| Resumo: |
Computational models are becoming more and more the central scientific paradigm for understanding the complexity of living systems. With the increasing number and size of these models there is a growing need for model reuse and exchange. Furthermore, detailed models are not manageable without computer support. There are efforts to formalise the mathematical structure of models (e.g. SBML) and to standardise the kinetic and biological meaning of model components (e.g. SBO, GO, UniProt). However, formalising only the structure of computational models is not sufficient to easily exchange and reuse models and to achieve full computer support for modelling. We also need to formalise the pragmatical and dynamical aspects of models.

For this purpose we propose two ontologies: The _Kinetic Simulation Algorithm Ontology_ (KiSAO) and the _TErminology for the Description of DYnamics_ (TEDDY). KiSAO covers algorithms used for simulation of computational models. The ontology classifies and puts into context existing simulation algorithms. For the classification, it uses several criteria such as deterministic/stochastic or spatial/nonspatial. The aim of TEDDY is to provide terms for describing and characterising dynamical behaviours, observable dynamical phenomena, and control elements of biological models and biological systems in Systems Biology and Synthetic Biology.

We demonstrate how these new ontologies can extend the formalisation of models beyond structure, using the well-known repressilator model as an example. The simulation results depend _pragmatically_ on the used algorithm: We compare the simulation results of the deterministic _Livermore solver for ordinary differential equations_ (KiSAO:0000071) to the simulation results of the stochastic _Gibson and Bruck’s next reaction method_ (KiSAO:0000027). The simulation results depend _dynamically_ on the parameter setting: While parameter  (maximum number of produced proteins per promotor) is increased the modelled dynamical system undergoes a _Supercritical Hopf Bifurcation_ (TEDDY_0000074). Below the critical value of  the system exhibits _Damped Oscillation_ (TEDDY_0000063) converging to a _Stable Spiral Point_ (TEDDY_0000126). Above the bifurcation the system possesses a Stable _Limit Cycle_ (TEDDY_0000114), i.e. it shows Sustained Oscillation. The _Negative Feedback_ (TEDDY_0000034) of the system is a necessary precondition for the ability of the system to oscillate.

For details on KiSAO see the "MIASE project page":http://sourceforge.net/projects/miase, for details on TEDDY see the "project page":http://sourceforge.net/projects/teddyontology.
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