A new look at the harmonic oscillator problem in a finite-dimensional Hilbert space

In this Letter some basic properties of a truncated oscillator are studied. By using finite-dimensional representation matrices of the truncated oscillator we construct new parasupersymmetric schemes and remark on their relevance to the transition operators of the non-interacting N-level system endowed with bosonic modes.     

Nonet symmetry,anomalous Ward identities and meson-gluonium mixing

TheSU(3) flavour structure of ι(1460) is exploited to seek consistency between vector meson dominance and anomalous Ward identities. Our analysis shows that a minimum of 10 to 20% breaking in nonet symmetry is necessary to get an overall fit with the radiative rates of low-lying η and η′.     

Dynamics of polar solvation: Route to single exponential relaxation via translational diffusion

A microscopic theoretical calculation of time-dependent solvation energy shows that the solvation of an ion or a dipole is dominated by a single relaxation time if the translational contribution to relaxation is significant. Contribution No. 545 from the Solid State and Structural Chemistry Unit     

Orientation-dependent potential of mean force for protein folding

We present a solvent-implicit minimalistic model potential among the amino acid residues of proteins, obtained by using the known native structures [deposited in the Protein Data Bank (PDB)]. In this model, the amino acid side chains are represented by a single ellipsoidal site, defined by the group of atoms about the center of mass of the side chain. These ellipsoidal sites interact with other sites through an orientation-dependent interaction potential which we construct in the following fashion. First, the site-site potential of mean force (PMF) between heavy atoms is calculated [following F. Melo and E. Feytsman, J. Mol. Biol. 267, 207 (1997)] from statistics of their distance separation obtained from crystal structures. These site-site potentials are then used to calculate the distance and the orientation-dependent potential between side chains of all the amino acid residues (AAR). The distance and orientation dependencies show several interesting results. For example, we find that the PMF between two hydrophobic AARs, such as phenylalanine, is strongly attractive at short distances (after the obvious repulsive region at very short separation) and is characterized by a deep minimum, for specific orientations. For the interaction between two hydrophilic AARs, such a deep minimum is absent and in addition, the potential interestingly reveals the combined effect of polar (charge) and hydrophobic interactions among some of these AARs. The effectiveness of our potential has been tested by calculating the Z-scores for a large set of proteins. The calculated Z-scores show high negative values for most of them, signifying the success of the potential to identify the native structure from among a large number of its decoy states.     

Hydration layer of a cationic micelle, C(10)TAB: structure, rigidity, slow reorientation, hydrogen bond lifetime, and solvation dynamics

We report a theoretical study of the structure and dynamics of the water layer (the hydration layer) present at the surface of the cationic micelle decyltrimethylammonium bromide (DeTAB) by using atomistic molecular dynamics simulations. The simulated micelle consisted of 47 surfactant molecules (and an equal number of bromide ions), in good agreement with the pioneering light scattering experiments by Debye which found an aggregation number of 50. In this micelle, three partially positively charged methyl groups of each surfactant headgroup face the surrounding water. The nature of the cationic micellar surface is found to play an important role in determining the arrangement of water which is quite different from that in the bulk or on the surface of an anionic micelle, like cesium perfluorooctanoate. Water molecules present in the hydration layer are found to be preferentially distributed in the region between the three partially charged methyl headgroups. It is found that both the translational and rotational motions of water exhibit appreciably slower dynamics in the layer than those in the bulk. The solvation time correlation function (TCF) of bromide ions exhibits a long time component which is found to originate primarily from the interaction of the probe with the micellar headgroups. Thus, the decay of the solvation TCF is controlled largely by the residence time of the probe in the surface. The residence time distribution of the water molecules also exhibits a slow time component. We also calculate the collective number density fluctuation in the layer and find a prominent slow component compared to the similar quantity in the bulk. This slow component demonstrates that water structure in the hydration layer is more rigid than that in the bulk. These results demonstrate that the slow dynamics of hydration layer water is generic to macromolecular surfaces of either polarity.