A nodal domain theorem for integrable billiards in two dimensions

Eigenfunctions of integrable planar billiards are studied - in particular, the number of nodal domains, nu of the eigenfunctions with Dirichlet boundary conditions are considered. The billiards for which the time-independent Schrodinger equation (Helmholtz equation) is separable admit trivial expressions for the number of domains. Here, we discover that for all separable and nonseparable integrable billiards, nu satisfies certain difference equations. This has been possible because the eigenfunctions can be classified in families labelled by the same value of m mod kn, given a particular k, for a set of quantum numbers, m, n. Further, we observe that the patterns in a family are similar and the algebraic representation of the geometrical nodal patterns is found. Instances of this representation are explained in detail to understand the beauty of the patterns. This paper therefore presents a mathematical connection between integrable systems and difference equations. (C) 2014 Elsevier Inc. All rights reserved.

Analysis on conservation of disulphide bonds and their structural features in homologous protein domain families

Background: Disulphide bridges are well known to play key roles in stability, folding and functions of proteins. Introduction or deletion of disulphides by site-directed mutagenesis have produced varying effects on stability and folding depending upon the protein and location of disulphide in the 3-D structure. Given the lack of complete understanding it is worthwhile to learn from an analysis of extent of conservation of disulphides in homologous proteins. We have also addressed the question of what structural interactions replaces a disulphide in a homologue in another homologue. Results: Using a dataset involving 34,752 pairwise comparisons of homologous protein domains corresponding to 300 protein domain families of known 3-D structures, we provide a comprehensive analysis of extent of conservation of disulphide bridges and their structural features. We report that only 54% of all the disulphide bonds compared between the homologous pairs are conserved, even if, a small fraction of the non-conserved disulphides do include cytoplasmic proteins. Also, only about one fourth of the distinct disulphides are conserved in all the members in protein families. We note that while conservation of disulphide is common in many families, disulphide bond mutations are quite prevalent. Interestingly, we note that there is no clear relationship between sequence identity between two homologous proteins and disulphide bond conservation. Our analysis on structural features at the sites where cysteines forming disulphide in one homologue are replaced by non-Cys residues show that the elimination of a disulphide in a homologue need not always result in stabilizing interactions between equivalent residues. Conclusion: We observe that in the homologous proteins, disulphide bonds are conserved only to a modest extent. Very interestingly, we note that extent of conservation of disulphide in homologous proteins is unrelated to the overall sequence identity between homologues. The non-conserved disulphides are often associated with variable structural features that were recruited to be associated with differentiation or specialisation of protein function.

Expression of the extracellular domain of the human heat-stable enterotoxin receptor in Escherichia coli and generation of neutralizing antibodies

The entire extracellular domain of the human heat-stable enterotoxin (ST) receptor as well as a truncated N-terminal domain were cloned as glutathione S-transferase fusion proteins and expressed in Escherichia coli. The recombinant fusion proteins were purified from both the cytosol and the inclusion body fractions by selective detergent extraction followed by glutathione-agarose affinity chromatography. The purified protein, corresponding to the entire extracellular domain, bound the stable toxin peptide with an affinity comparable to that of the native receptor characterized from the human colonic T84 cell line. No binding was observed with the N-terminal truncated fragment of the receptor under similar conditions, Polyclonal antibodies were raised to the entire extracellular domain fusion protein as well as the truncated extracellular domain fusion protein, and the antibodies were purified by affinity chromatography. Addition of the purified antibodies to T84 cells inhibited ST binding and abolished ST-mediated cGMP production, indicating that critical epitopes involved in ligand interaction are present in the N-terminal fragment of the receptor, Purified antibodies recognized a single protein of M(r) 160,000 Da on Western blotting with T84 membranes, corresponding to a size of the native glycosylated receptor in T84 cells. These studies are the first report of the expression, purification, and characterization of any member of the guanylyl cyclase family of receptors in E. coli and show that binding of the toxin to the extracellular domain of the receptor is possible in the absence of any posttranslational modifications such as glycosylation. The recombinant fusion proteins as well as the antibodies that we have generated could serve as useful tools in the identification of critical residues of the extracellular domain involved in ligand interaction.

Comparative kinomics of human and chimpanzee reveal unique kinship and functional diversity generated by new domain combinations

Background: Phosphorylation by protein kinases is a common event in many cellular processes. Further, many kinases perform specialized roles and are regulated by non-kinase domains tethered to kinase domain. Perturbation in the regulation of kinases leads to malignancy. We have identified and analysed putative protein kinases encoded in the genome of chimpanzee which is a close evolutionary relative of human. Result: The shared core biology between chimpanzee and human is characterized by many orthologous protein kinases which are involved in conserved pathways. Domain architectures specific to chimp/human kinases have been observed. Chimp kinases with unique domain architectures are characterized by deletion of one or more non-kinase domains in the human kinases. Interestingly, counterparts of some of the multi-domain human kinases in chimp are characterized by identical domain architectures but with kinase-like non-kinase domain. Remarkably, out of 587 chimpanzee kinases no human orthologue with greater than 95% sequence identity could be identified for 160 kinases. Variations in chimpanzee kinases compared to human kinases are brought about also by differences in functions of domains tethered to the catalytic kinase domain. For example, the heterodimer forming PB1 domain related to the fold of ubiquitin/Ras-binding domain is seen uniquely tethered to PKC-like chimpanzee kinase. Conclusion: Though the chimpanzee and human are evolutionary very close, there are chimpanzee kinases with no close counterpart in the human suggesting differences in their functions. This analysis provides a direction for experimental analysis of human and chimpanzee protein kinases in order to enhance our understanding on their specific biological roles.

Linear filtering in DCT IV/DST IV and MDCT/MDST domain

In this paper, expressions for convolution multiplication properties of DCT IV and DST IV are derived starting from equivalent DFT representations. Using these expressions methods for implementing linear filtering through block convolution in the DCT IV and DST IV domain are proposed. Techniques developed for DCT IV and DST IV are further extended to MDCT and MDST where the filter implementation is near exact for symmetric filters and approximate for non-symmetric filters. No additional overlapping is required for implementing the symmetric filtering in the MDCT domain and hence the proposed algorithm is computationally competitive with DFT based systems. Moreover, inherent 50% overlap between the adjacent frames used for MDCT/MDST domain reduces the blocking artifacts due to block processing or quantization. The techniques are computationally efficient for symmetric filters and provides a new alternative to DFT based convolution.

Structure and Rheology of Cationic Molecular Hydrogels of Quinuclidine Grafted Bile Salts. Influence of the Ionic Strength and Counter-Ion type

Quinuclidine grafted cationic bile salts are forming salted hydrogels. An extensive investigation of the effect of the electrolyte and counterions on the gelation has been envisaged. The special interest of the quinuclidine grafted bile salt is due to its broader experimental range of gelation to study the effect of electrolyte. Rheological features of the hydrogels are typical of enthalpic networks exhibiting a scaling law of the elastic shear modulus with the concentration (scaling exponent 2.2) modeling cellular solids in which the bending modulus is the dominant parameter. The addition of monovalent salt (NaCl) favors the formation of gels in a first range (0.00117 g cm-3 (0.02 M) < TNaCl < 0.04675 g cm-3 (0.8 M)). At larger salt concentrations, the gels become more heterogeneous with nodal zones in the micron scale. Small-angle neutron scattering experiments have been used to characterize the rigid fibers ( ≈ 68 Å) and the nodal zones. Stress sweep and creeprecovery measurements are used to relate the lack of linear viscoelastic domain to a mechanism of disentanglement of the fibers from their associations into fagots. The electrostatic interactions can be screened by addition of salt to induce a progressive evolution toward flocculation. SEM, UV absorbance, and SAXS study of the Bragg peak at large Q-values complete the investigation.

Interaction Between Two Residues in the Inter-Domain Interface of Escherichia coli Peptidase N Modulates Catalytic Activity

The role of interaction between Asn259 (catalytic domain) with Gln821 (C-terminal domain) in PeptidaseN was investigated. The k(cat) of PeptidaseN containing Asn259Asp or Gln821Glu is enhanced whereas it is suppressed in Asn259AspGln821Glu. Structural analysis shows this interaction to change the relative disposition of active site residues, which modulates catalytic activity.

The Evolution of Guanylyl Cyclases as Multidomain Proteins: Conserved Features of Kinase-Cyclase Domain Fusions

Guanylyl cyclases (GCs) are enzymes that generate cyclic GMP and regulate different physiologic and developmental processes in a number of organisms. GCs possess sequence similarity to class III adenylyl cyclases (ACs) and are present as either membrane-bound receptor GCs or cytosolic soluble GCs. We sought to determine the evolution of GCs using a large-scale bioinformatic analysis and found multiple lineage-specific expansions of GC genes in the genomes of many eukaryotes. Moreover, a few GC-like proteins were identified in prokaryotes, which come fused to a number of different domains, suggesting allosteric regulation of nucleotide cyclase activity Eukaryotic receptor GCs are associated with a kinase homology domain (KHD), and phylogenetic analysis of these proteins suggest coevolution of the KHD and the associated cyclase domain as well as a conservation of the sequence and the size of the linker region between the KHD and the associated cyclase domain. Finally, we also report the existence of mimiviral proteins that contain putative active kinase domains associated with a cyclase domain, which could suggest early evolution of the fusion of these two important domains involved in signa transduction.

Crystallographic and modelling studies on Mycobacterium tuberculosis RuvA: Additional role of RuvB-binding domain and inter species variability

RuvA, along with RuvB, is involved in branch migration of heteroduplex DNA in homologous recombination. The structures of three new crystal forms of RuvA from Mycobacterium tuberculosis (MtRuvA) have been determined. The RuvB-binding domain is cleaved off in one of them. Detailed models of the complexes of octameric RuvA from different species with the Holliday junction have also been constructed. A thorough examination of the structures presented here and those reported earlier brings to light the hitherto unappreciated role of the RuvB-binding domain in determining inter-domain orientation and oligomerization. These structures also permit an exploration of the interspecies variability of structural features such as oligomerization and the conformation of the loop that carries the acidic pin, in terms of amino acid substitutions. These models emphasize the additional role of the RuvB-binding domain in Holliday junction binding. This role along with its role in oligomerization could have important biological implications.

Analysis-By-Synthesis Based Switched Transform Domain Split Vq Using Gaussian Mixture Model

Using analysis-by-synthesis (AbS) approach, we develop a soft decision based switched vector quantization (VQ) method for high quality and low complexity coding of wideband speech line spectral frequency (LSF) parameters. For each switching region, a low complexity transform domain split VQ (TrSVQ) is designed. The overall rate-distortion (R/D) performance optimality of new switched quantizer is addressed in the Gaussian mixture model (GMM) based parametric framework. In the AbS approach, the reduction of quantization complexity is achieved through the use of nearest neighbor (NN) TrSVQs and splitting the transform domain vector into higher number of subvectors. Compared to the current LSF quantization methods, the new method is shown to provide competitive or better trade-off between R/D performance and complexity.

Continuously equivalent networks in state space

Schoeffler has derived continuously equivalent networks in the nodal-admittance domain. The letter derives a corresponding result in state space that combines the usefulness of Schoeffler's result and the power of the state-variable approach.

Resistivity noise in crystalline magnetic nanowires and its implications to domain formation and kinetics

We have investigated the time-dependent fluctuations in electrical resistance, or noise, in high quality crystalline magnetic nanowires within nanoporous templates. The noise increases exponentially with increasing temperature and magnetic field, and has been analyzed in terms of domain wall depinning within the Neel-Brown framework. The frequency-dependence of noise also indicates a crossover from nondiffusive kinetics to long-range diffusion at higher temperatures, as well as a strong collective depinning, which need to be considered when implementing these nanowires in magnetoelectronic devices.

L2-stability of nonstationary feedback systems: Frequency-domain criteria

A frequency-domain positivity condition is derived for linear time-varying operators in2and is used to develop2stability criteria for linear and nonlinear feedback systems. These criteria permit the use of a very general class of operators in2with nonstationary kernels, as multipliers. More specific results are obtained by using a first-order differential operator with a time-varying coefficient as multiplier. Finally, by employing periodic multipliers, improved stability criteria are derived for the nonlinear damped Mathieu equation with a forcing function.

Time-domain criteria for theL_{2}-stability of nonstationary feedback systems

Criteria for the L2-stability of linear and nonlinear time-varying feedback systems are given. These are conditions in the time domain involving the solution of certain associated matrix Riccati equations and permitting the use of a very general class of L2-operators as multipliers.

Effect of fourier domain quantization on matched filtering

It is shown that the use of a coarsely quantized binary digital hologram as a matched filter on an optical computer does not degrade signal-to-noise ratio (SNR) appreciably.