the three guanosine monophosphate inhibitors 2'-GMP, 3'-GMP, and 5'-GMP to ribonuclease (RNase) T1 have been carried out by energy minimization in Cartesian-coordinate space. The inhibitory power was found to decrease in the order 2'-GMP > 3'-GMP > 5'-GMP in agreement with the experimental observations. The ribose moiety was found to form hydrogen bonds with the protein in all the enzyme-inhibitor complexes, indicating that it contributes to the binding energy and does not merely act as a spacer between the base and the phosphate moieties as suggested earlier. 2'-GMP and 5'-GMP bind to RNase T1 in either of the two ribose puckered forms (with C3'-endo more favoured over the C2'-endo) and 3'-GMP binds to RNase T1 predominantly in C3'-endo form. The catalytically important residue His-92 was found to form hydrogen bond with the phosphate moiety in all the enzyme-inhibitor complexes, indicating that this residue may serve as a general acid group during catalysis. Such an interaction was not found in either X-ray or two-dimensional NMR studies.

Solvation dynamics in liquid water. A novel interplay between librational and diffusive modes

A microscopic calculation of the solvation dynamics of an ion in liquid water is presented. The calculated solvation time correlation function shows an ultrafast Gaussian decay which carries about 70%–90% of the strength followed by a biexponential decay with time constants equal to 250 fs and 1 ps. These results are in excellent agreement with the computer simulations of Maroncelli and Fleming and also with the experimental findings of Barbara and Jarzeba. In addition, we find that both the rotational librations and the intermolecular translational vibrational modes of water contribute significantly to the initial Gaussian decay.

Unsteady three-dimensional boundary layer flow due to a stretching surface

In this numerical study, the unsteady laminar incompressible boundary-layer flow over a continuously stretching surface has been investigated when the velocity of the stretching surface varies arbitrarily with time. Both the nodal and the saddle point regions of flow have been considered for the analysis. Also, constant wall temperature/concentration and constant heat/mass flux at the stretching surface have been taken into account. The quasilinearisation method with an implicit finite-difference scheme is used in the nodal point region (0 less-than-or-equal-to c less-than-or-equal-to 1) where c denotes the stretching ratio. This method fails in the saddle point region (-1 less-than-or-equal-to c less-than-or-equal-to 0) due to the occurrence of reverse flow in the y-component of velocity. In order to overcome this difficulty, the method of parametric differentiation with an implicit finite-difference scheme is used, where the values at c = 0 are taken as starting values. Results have been obtained for the stretching velocities which are accelerating and decelerating with time. Results show that the skin friction, the heat transfer and the mass transfer parameters respond significantly to the time dependent stretching velocities. Suction (A > 0) is found to be an important parameter in obtaining convergent solution in the case of the saddle point region of flow. The Prandtl number and the Schmidt number strongly affect the heat and mass transfer of the diffusing species, respectively.

Electron transfer reaction in the marcus inverted region: role of high frequency vibrational modes

A theoretical study of the dynamics of photo-electron transfer reactions in the Marcus inverted regime is presented. This study is motivated partly by the recent proposal of Barbara et al. (J. Phys. Chem. 96, 3728, 1991) that a minimal model of an electron transfer reaction should consist of a polar solvent mode (X), a low frequency vibrational mode (Q) and one high frequency mode (q). Interplay between these modes may be responsible for the crossover observed in the dynamics from a solvent controlled to a vibrational controlled electron transfer. The following results have been obtained. (i) In the case of slowly relaxing solvents, the proximity of the point of excitation to an effective sink on the excited surface is critical in determining the decay of the reactant population. This is because the Franck-Condon overlap between the reactant ground and the product excited states decreases rapidly with increase in the quantum number of the product vibrational state. (ii) Non-exponential solvation dynamics has an important effect in determining the rates of electron transfer. Especially, a biphasic solvation and a large coupling between the reactant and the product states both may be needed to explain the experimental results. ©1996 American Institute of Physics

Modes of binding of 2'-AMP to RNase T1. A computer modeling study

The modes of binding of adenosine 2'-monophosphate (2'-AMP) to the enzyme ribonuclease (RNase) T1 were determined by computer modelling studies. The phosphate moiety of 2'-AMP binds at the primary phosphate binding site. However, adenine can occupy two distinct sites--(1) The primary base binding site where the guanine of 2'-GMP binds and (2) The subsite close to the N1 subsite for the base on the 3'-side of guanine in a guanyl dinucleotide. The minimum energy conformers corresponding to the two modes of binding of 2'-AMP to RNase T1 were found to be of nearly the same energy implying that in solution 2'-AMP binds to the enzyme in both modes. The conformation of the inhibitor and the predicted hydrogen bonding scheme for the RNase T1-2'-AMP complex in the second binding mode (S) agrees well with the reported x-ray crystallographic study. The existence of the first mode of binding explains the experimental observations that RNase T1 catalyses the hydrolysis of phosphodiester bonds adjacent to adenosine at high enzyme concentrations. A comparison of the interactions of 2'-AMP and 2'-GMP with RNase T1 reveals that Glu58 and Asn98 at the phosphate binding site and Glu46 at the base binding site preferentially stabilise the enzyme-2'-GMP complex.