SBML Level 3 Package: Flux Balance Constraints ('fbc')

Constraint based modeling is a widely accepted methodology used to analyze and study biological networks on both a small and whole organism (genome) scale. Typically these models are underdetermined and constraint based methods (e.g. linear, quadratic optimization) are used to optimize specific model properties. This is assumed to occur under a defined set of constraints (e.g. stoichiometric, metabolic) and bounds (e.g. thermodynamic, experimental and environmental) on the values that the solution fluxes can obtain. Perhaps the most well known (and widely used) analysis method is Flux Balance Analysis (FBA; Orth et al., 2010) which is performed on Genome Scale Reconstructions (GSR’s; Oberhardt et al., 2009). Using FBA a target flux is optimized (e.g. maximizing a flux to biomass or minimizing ATP production) while other fluxes can be bounded to simulate a selected growth environment or specific metabolic state. As constraint based models are generally underdetermined, i.e. few or none of the kinetic rate equations and related parameters are known, it is crucial that a model definition includes the ability to define optimization parameters such as objective functions, flux bounds and constraints. Currently this is not possible in the Systems Biology Markup Language (SBML) Level 2 or Level 3 core specification (Hucka et al., 2011, 2003). The question of how to encode constraint based (also referred to as steady state or FBA) models in SBML is not new. However, advances in the methods used to construct genome scale constraint based models and the wider adoption of constraint based modeling in biotechnological/medical applications have led to a rapid increase in both the number of models being constructed and the tools used to analyze them. Faced with such growth, both in number and diversity, the need for a standardized data format for the definition, exchange and annotation of constraint based models has become critical. As the core model components (e.g. species, reactions, stoichiometry) can already be efficiently described in SBML (with its associated active community, software and tool support) the Flux Balance Constraints package aims to extend SBML Level 3 core by adding the elements necessary to encode current and future constraint based models

SBML Level 3 Package: Flux Balance Constraints version 2

Constraint-based modeling is a well established modeling methodology used to analyze and study biological networks on both a medium and genome scale. Due to their large size and complexity such steady-state flux models are, typically, analyzed using constraint-based optimization techniques, for example, flux balance analysis (FBA). The Flux balance constraints (FBC) Package extends SBML Level 3 and provides a standardized format for the encoding, exchange and annotation of constraint-based models. It includes support for modeling concepts such as objective functions, flux bounds and model component annotation that facilitates reaction balancing. Version two expands on the original release by adding official support for encoding gene-protein associations and their associated elements. In addition to providing the elements necessary to unambiguously encode existing constraint-based models, the FBC Package provides an open platform facilitating the continued, cross-community development of an interoperable, constraint-based model encoding format

Progress report: SBML Level 3 package FBA

The SBML Level 3 "FBA" package is a proposal for an extension to the current Level 3 Core specification that allows for the description and annotation of constraint based models.

This allows one to e.g. store information related to flux balance analysis in SBML Level 3 models

Coordinate time and proper time in the GPS

The Global Positioning System (GPS) provides an excellent educational example as to how the theory of general relativity is put into practice and becomes part of our everyday life. This paper gives a short and instructive derivation of an important formula used in the GPS, and is aimed at graduate students and general physicists. The theoretical background of the GPS (see \cite{ashby}) uses the Schwarzschild spacetime to deduce the {\it approximate} formula, ds/dt\approx 1+V-\frac{|\vv|^2}{2}, for the relation between the proper time rate $s$ of a satellite clock and the coordinate time rate $t$. Here $V$ is the gravitational potential at the position of the satellite and \vv is its velocity (with light-speed being normalized as $c=1$). In this note we give a different derivation of this formula, {\it without using approximations}, to arrive at ds/dt=\sqrt{1+2V-|\vv|^2 -\frac{2V}{1+2V}(\n\cdot\vv)^2}, where \n is the normal vector pointing outward from the center of Earth to the satellite. In particular, if the satellite moves along a circular orbit then the formula simplifies to ds/dt=\sqrt{1+2V-|\vv|^2}. We emphasize that this derivation is useful mainly for educational purposes, as the approximation above is already satisfactory in practice.Comment: 5 pages, revised, over-over-simplified... Does anyone care that the GPS uses an approximate formula, while a precise one is available in just a few lines??? Physicists don'

Oscillations of the magnetic polarization in a Kondo impurity at finite magnetic fields

The electronic properties of a Kondo impurity are investigated in a magnetic field using linear response theory. The distribution of electrical charge and magnetic polarization are calculated in real space. The (small) magnetic field does not change the charge distribution. However, it unmasks the Kondo cloud. The (equal) weight of the d-electron components with their magnetic moment up and down is shifted and the compensating s-electron clouds don't cancel any longer (a requirement for an experimental detection of the Kondo cloud). In addition to the net magnetic polarization of the conduction electrons an oscillating magnetic polarization with a period of half the Fermi wave length is observed. However, this oscillating magnetic polarization does not show the long range behavior of Rudermann-Kittel-Kasuya-Yosida oscillations because the oscillations don't extend beyond the Kondo radius. They represent an internal electronic structure of the Kondo impurity in a magnetic field. PACS: 75.20.Hr, 71.23.An, 71.27.+

A New Superwind Wolf-Rayet Galaxy Mrk 1259

We report the discovery of a starburst-driven wind (superwind) from the starburst nucleus galaxy Mrk 1259. The estimated number ratio of Wolf-Rayet (WR) to O stars amounts to ~0.09. While the nuclear emission-line region is due to usual photoionization by massive stars, the circumnuclear emission-line regions show anomalous line ratios that can be due to cooling shocks. Since the host galaxy seems to be a face-on disk galaxy and the excitation conditions of the circumnuclear emission-line regions show the spatial symmetry, we consider that we are seeing the superwind nearly from a pole-on view. Cooling shock models may explain the observed emission line ratios of the circumnuclear regions although a factor of 2 overabundance of nitrogen is necessary. All these suggest that the high-mass enhanced starburst occurred ~5X10^6 years ago in the nuclear region of Mrk 1259.Comment: To be published in the Astrophysical Journal Letters, 15 pages, 4 figure

On the Energy-Momentum Tensor of the Scalar Field in Scalar--Tensor Theories of Gravity

We study the dynamical description of gravity, the appropriate definition of the scalar field energy-momentum tensor, and the interrelation between them in scalar-tensor theories of gravity. We show that the quantity which one would naively identify as the energy-momentum tensor of the scalar field is not appropriate because it is spoiled by a part of the dynamical description of gravity. A new connection can be defined in terms of which the full dynamical description of gravity is explicit, and the correct scalar field energy-momentum tensor can be immediately identified. Certain inequalities must be imposed on the two free functions (the coupling function and the potential) that define a particular scalar-tensor theory, to ensure that the scalar field energy density never becomes negative. The correct dynamical description leads naturally to the Einstein frame formulation of scalar-tensor gravity which is also studied in detail.Comment: Submitted to Phys. Rev D15, 10 pages. Uses ReVTeX macro

Gap to Transition Temperature Ratio in Density Wave Ordering: a Dynamical Mean Field Study

We use the dynamical mean-field method to determine the origin of the large ratio of the zero temperature gap to the transition temperature observed in most charge density wave materials. The method is useful because it allows an exact treatment of thermal fluctuations. We establish the relation of the dynamical mean-field results to conventional diagrammatics and thereby determine that in the physically relevant regime the origin of the large ratio is a strong inelastic scattering.Comment: 4 figure

Coulomb and quantum oscillator problems in conical spaces with arbitrary dimensions

The Schr\"odinger equations for the Coulomb and the Harmonic oscillator potentials are solved in the cosmic-string conical space-time. The spherical harmonics with angular deficit are introduced. The algebraic construction of the harmonic oscillator eigenfunctions is performed through the introduction of non-local ladder operators. By exploiting the hidden symmetry of the two-dimensional harmonic oscillator the eigenvalues for the angular momentum operators in three dimensions are reproduced. A generalization for N-dimensions is performed for both Coulomb and harmonic oscillator problems in angular deficit space-times. It is thus established the connection among the states and energies of both problems in these topologically non-trivial space-times.Comment: 15 page