An exploration of alternative visualisations of the basic helix-loop-helix protein interaction network

Background: Alternative representations of biochemical networks emphasise different aspects of the data and contribute to the understanding of complex biological systems. In this study we present a variety of automated methods for visualisation of a protein-protein interaction network, using the basic helix-loop-helix ( bHLH) family of transcription factors as an example. Results: Network representations that arrange nodes ( proteins) according to either continuous or discrete information are investigated, revealing the existence of protein sub-families and the retention of interactions following gene duplication events. Methods of network visualisation in conjunction with a phylogenetic tree are presented, highlighting the evolutionary relationships between proteins, and clarifying the context of network hubs and interaction clusters. Finally, an optimisation technique is used to create a three-dimensional layout of the phylogenetic tree upon which the protein-protein interactions may be projected. Conclusion: We show that by incorporating secondary genomic, functional or phylogenetic information into network visualisation, it is possible to move beyond simple layout algorithms based on network topology towards more biologically meaningful representations. These new visualisations can give structure to complex networks and will greatly help in interpreting their evolutionary origins and functional implications. Three open source software packages (InterView, TVi and OptiMage) implementing our methods are available

Bioinformatic analysis of the neprilysin (M13) family of peptidases reveals complex evolutionary and functional relationships

<p>Abstract</p> <p>Background</p> <p>The neprilysin (M13) family of endopeptidases are zinc-metalloenzymes, the majority of which are type II integral membrane proteins. The best characterised of this family is neprilysin, which has important roles in inactivating signalling peptides involved in modulating neuronal activity, blood pressure and the immune system. Other family members include the endothelin converting enzymes (ECE-1 and ECE-2), which are responsible for the final step in the synthesis of potent vasoconstrictor endothelins. The ECEs, as well as neprilysin, are considered valuable therapeutic targets for treating cardiovascular disease. Other members of the M13 family have not been functionally characterised, but are also likely to have biological roles regulating peptide signalling. The recent sequencing of animal genomes has greatly increased the number of M13 family members in protein databases, information which can be used to reveal evolutionary relationships and to gain insight into conserved biological roles.</p> <p>Results</p> <p>The phylogenetic analysis successfully resolved vertebrate M13 peptidases into seven classes, one of which appears to be specific to mammals, and insect genes into five functional classes and a series of expansions, which may include inactive peptidases. Nematode genes primarily resolved into groups containing no other taxa, bar the two nematode genes associated with <it>Drosophila </it>DmeNEP1 and DmeNEP4. This analysis reconstructed only one relationship between chordate and invertebrate clusters, that of the ECE sub-group and the DmeNEP3 related genes. Analysis of amino acid utilisation in the active site of M13 peptidases reveals a basis for their biochemical properties. A relatively invariant S1' subsite gives the majority of M13 peptidases their strong preference for hydrophobic residues in P1' position. The greater variation in the S2' subsite may be instrumental in determining the specificity of M13 peptidases for their substrates and thus allows M13 peptidases to fulfil a broad range of physiological roles.</p> <p>Conclusion</p> <p>The M13 family of peptidases have diversified extensively in all species examined, indicating wide ranging roles in numerous physiological processes. It is predicted that differences in the S2' subsite are fundamental to determining the substrate specificities that facilitate this functional diversity.</p

Solutions to Maxwell's Equations using Spheroidal Coordinates

Analytical solutions to the wave equation in spheroidal coordinates in the short wavelength limit are considered. The asymptotic solutions for the radial function are significantly simplified, allowing scalar spheroidal wave functions to be defined in a form which is directly reminiscent of the Laguerre-Gaussian solutions to the paraxial wave equation in optics. Expressions for the Cartesian derivatives of the scalar spheroidal wave functions are derived, leading to a new set of vector solutions to Maxwell's equations. The results are an ideal starting point for calculations of corrections to the paraxial approximation

Unified Treatment of Heterodyne Detection: the Shapiro-Wagner and Caves Frameworks

A comparative study is performed on two heterodyne systems of photon detectors expressed in terms of a signal annihilation operator and an image band creation operator called Shapiro-Wagner and Caves' frame, respectively. This approach is based on the introduction of a convenient operator $\hat \psi$ which allows a unified formulation of both cases. For the Shapiro-Wagner scheme, where $[\hat \psi, \hat \psi^{\dag}] =0$, quantum phase and amplitude are exactly defined in the context of relative number state (RNS) representation, while a procedure is devised to handle suitably and in a consistent way Caves' framework, characterized by $[\hat \psi, \hat \psi^{\dag}] \neq 0$, within the approximate simultaneous measurements of noncommuting variables. In such a case RNS phase and amplitude make sense only approximately.Comment: 25 pages. Just very minor editorial cosmetic change

Lie symmetries for two-dimensional charged particle motion

We find the Lie point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries comprise a quasi-invariance transformation, a time-dependent rotation, a time-dependent spatial translation and a dilation. The associated electromagnetic fields satisfy a system of first-order linear partial differential equations. This system is solved exactly, yielding four classes of electromagnetic fields compatible with Lie point symmetries

PathwayBooster:a tool to support the curation of metabolic pathways

BACKGROUND: Despite several recent advances in the automated generation of draft metabolic reconstructions, the manual curation of these networks to produce high quality genome-scale metabolic models remains a labour-intensive and challenging task. RESULTS: We present PathwayBooster, an open-source software tool to support the manual comparison and curation of metabolic models. It combines gene annotations from GenBank files and other sources with information retrieved from the metabolic databases BRENDA and KEGG to produce a set of pathway diagrams and reports summarising the evidence for the presence of a reaction in a given organism’s metabolic network. By comparing multiple sources of evidence within a common framework, PathwayBooster assists the curator in the identification of likely false positive (misannotated enzyme) and false negative (pathway hole) reactions. Reaction evidence may be taken from alternative annotations of the same genome and/or a set of closely related organisms. CONCLUSIONS: By integrating and visualising evidence from multiple sources, PathwayBooster reduces the manual effort required in the curation of a metabolic model. The software is available online at http://www.theosysbio.bio.ic.ac.uk/resources/pathwaybooster/. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12859-014-0447-2) contains supplementary material, which is available to authorized users

Backlund transformations for many-body systems related to KdV

We present Backlund transformations (BTs) with parameter for certain classical integrable n-body systems, namely the many-body generalised Henon-Heiles, Garnier and Neumann systems. Our construction makes use of the fact that all these systems may be obtained as particular reductions (stationary or restricted flows) of the KdV hierarchy; alternatively they may be considered as examples of the reduced sl(2) Gaudin magnet. The BTs provide exact time-discretizations of the original (continuous) systems, preserving the Lax matrix and hence all integrals of motion, and satisfy the spectrality property with respect to the Backlund parameter.Comment: LaTeX2e, 8 page

Symmetry, singularities and integrability in complex dynamics III: approximate symmetries and invariants

The different natures of approximate symmetries and their corresponding first integrals/invariants are delineated in the contexts of both Lie symmetries of ordinary differential equations and Noether symmetries of the Action Integral. Particular note is taken of the effect of taking higher orders of the perturbation parameter. Approximate symmetries of approximate first integrals/invariants and the problems of calculating them using the Lie method are considered

Anisotropic Bose-Einstein condensates and completely integrable dynamical systems

A Gaussian ansatz for the wave function of two-dimensional harmonically trapped anisotropic Bose-Einstein condensates is shown to lead, via a variational procedure, to a coupled system of two second-order, nonlinear ordinary differential equations. This dynamical system is shown to be in the general class of Ermakov systems. Complete integrability of the resulting Ermakov system is proven. Using the exact solution, collapse of the condensate is analyzed in detail. Time-dependence of the trapping potential is allowed

Oval Domes: History, Geometry and Mechanics

An oval dome may be defined as a dome whose plan or profile (or both) has an oval form. The word Aoval@ comes from the latin Aovum@, egg. Then, an oval dome has an egg-shaped geometry. The first buildings with oval plans were built without a predetermined form, just trying to close an space in the most economical form. Eventually, the geometry was defined by using arcs of circle with common tangents in the points of change of curvature. Later the oval acquired a more regular form with two axis of symmetry. Therefore, an “oval” may be defined as an egg-shaped form, doubly symmetric, constructed with arcs of circle; an oval needs a minimum of four centres, but it is possible also to build polycentric ovals. The above definition corresponds with the origin and the use of oval forms in building and may be applied without problem until, say, the XVIIIth century. Since then, the teaching of conics in the elementary courses of geometry made the cultivated people to define the oval as an approximation to the ellipse, an “imperfect ellipse”: an oval was, then, a curve formed with arcs of circles which tries to approximate to the ellipse of the same axes. As we shall see, the ellipse has very rarely been used in building. Finally, in modern geometrical textbooks an oval is defined as a smooth closed convex curve, a more general definition which embraces the two previous, but which is of no particular use in the study of the employment of oval forms in building. The present paper contains the following parts: 1) an outline the origin and application of the oval in historical architecture; 2) a discussion of the spatial geometry of oval domes, i. e., the different methods employed to trace them; 3) a brief exposition of the mechanics of oval arches and domes; and 4) a final discussion of the role of Geometry in oval arch and dome design