Graded Symmetry Algebras of Time-Dependent Evolution Equations and Application to the Modified KP equations

By starting from known graded Lie algebras, including Virasoro algebras, new kinds of time-dependent evolution equations are found possessing graded symmetry algebras. The modified KP equations are taken as an illustrative example: new modified KP equations with $m$ arbitrary time-dependent coefficients are obtained possessing symmetries involving $m$ arbitrary functions of time. A particular graded symmetry algebra for the modified KP equations is derived in this connection homomorphic to the Virasoro algebras.Comment: 19 pages, latex, to appear in J. Nonlinear Math. Phy

Characterization of the spore surface and exosporium proteins of Clostridium sporogenes; implications for Clostridium botulinum group I strains.

Clostridium sporogenes is a non-pathogenic close relative and surrogate for Group I (proteolytic) neurotoxin-producing Clostridium botulinum strains. The exosporium, the sac-like outermost layer of spores of these species, is likely to contribute to adhesion, dissemination, and virulence. A paracrystalline array, hairy nap, and several appendages were detected in the exosporium of C. sporogenes strain NCIMB 701792 by EM and AFM. The protein composition of purified exosporium was explored by LC-MS/MS of tryptic peptides from major individual SDS-PAGE-separated protein bands, and from bulk exosporium. Two high molecular weight protein bands both contained the same protein with a collagen-like repeat domain, the probable constituent of the hairy nap, as well as cysteine-rich proteins CsxA and CsxB. A third cysteine-rich protein (CsxC) was also identified. These three proteins are also encoded in C. botulinum Prevot 594, and homologues (75-100% amino acid identity) are encoded in many other Group I strains. This work provides the first insight into the likely composition and organization of the exosporium of Group I C. botulinum spores

Time-Dependent Symmetries of Variable-Coefficient Evolution Equations and Graded Lie Algebras

Polynomial-in-time dependent symmetries are analysed for polynomial-in-time dependent evolution equations. Graded Lie algebras, especially Virasoro algebras, are used to construct nonlinear variable-coefficient evolution equations, both in 1+1 dimensions and in 2+1 dimensions, which possess higher-degree polynomial-in-time dependent symmetries. The theory also provides a kind of new realisation of graded Lie algebras. Some illustrative examples are given.Comment: 11 pages, latex, to appear in J. Phys. A: Math. Ge

Invariant solutions of the supersymmetric sine-Gordon equation

A comprehensive symmetry analysis of the N=1 supersymmetric sine-Gordon equation is performed. Two different forms of the supersymmetric system are considered. We begin by studying a system of partial differential equations corresponding to the coefficients of the various powers of the anticommuting independent variables. Next, we consider the super-sine-Gordon equation expressed in terms of a bosonic superfield involving anticommuting independent variables. In each case, a Lie (super)algebra of symmetries is determined and a classification of all subgroups having generic orbits of codimension 1 in the space of independent variables is performed. The method of symmetry reduction is systematically applied in order to derive invariant solutions of the supersymmetric model. Several types of algebraic, hyperbolic and doubly periodic solutions are obtained in explicit form.Comment: 27 pages, major revision, the published versio

The architecture of the Gram-positive bacterial cell wall

The primary structural component of the bacterial cell wall is peptidoglycan, which is essential for viability and the synthesis of which is the target for crucial antibiotics1,2. Peptidoglycan is a single macromolecule made of glycan chains crosslinked by peptide side branches that surrounds the cell, acting as a constraint to internal turgor1,3. In Gram-positive bacteria, peptidoglycan is tens of nanometres thick, generally portrayed as a homogeneous structure that provides mechanical strength4,5,6. Here we applied atomic force microscopy7,8,9,10,11,12 to interrogate the morphologically distinct Staphylococcus aureus and Bacillus subtilis species, using live cells and purified peptidoglycan. The mature surface of live cells is characterized by a landscape of large (up to 60 nm in diameter), deep (up to 23 nm) pores constituting a disordered gel of peptidoglycan. The inner peptidoglycan surface, consisting of more nascent material, is much denser, with glycan strand spacing typically less than 7 nm. The inner surface architecture is location dependent; the cylinder of B. subtilis has dense circumferential orientation, while in S. aureus and division septa for both species, peptidoglycan is dense but randomly oriented. Revealing the molecular architecture of the cell envelope frames our understanding of its mechanical properties and role as the environmental interface13,14, providing information complementary to traditional structural biology approaches

Structure and function of the bacterial heterodimeric ABC transporter CydDC: stimulation of ATPase activity by thiol and heme compounds.

In Escherichia coli, the biogenesis of both cytochrome bd-type quinol oxidases and periplasmic cytochromes requires the ATP-binding cassette-type cysteine/GSH transporter, CydDC. Recombinant CydDC was purified as a heterodimer and found to be an active ATPase both in soluble form with detergent and when reconstituted into a lipid environment. Two-dimensional crystals of CydDC were analyzed by electron cryomicroscopy, and the protein was shown to be made up of two non-identical domains corresponding to the putative CydD and CydC subunits, with dimensions characteristic of other ATP-binding cassette transporters. CydDC binds heme b. Detergent-solubilized CydDC appears to adopt at least two structural states, each associated with a characteristic level of bound heme. The purified protein in detergent showed a weak basal ATPase activity (approximately 100 nmol Pi/min/mg) that was stimulated ∼3-fold by various thiol compounds, suggesting that CydDC could act as a thiol transporter. The presence of heme (either intrinsic or added in the form of hemin) led to a further enhancement of thiol-stimulated ATPase activity, although a large excess of heme inhibited activity. Similar responses of the ATPase activity were observed with CydDC reconstituted into E. coli lipids. These results suggest that heme may have a regulatory role in CydDC-mediated transmembrane thiol transport

New Integrable Sectors in Skyrme and 4-dimensional CP^n Model

The application of a weak integrability concept to the Skyrme and $CP^n$ models in 4 dimensions is investigated. A new integrable subsystem of the Skyrme model, allowing also for non-holomorphic solutions, is derived. This procedure can be applied to the massive Skyrme model, as well. Moreover, an example of a family of chiral Lagrangians providing exact, finite energy Skyrme-like solitons with arbitrary value of the topological charge, is given. In the case of $CP^n$ models a tower of integrable subsystems is obtained. In particular, in (2+1) dimensions a one-to-one correspondence between the standard integrable submodel and the BPS sector is proved. Additionally, it is shown that weak integrable submodels allow also for non-BPS solutions. Geometric as well as algebraic interpretations of the integrability conditions are also given.Comment: 23 page

A Study Of A New Class Of Discrete Nonlinear Schroedinger Equations

A new class of 1D discrete nonlinear Schr${\ddot{\rm{o}}}$dinger Hamiltonians with tunable nonlinerities is introduced, which includes the integrable Ablowitz-Ladik system as a limit. A new subset of equations, which are derived from these Hamiltonians using a generalized definition of Poisson brackets, and collectively refered to as the N-AL equation, is studied. The symmetry properties of the equation are discussed. These equations are shown to possess propagating localized solutions, having the continuous translational symmetry of the one-soliton solution of the Ablowitz-Ladik nonlinear Schr${\ddot{\rm{o}}}$dinger equation. The N-AL systems are shown to be suitable to study the combined effect of the dynamical imbalance of nonlinearity and dispersion and the Peierls-Nabarro potential, arising from the lattice discreteness, on the propagating solitary wave like profiles. A perturbative analysis shows that the N-AL systems can have discrete breather solutions, due to the presence of saddle center bifurcations in phase portraits. The unstaggered localized states are shown to have positive effective mass. On the other hand, large width but small amplitude staggered localized states have negative effective mass. The collison dynamics of two colliding solitary wave profiles are studied numerically. Notwithstanding colliding solitary wave profiles are seen to exhibit nontrivial nonsolitonic interactions, certain universal features are observed in the collison dynamics. Future scopes of this work and possible applications of the N-AL systems are discussed.Comment: 17 pages, 15 figures, revtex4, xmgr, gn

Cavity-induced coherence effects in spontaneous emission from pre-Selection of polarization

Spontaneous emission can create coherences in a multilevel atom having close lying levels, subject to the condition that the atomic dipole matrix elements are non-orthogonal. This condition is rarely met in atomic systems. We report the possibility of bypassing this condition and thereby creating coherences by letting the atom with orthogonal dipoles to interact with the vacuum of a pre-selected polarized cavity mode rather than the free space vacuum. We derive a master equation for the reduced density operator of a model four level atomic system, and obtain its analytical solution to describe the interference effects. We report the quantum beat structure in the populations.Comment: 6 pages in REVTEX multicolumn format, 5 figures, new references added, journal reference adde

A New Nonlinear Liquid Drop Model. Clusters as Solitons on The Nuclear Surface

By introducing in the hydrodynamic model, i.e. in the hydrodynamic equations and the corresponding boundary conditions, the higher order terms in the deviation of the shape, we obtain in the second order the Korteweg de Vries equation (KdV). The same equation is obtained by introducing in the liquid drop model (LDM), i.e. in the kinetic, surface and Coulomb terms, the higher terms in the second order. The KdV equation has the cnoidal waves as steady-state solutions. These waves could describe the small anharmonic vibrations of spherical nuclei up to the solitary waves. The solitons could describe the preformation of clusters on the nuclear surface. We apply this nonlinear liquid drop model to the alpha formation in heavy nuclei. We find an additional minimum in the total energy of such systems, corresponding to the solitons as clusters on the nuclear surface. By introducing the shell effects we choose this minimum to be degenerated with the ground state. The spectroscopic factor is given by the ratio of the square amplitudes in the two minima.Comment: 27 pages, LateX, 8 figures, Submitted J. Phys. G: Nucl. Part. Phys., PACS: 23.60.+e, 21.60.Gx, 24.30.-v, 25.70.e