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Bioinformatics Advance Access originally published online on May 11, 2007
Bioinformatics 2007 23(19):2638-2640; doi:10.1093/bioinformatics/btm245
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© The Author 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

PLMaddon: a power-law module for the MatlabTM SBToolbox

Julio Vera *, Cheng Sun , Yvonne Oertel and Olaf Wolkenhauer

Systems Biology and Bioinformatics Group, Department of Computer Science. University of Rostock, 18051 Rostock, Germany

*To whom correspondence should be addressed.


   ABSTRACT
TOP
 ABSTRACT
1 INTRODUCTION
 2 FEATURES
 3 IMPLEMENTATION
 ACKNOWLEDGEMENTS
 REFERENCES
 

Summary: PLMaddon is a General Public License (GPL) software module designed to expand the current version of the SBToolbox (a Matlab TM toolbox for systems biology; www.sbtoolbox.org) with a set of functions for the analysis of power-law models, a specific class of kinetic models, set in ordinary differential equations (ODE) and in which the kinetic orders can have positive/negative non-integer values. The module includes functions to generate power-law Taylor expansions of other ODE models (e.g. Michaelis-Menten type models), as well as algorithms to estimate steady-states. The robustness and sensitivity of the models can also be analysed and visualized by computing the power-law's logarithmic gains and sensitivities.

Availability: PLMaddon is an open source module for the analysis of power-law models based on the SBToolbox. The latest version of PLMaddon is freely available from:

www.sbi.uni-rostock.de/plmaddon

The website contains a tutorial with examples, as well as an interactive introductory course on power-law models in systems biology.

Contact: olaf.wolkenhauer{at}uni-rostock.de


   1 INTRODUCTION
TOP
 ABSTRACT
 1 INTRODUCTION
2 FEATURES
 3 IMPLEMENTATION
 ACKNOWLEDGEMENTS
 REFERENCES
 
Systems biology is an emerging field in which knowledge coming from experimental biology and systems theory are merged to facilitate the analysis of essential properties of living systems. The complexity of these systems, the novelty of analytical methods used and the special nature of the data used, require the development of new software tools. On the other hand, one of the key features of this new scientific field is its interdisciplinarity: an increasing number of new researchers are coming to systems biology from a purely experimental background and therefore it is necessary software adapted to their requirements. There is a need for computationally powerful and open/expandable tools, which at the same time must be easy-to-use.

The SBToolbox is a recent MatlabTM (2007) toolbox for systems biology (Schmidt and Jirstrand, 2005) developed for the analysis of biochemical systems modelled by ODEs. It was developed as a user-friendly and user-extensible environment that facilitates the exchange of analytical methods and models. The PLMaddon is a module, based on the SBToolbox, extending its functionality by including additional features for the analysis of power-law models. Power-law models are a modelling framework in which biochemical processes are modelled through power-law expansions in the system variables, leading to the following structure:


Formula

where Xi represents any of the nd dependent variables of the model (e.g. metabolite concentrations, proteins or phosphoprotein concentrations or levels of gene expression). Here, the biochemical rate j is expanded as product of a rate constant ({gamma}j) and the p variables of the system to characteristic kinetic orders (gjk). cij are the stoichiometric coefficients of the system that account for mass conservation. The essential property of power-law models that distinguishes them from other ODE models is that kinetic orders can have positive non-integer values, even negative values when inhibition is modelled. Power-law models have been used for decades in the analysis of metabolic systems (Voit, 2000), gene networks (Savageau, 2000), and recently also in cell signalling systems (Vera et al., 2006). There are two main classes of power-law models: S-system models, a subclass of simplified power-law models in which there are only net (aggregated) input and net (aggregated) output fluxes (or rates) in each differential equation, and Generalised Mass Action models (GMA models) in which this generalised aggregation is not implemented and every biochemical process described is modelled with a separated power-law term.

There are a few software tools developed for the analysis of power-law models. The PLAS software (www.dqb.fc.ul.pt/docentes/aferreira/plas.html) is a stand-alone tool which allows the basic analysis and simulation of power-law models, but it has not been updated in recent times and lacks several important functions (e.g. routines for import/export SBML models). The MetMAP toolbox (Vera et al., 2003) is a freely available Matlab toolbox that allows the analysis, simulation and optimization of S-system models but cannot deal with GMA models. Finally, the BSTlab is a Matlab toolbox which allows the basic analysis or simulation of any power-law model and includes SBML import/export routines, but is not able to perform optimization (www.bioinformatics.musc.edu/bstlab). The distinctive features of PLMaddon are integration and extensibility. By integrating the PLMaddon as an addon to the SBToolbox, the user can perform basic power-law analyses as well as other mathematical analysis provided by the SBToolbox (e.g. bifurcation analysis, model reduction, etc.). Moreover, the addon is open code and the user can extend the tool by including additional power-law analysis features. The toolbox is supported by a user's manual, a complete webpage with examples and an on-line tutorial on power-law models the purpose of which is to facilitate the use of the software for beginners.


Figure 1
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  		Fig. 1. Interaction between the basic functions integrated in the PLMaddon in the case of a GMA power-law model.

 

   2 FEATURES
TOP
 ABSTRACT
 1 INTRODUCTION
 2 FEATURES
3 IMPLEMENTATION
 ACKNOWLEDGEMENTS
 REFERENCES
 
The PLMaddon incorporates some functions specifically developed for the analysis of power-law models. The module is able to analyse any kind of power-law model (either S-system or GMA). The power-law models can be implemented either using the SBToolbox function SBedit or from a set of matrices and vectors containing the essential information about the model (stoichiometric matrix, kinetic orders matrices, steady-state value of variables, rate constants vectors). An additional function has been included (pl_estimate) to obtain a power-law Taylor expansion of other ODE models (e.g. Michaelis-Menten type models) around a steady-state of the system. This strategy has proven useful for the analysis of metabolic systems (Voit, 2000). In any case, the information is converted into the standard data structure of SBToolbox (SBmodel), which is used for the calculations, to save modifications in the model and allow the export to SBML format (Hucka et al., 2003).

Most of the functions implemented in the current version are for steady-state analysis. In case of S-system models, steady-states are estimated by applying a logarithmic transformation to the steady-state equations; this transformation linearizes the equations for the logarithm of the variables and makes them solvable using linear algebra (Voit, 2000). In case of GMA models, the application of a modified logarithmic transformation yields the equations that define the steady-states of the system partially linear for the logarithm of variables and biochemical rates (Torres and Voit, 2002); then, an iterative linearization of the remaining equations allows the easy calculation of steady-states.

Functions for stability analysis were implemented by taking advantage of the structural properties of power-law models to calculate the Jacobian matrix. We have included specific functions to compute power-law logarithmic gains (which predict the influence that changes of the independent variables have on the steady-state values of dependent variables and rates) as well as the assessment of the robustness (as a measure of the stability of the system properties with respect to perturbations in parameter values); in this vein, a function to compute the power-law's sensitivities (which measure the effect of changes in model parameters, either rate constants or kinetic orders) is also available. The structural properties of power-law models allow computing such properties using linear algebra. Additionally, a function that allows the easy visualization and analysis of logarithmic gains and sensitivities was also included. For further explanations about the methods used, visit www.sbi.uni-rostock.de/plmaddon.

We are currently including new functions that expand the analytical capabilities of the PLMaddon. The module is being adapted for the analysis of power-law models with moiety conservation equations. We are also considering the integration of additional functions especially developed for the parameter estimation in power-law models. Moreover, we are implementing specific functions for the mathematical optimization of the biochemical systems, which has proven its utility in the analysis of metabolic systems with biotechnological purposes (Vera et al., 2003).


   3 IMPLEMENTATION
TOP
 ABSTRACT
 1 INTRODUCTION
 2 FEATURES
 3 IMPLEMENTATION
ACKNOWLEDGEMENTS
 REFERENCES
 
The module was designed to allow a complete interaction with the basic distribution of SBToolbox. In this vein, the information about the model is extracted from the Sbmodel data structure and converted into a new specific data structure that contains the essential information about the power-law model (variables, state values, matrices of kinetic orders and vectors with rate constants). The functions for the analysis of power-law models extract the required information from this data structure and compute the results. Modifications in the model can be stored in the SBToolbox formatted text file and be reused. In this way, either the functions of the basic distribution or the functions of the PLMaddon can be used with the information contained in the Sbmodel data structure.

The PLMaddon requires at least MatlabTM R14 SP1 and runs under Windows, Linux, Unix and MAC OS machines. The pl_estimate function requires the MatlabTM Symbolic Math Toolbox.


   ACKNOWLEDGEMENTS
TOP
 ABSTRACT
 1 INTRODUCTION
 2 FEATURES
 3 IMPLEMENTATION
 ACKNOWLEDGEMENTS
REFERENCES
 
The authors appreciate the comments they have received from Ulf Schmitz (Rostock) and Dr Henning Schmidt from the Fraunhofer Chalmers Center (Gothenburg, Sweden). This work was supported by a STREP research grant from the European Commission (6th Framework program, COSBICS project, contract number LSHG-CT-2004-512060).

Conflict of Interest: none declared.


   FOOTNOTES
 
Associate Editor: Thomas Lengauer

Received on January 8, 2007; revised on April 11, 2007; accepted on April 30, 2007

   REFERENCES
TOP
 ABSTRACT
 1 INTRODUCTION
 2 FEATURES
 3 IMPLEMENTATION
 ACKNOWLEDGEMENTS
 REFERENCES
 

    Hucka M, et al. The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models. Bioinformatics (2003) 19:524–531.[Abstract/Free Full Text]

    Matlab (2007) The MathWorks, Inc. Natick, MA (US). www.mathworks.com.

    Savageau MA. Design principles for elementary gene circuits: elements, methods, and examples. Chaos (2000) 11:142–159.[CrossRef][Web of Science]

    Schmidt H, Jirstrand M. Systems Biology Toolbox for MATLABTM: a computational platform for research in Systems Biology. Bioinformatics (2005) doi 10.1093/bioinformatics/bti799.

    Torres NV, Voit EO. Pathway Analysis and Optimization in Metabolic Engineering (2002) Cambridge University Press. UK.

    Vera J, et al. Multicriteria optimization of biochemical systems by linear programming: application to production of ethanol by Saccharomyces cerevisiae. Biotechnol. Bioengin. (2003) 83:335–343.[CrossRef][Web of Science][Medline]

    Vera J, et al. Power-law models of signal transduction pathways. Cell. Signal (2006) doi: 10.1016/j.cellsig.2007.01.029.

    Vera J, Torres NV. MetMAP: an integrated Matlab. In Silico. Biol. (2003) 4:0010.

    Voit EO. Computational Analysis of Biochemical Systems. A practical Guide for Biochemists and Molecular Biologists (2000) UK: Cambridge University Press.


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