SBMLsqueezer: A CellDesigner plug-in to generate kinetic rate equations for biochemical networks

<p>Abstract</p> <p>Background</p> <p>The development of complex biochemical models has been facilitated through the standardization of machine-readable representations like SBML (Systems Biology Markup Language). This effort is accompanied by the ongoing development of the human-readable diagrammatic representation SBGN (Systems Biology Graphical Notation). The graphical SBML editor CellDesigner allows direct translation of SBGN into SBML, and vice versa. For the assignment of kinetic rate laws, however, this process is not straightforward, as it often requires manual assembly and specific knowledge of kinetic equations.</p> <p>Results</p> <p>SBMLsqueezer facilitates exactly this modeling step via automated equation generation, overcoming the highly error-prone and cumbersome process of manually assigning kinetic equations. For each reaction the kinetic equation is derived from the stoichiometry, the participating species (e.g., proteins, mRNA or simple molecules) as well as the regulatory relations (activation, inhibition or other modulations) of the SBGN diagram. Such information allows distinctions between, for example, translation, phosphorylation or state transitions. The types of kinetics considered are numerous, for instance generalized mass-action, Hill, convenience and several Michaelis-Menten-based kinetics, each including activation and inhibition. These kinetics allow SBMLsqueezer to cover metabolic, gene regulatory, signal transduction and mixed networks. Whenever multiple kinetics are applicable to one reaction, parameter settings allow for user-defined specifications. After invoking SBMLsqueezer, the kinetic formulas are generated and assigned to the model, which can then be simulated in CellDesigner or with external ODE solvers. Furthermore, the equations can be exported to SBML, LaTeX or plain text format.</p> <p>Conclusion</p> <p>SBMLsqueezer considers the annotation of all participating reactants, products and regulators when generating rate laws for reactions. Thus, for each reaction, only applicable kinetic formulas are considered. This modeling scheme creates kinetics in accordance with the diagrammatic representation. In contrast most previously published tools have relied on the stoichiometry and generic modulators of a reaction, thus ignoring and potentially conflicting with the information expressed through the process diagram. Additional material and the source code can be found at the project homepage (URL found in the Availability and requirements section).</p

Critical dimensions for random walks on random-walk chains

The probability distribution of random walks on linear structures generated by random walks in $d$-dimensional space, $P_d(r,t)$, is analytically studied for the case $\xi\equiv r/t^{1/4}\ll1$. It is shown to obey the scaling form $P_d(r,t)=\rho(r) t^{-1/2} \xi^{-2} f_d(\xi)$, where $\rho(r)\sim r^{2-d}$ is the density of the chain. Expanding $f_d(\xi)$ in powers of $\xi$, we find that there exists an infinite hierarchy of critical dimensions, $d_c=2,6,10,\ldots$, each one characterized by a logarithmic correction in $f_d(\xi)$. Namely, for $d=2$, $f_2(\xi)\simeq a_2\xi^2\ln\xi+b_2\xi^2$; for $3\le d\le 5$, $f_d(\xi)\simeq a_d\xi^2+b_d\xi^d$; for $d=6$, $f_6(\xi)\simeq a_6\xi^2+b_6\xi^6\ln\xi$; for $7\le d\le 9$, $f_d(\xi)\simeq a_d\xi^2+b_d\xi^6+c_d\xi^d$; for $d=10$, $f_{10}(\xi)\simeq a_{10}\xi^2+b_{10}\xi^6+c_{10}\xi^{10}\ln\xi$, {\it etc.\/} In particular, for $d=2$, this implies that the temporal dependence of the probability density of being close to the origin $Q_2(r,t)\equiv P_2(r,t)/\rho(r)\simeq t^{-1/2}\ln t$.Comment: LATeX, 10 pages, no figures submitted for publication in PR

LiCaFeF6 A zero strain cathode material for use in Li ion batteries

A new zero strain LiCaFeF6 cathode material for reversible insertion and extraction of lithium ions is presented. LiCaFeF6 is synthesized by a solid state reaction and processed to a conductive electrode composite via high energy ball milling. In the first cycle, a discharge capacity of 112 mAh g amp; 8315; is achieved in the voltage range from 2.0 V to 4.5 V. The electrochemically active redox couple is Fe3 amp; 8314; Fe2 amp; 8314; as confirmed by Mössbauer spectroscopy and X ray absorption spectroscopy. The compound has a trigonal colquiriite type crystal structure space group . By means of in situ and ex situ XRD as well as X ray absorption fine structure spectroscopy a reversible response to Li uptake release is found. For an uptake of 0.8 mol Li per formula unit only minimal changes occur in the lattice parameters causing a total change in unit cell volume of less than 0.5 . The spatial distribution of cations in the crystal structure as well as the linkage between their corresponding fluorine octahedra is responsible for this very small structural response. With its zero strain behaviour this material is expected to exhibit only negligible mechanical degradation. It may be used as a cathode material in future lithium ion batteries with strongly improved safety and cycle lif

Order statistics of the trapping problem

When a large number N of independent diffusing particles are placed upon a site of a d-dimensional Euclidean lattice randomly occupied by a concentration c of traps, what is the m-th moment of the time t_{j,N} elapsed until the first j are trapped? An exact answer is given in terms of the probability Phi_M(t) that no particle of an initial set of M=N, N-1,..., N-j particles is trapped by time t. The Rosenstock approximation is used to evaluate Phi_M(t), and it is found that for a large range of trap concentracions the m-th moment of t_{j,N} goes as x^{-m} and its variance as x^{-2}, x being ln^{2/d} (1-c) ln N. A rigorous asymptotic expression (dominant and two corrective terms) is given for for the one-dimensional lattice.Comment: 11 pages, 7 figures, to be published in Phys. Rev.

On the joint residence time of N independent two-dimensional Brownian motions

We study the behavior of several joint residence times of N independent Brownian particles in a disc of radius $R$ in two dimensions. We consider: (i) the time T_N(t) spent by all N particles simultaneously in the disc within the time interval [0,t]; (ii) the time T_N^{(m)}(t) which at least m out of N particles spend together in the disc within the time interval [0,t]; and (iii) the time {\tilde T}_N^{(m)}(t) which exactly m out of N particles spend together in the disc within the time interval [0,t]. We obtain very simple exact expressions for the expectations of these three residence times in the limit t\to\infty.Comment: 8 page

Standard Anatomical and Visual Space for the Mouse Retina: Computational Reconstruction and Transformation of Flattened Retinae with the Retistruct Package

The concept of topographic mapping is central to the understanding of the visual system at many levels, from the developmental to the computational. It is important to be able to relate different coordinate systems, e.g. maps of the visual field and maps of the retina. Retinal maps are frequently based on flat-mount preparations. These use dissection and relaxing cuts to render the quasi-spherical retina into a 2D preparation. The variable nature of relaxing cuts and associated tears limits quantitative cross-animal comparisons. We present an algorithm, "Retistruct," that reconstructs retinal flat-mounts by mapping them into a standard, spherical retinal space. This is achieved by: stitching the marked-up cuts of the flat-mount outline; dividing the stitched outline into a mesh whose vertices then are mapped onto a curtailed sphere; and finally moving the vertices so as to minimise a physically-inspired deformation energy function. Our validation studies indicate that the algorithm can estimate the position of a point on the intact adult retina to within 8° of arc (3.6% of nasotemporal axis). The coordinates in reconstructed retinae can be transformed to visuotopic coordinates. Retistruct is used to investigate the organisation of the adult mouse visual system. We orient the retina relative to the nictitating membrane and compare this to eye muscle insertions. To align the retinotopic and visuotopic coordinate systems in the mouse, we utilised the geometry of binocular vision. In standard retinal space, the composite decussation line for the uncrossed retinal projection is located 64° away from the retinal pole. Projecting anatomically defined uncrossed retinal projections into visual space gives binocular congruence if the optical axis of the mouse eye is oriented at 64° azimuth and 22° elevation, in concordance with previous results. Moreover, using these coordinates, the dorsoventral boundary for S-opsin expressing cones closely matches the horizontal meridian

Order statistics for d-dimensional diffusion processes

We present results for the ordered sequence of first passage times of arrival of N random walkers at a boundary in Euclidean spaces of d dimensions