Non-periodic tilings in 2-dimensions: 4- and 7-fold symmetries

By inflating basic rhombuses, with a self-similarity principle, non-periodic tiling of 2-d planes is possible with 4, 5, 6, 7, 8, … -fold symmetries. As examples, non-periodic tilings with crystallographically allowed 4-fold symmetry and crystallographically forbidden 7-fold symmetry are presented in detail. The computed diffraction patterns of these tilings are also discussed.

A Vicarious One-Pot Transformation of a Fluorocyclitol to a Polycyclitol: Observation of a Formal 4-Fold Axial-Equatorial Epimerization on a Conformationally Locked Scaffold

A conformationally locked fluoropentol undergoes an interesting transformation to (trans,anti,trans,anti,trans)-perhydro-2,3,4a,6,7,8a-naphthalenehexol essentially under conditions of base-induced transesterification. The proposed rationale for the observed metamorphosis involves a nucleophilic displacement of fluoride, and subsequent stereo- and regioselective anti-Furst-Plattner-type ring-opening of the epoxide thus formed.

Five-fold quasiperiodic tilings generated by inflated rhombuses with identical boundaries: possible application to the growth of quasicrystals

In order to generate normal Penrose tilings by inflation/deflation, decisions have to be made regarding the matching of the rhombuses/tilings with their neighbours. We show here that this decision-making problem can be avoided by adopting a deflation/inflation procedure which uses the decorated rhombuses with identical boundaries. The procedure enables both kinds of inflated rhombuses to match in any orientation along their edges. The tilings so generated are quasiperiodic. These structures appear to have a close relationship with the growth mechanism of quasicrystals.

Integrability and singularity structure of predator‐prey system

The ‘‘extended’’ ARS (Ablowitz, Ramani, and Segur) algorithm is introduced to characterize a dynamical system as Painlevé or otherwise; to that end, it is required that the formal series—the Laurent series, logarithmic, algebraic psi series about a movable singularity—are shown to converge in the deleted neighborhood of the singularity. The determinations thus obtained are compared with those following from the α method of Painlevé. An attempt is made to relate the structure of solutions about a movable singularity with that of first integrals (when they exist). All these ideas are illustrated by a comprehensive analysis of the general two‐dimensional predator‐prey system.

Influence of glycosidic linkage on the nature of carbohydrate binding in beta-prism I fold lectins: An X-ray and molecular dynamics investigation on banana lectin-carbohydrate complexes

The three crystal structures reported here provide details of the interactions of mannose and the mannosyl-alpha-1,3-mannose component of a pentamannose with banana lectin and evidence for the binding of glucosyl-alpha-1,2-glucose to the lectin. The known structures involving the lectin include a complex with glucosyl-beta-1,3-glucose. Modeling studies on the three disaccharide complexes with the reducing end and the nonreducing end at the primary binding site are also provided here. The results of the Xray and modeling studies show that the disaccharides with an alpha-1,3 linkage prefer to have the nonreducing end at the primary binding site, whereas the reducing end is preferred at the site when the linkage is beta-1,3 in mannose/glucose-specific beta-prism I fold lectins. In the corresponding galactose-specific lectins, however, alpha-1,3-linked disaccharides cannot bind the lectin with the nonreducing end at the primary binding site on account of steric clashes with an aromatic residue that occurs only when the lectin is galactose-specific. Molecular dynamics simulations based on the known structures involving banana lectin enrich the information on lectin-carbohydrate interactions obtained from crystal structures. They demonstrate that conformational selection as well as induced fit operate when carbohydrates bind to banana lectin.

Singularity structure and chaotic behavior of the homopolar disk dynamo

We study in great detail a system of three first-order ordinary differential equations describing a homopolar disk dynamo (HDD). This system displays a large variety of behaviors, both regular and chaotic. Existence of periodic solutions is proved for certain ranges of parameters. Stability criteria for periodic solutions are given. The nonintegrability aspects of the HDD system are studied by investigating analytically the singularity structure of the system in the complex domain. Coexisting attractors (including period-doubling sequence) and coexisting strange attractors appear in some parametric regimes. The gluing of strange attractors and the ungluing of a strange attractor are also shown to occur. A period of bifurcation leading to chaos, not observed for other chaotic systems, is shown to characterize the chaotic behavior in some parametric ranges. The limiting case of the Lorenz system is also studied and is related to HDD.

Nonequilibrium-phase transition and 'specific-heat' singularity in the kinetic Ising model: A Monte Carlo study

The nonequilibrium-phase transition has been studied by Monte Carlo simulation in a ferromagnetically interacting (nearest-neighbour) kinetic Ising model in presence of a sinusoidally oscillating magnetic field. The ('specific-heat') temperature derivative of energies (averaged over a full cycle of the oscillating field) diverge near the dynamic transition point.

Nonequilibrium phase transition in the kinetic Ising model: Critical slowing down and the specific-heat singularity

The nonequilibrium dynamic phase transition, in the kinetic Ising model in the presence of an oscillating magnetic field has been studied both by Monte Carlo simulation and by solving numerically the mean-field dynamic equation of motion for the average magnetization. In both cases, the Debye ''relaxation'' behavior of the dynamic order parameter has been observed and the ''relaxation time'' is found to diverge near the dynamic transition point. The Debye relaxation of the dynamic order parameter and the power law divergence of the relaxation time have been obtained from a very approximate solution of the mean-field dynamic equation. The temperature variation of appropriately defined ''specific heat'' is studied by the Monte Carlo simulation near the transition point. The specific heat has been observed to diverge near the dynamic transition point.

Singularity structure of third-order dynamical systems .2

The singularity structure of the solutions of a general third-order system, with polynomial right-hand sides of degree less than or equal to two, is studied about a movable singular point, An algorithm for transforming the given third-order system to a third-order Briot-Bouquet system is presented, The dominant behavior of a solution of the given system near a movable singularity is used to construct a transformation that changes the given system directly to a third-order Briot-Bouquet system. The results of Horn for the third-order Briot-Bouquet system are exploited to give the complete form of the series solutions of the given third-order system; convergence of these series in a deleted neighborhood of the singularity is ensured, This algorithm is used to study the singularity structure of the solutions of the Lorenz system, the Rikitake system, the three-wave interaction problem, the Rabinovich system, the Lotka-Volterra system, and the May-Leonard system for different sets of parameter values. The proposed approach goes far beyond the ARS algorithm.

Motion of a charged particle in superposed Heliotron and biconical cusp fields

We have studied the behaviour of a charged particle in an axially symmetric magnetic field having a neutral point, so as to find a possibility of confining a charged particle in a thermonuclear device. In order to study the motion we have reduced a three-dimensional motion to a two-dimensional one by introducing a fictitious potential. Following Schmidt we have classified the motion, as an ‘off-axis motion’ and ‘encircling motion’ depending on the behaviour of this potential. We see that the particle performs a hybrid type of motion in the negative z-axis, i.e. at some instant it is in ‘off-axis motion’ while at another instant it is in ‘encircling motion’. We have also solved the equation of motion numerically and the graphs of the particle trajectory verify our analysis. We find that in most of the cases the particle is contained. The magnetic moment is found to be moderately adiabatic.

Anomalous Temperature dependence of Fermi-edge Singularity in Modulation-doped AlGaAs/InGaAs/GaAs hetero-structures

The temperature and power dependence of Fermi-edge singularity (FES) in high-density two-dimensional electron gas, specific to pseudomorphic AlxGa1-xAs/InyGa1-yAs/GaAs heterostructures is studied by photoluminescence (PL). In all these structures, there are two prominent transitions E11 and E21 considered to be the result of electron-hole recombination from first and second electron sub-bands with that of first heavy-hole sub-band. FES is observed approximately 5 -10 meV below the E21 transition. At 4.2 K, FES appears as a lower energy shoulder to the E21 transition. The PL intensity of all the three transitions E11, FES and E21 grows linearly with excitation power. However, we observe anomalous behavior of FES with temperature. While PL intensity of E11 and E21 decrease with increasing temperature, FES transition becomes stronger initially and then quenches-off slowly (till 40K). Though it appears as a distinct peak at about 20 K, its maximum is around 7 - 13 K.

Unique Utilization of a Phosphoprotein Phosphatase Fold by a Mammalian Phosphodiesterase Associated with WAGR Syndrome

Metallophosphoesterase-domain-containing protein 2 (MPPED2) is a highly evolutionarily conserved protein with orthologs found from worms to humans. The human MPPED2 gene is found in a region of chromosome 11 that is deleted in patients with WAGR (Wilms tumor, aniridia, genitourinary anomalies, and mental retardation) syndrome, and MPPED2 may function as a tumor suppressor. However, the precise cellular roles of MPPED2 are unknown, and its low phosphodiesterase activity suggests that substrate hydrolysis may not be its prime function. We present here the structures of MPPED2 and two mutants, which show that the poor activity of MPPED2 is not only a consequence of the substitution of an active-site histidine residue by glycine but also due to binding of AMP or GMP to the active site. This feature, enhanced by structural elements of the protein, allows MPPED2 to utilize the conserved phosphoprotein-phosphatase-like fold in a unique manner, ensuring that its enzymatic activity can be combined with a possible role as a scaffolding or adaptor protein. (C) 2011 Elsevier Ltd. All rights reserved.

Quaternary association in beta-prism I fold plant lectins: Insights from X-ray crystallography, modelling and molecular dynamics

Dimeric banana lectin and calsepa, tetrameric artocarpin and octameric heltuba are mannose-specific beta-prism I fold lectins of nearly the same tertiary structure. MD simulations on individual subunits and the oligomers provide insights into the changes in the structure brought about in the protomers on oligomerization, including swapping of the N-terminal stretch in one instance. The regions that undergo changes also tend to exhibit dynamic flexibility during MD simulations. The internal symmetries of individual oligomers are substantially retained during the calculations. Energy minimization and simulations were also carried out on models using all possible oligomers by employing the four different protomers. The unique dimerization pattern observed in calsepa could be traced to unique substitutions in a peptide stretch involved in dimerization. The impossibility of a specific mode of oligomerization involving a particular protomer is often expressed in terms of unacceptable steric contacts or dissociation of the oligomer during simulations. The calculations also led to a rationale for the observation of a heltuba tetramer in solution although the lectin exists as an octamer in the crystal, in addition to providing insights into relations among evolution, oligomerization and ligand binding.

Fermi-edge singularity in photoluminescence spectra of modulation-doped AlGaAs/InGaAs/GaAs quantum wells

The photoluminescence study of Fermi-edge singularity (FES) in modulation-doped pseudomorphic AlxGa1-xAs/InyGa1-yAs/GaAs quantum well (QW) heterostructures is presented. In the above QW structures the optical transitions between n = 1 and n = 2 electronic subband to the n = 1 heavy hole subband (E-11 and E-21 transitions, respectively) are observed with FES appearing as a lower energy shoulder to the E-21 transition. The observed FES is attributed to the Fermi wave vector in the first electronic subband under the conditions of population of the second electronic subband. The FES appears at about 10 meV below E-21 transition around 4.2 K. Initially it gets stronger with increasing temperature and becomes a distinct peak at about 20 K. Further increase in temperature quenches FES and reaches the base line at around 40 K.

Insights into the Fold Organization of TIM Barrel from Interaction Energy Based Structure Networks

There are many well-known examples of proteins with low sequence similarity, adopting the same structural fold. This aspect of sequence-structure relationship has been extensively studied both experimentally and theoretically, however with limited success. Most of the studies consider remote homology or ``sequence conservation'' as the basis for their understanding. Recently ``interaction energy'' based network formalism (Protein Energy Networks (PENs)) was developed to understand the determinants of protein structures. In this paper we have used these PENs to investigate the common non-covalent interactions and their collective features which stabilize the TIM barrel fold. We have also developed a method of aligning PENs in order to understand the spatial conservation of interactions in the fold. We have identified key common interactions responsible for the conservation of the TIM fold, despite high sequence dissimilarity. For instance, the central beta barrel of the TIM fold is stabilized by long-range high energy electrostatic interactions and low-energy contiguous vdW interactions in certain families. The other interfaces like the helix-sheet or the helix-helix seem to be devoid of any high energy conserved interactions. Conserved interactions in the loop regions around the catalytic site of the TIM fold have also been identified, pointing out their significance in both structural and functional evolution. Based on these investigations, we have developed a novel network based phylogenetic analysis for remote homologues, which can perform better than sequence based phylogeny. Such an analysis is more meaningful from both structural and functional evolutionary perspective. We believe that the information obtained through the ``interaction conservation'' viewpoint and the subsequently developed method of structure network alignment, can shed new light in the fields of fold organization and de novo computational protein design.