title: The systems biology simulation core algorithm.
abstract: BACKGROUND
  With the increasing availability of high dimensional time course data for metabolites, genes, and fluxes, the mathematical description of dynamical systems has become an essential aspect of research in systems biology. Models are often encoded in formats such as SBML, whose structure is very complex and difficult to evaluate due to many special cases.
  
  
  RESULTS
  This article describes an efficient algorithm to solve SBML models that are interpreted in terms of ordinary differential equations. We begin our consideration with a formal representation of the mathematical form of the models and explain all parts of the algorithm in detail, including several preprocessing steps. We provide a flexible reference implementation as part of the Systems Biology Simulation Core Library, a community-driven project providing a large collection of numerical solvers and a sophisticated interface hierarchy for the definition of custom differential equation systems. To demonstrate the capabilities of the new algorithm, it has been tested with the entire SBML Test Suite and all models of BioModels Database.
  
  
  CONCLUSIONS
  The formal description of the mathematics behind the SBML format facilitates the implementation of the algorithm within specifically tailored programs. The reference implementation can be used as a simulation backend for Java™-based programs. Source code, binaries, and documentation can be freely obtained under the terms of the LGPL version 3 from http://simulation-core.sourceforge.net. Feature requests, bug reports, contributions, or any further discussion can be directed to the mailing list simulation-core-development@lists.sourceforge.net.
authors.affiliation: Center for Bioinformatics Tuebingen (ZBIT), University of Tuebingen, Tübingen, Germany.
authors.forename: Roland
authors.initials: R
authors.lastname: Keller
authors.forename: Alexander
authors.initials: A
authors.lastname: Dörr
authors.forename: Akito
authors.initials: A
authors.lastname: Tabira
authors.forename: Akira
authors.initials: A
authors.lastname: Funahashi
authors.forename: Michael J
authors.initials: MJ
authors.lastname: Ziller
authors.forename: Richard
authors.initials: R
authors.lastname: Adams
authors.forename: Nicolas
authors.initials: N
authors.lastname: Rodriguez
authors.forename: Nicolas
authors.initials: N
authors.lastname: Le Novère
authors.forename: Noriko
authors.initials: N
authors.lastname: Hiroi
authors.forename: Hannes
authors.initials: H
authors.lastname: Planatscher
authors.forename: Andreas
authors.initials: A
authors.lastname: Zell
authors.forename: Andreas
authors.initials: A
authors.lastname: Dräger
mesh_terms: D000465:Algorithms; D015233:Models, Statistical; D049490:Systems Biology / Q000379:methods*