General principle to construct a CPN for an arbitrary ODEs.

<p> denotes the domain of the function .</p

Arbitrary complex kinetics may hide essential structure.

<p>The example is an excerpt from the network model discussed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0014284#pone.0014284-Brightman1" target="_blank">[33]</a>. (A) Structure as suggested by the schematic representation in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0014284#pone.0014284-Brightman1" target="_blank">[33]</a> and the list of reactions in the model's SBML format (Created by COPASI version 4.0 (Build 18) on 2006-10-24); (B) Correct structure, which is hidden in the kinetics of reactions 23 and 25. The two structures obviously differ in their discrete behaviour.</p

Thymus indet.

<p>This illustrates the need for symbolic parameters in order to avoid confusion when inferring the structure.</p

Beginning of the Appendix II of [<b>30</b>] describing the full ODE model of that article.

<p>The 68 ODEs actually allow the extraction of a unique model fulfilling the three established conditions. It not only correctly reflects the structure described in the article, but also avoids the typos introduced in the hand-written model 151 of the BioModels database; hand-typing an SBML model for that many ODEs with numerous parameters is definitely error-prone.</p

<b>Figure 1</b> of [<b>29</b>] representing a schematic view of the JAK/STAT pathway.

<p>The incorrect structure of the corresponding SBML models (93 and 94) of the BioModels database can be automatically fixed by going back to the differential equations and extracting the unique structure fulfilling our three conditions. It then correctly includes the reversibility of reactions (1), (2), (3), (6), etc. highlighted in red, and absent from the BioModels database version.</p

Another possible structure for the same equations as for <b>Figure 3</b>, as explained in Example 3.

<p>Even with symbolic parameters and pure mass action kinetics, if it is allowed to use the same parameter for two distinct reactions with the same reactants, one can obtain several structures for the same ODEs.</p

Decomposition of a fuzzy number into its <i>α</i>-cuts.

<p>Decomposition of a fuzzy number into its <i>α</i>-cuts.</p

The membership function of the steady mean for each species of the yeast polarization model in the setting of one fuzzy parameter <i>k</i>₆ = (0.08, 0.1, 0.12).

<p>The membership function of the steady mean for each species of the yeast polarization model in the setting of one fuzzy parameter <i>k</i>₆ = (0.08, 0.1, 0.12).</p

An FSPN model for yeast polarization based on the eight reactions given above.

<p>An FSPN model for yeast polarization based on the eight reactions given above.</p

A triangular fuzzy number.

<p>A triangular fuzzy number.</p