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Formal Semantics of Dynamical Bio-Models
Systems Biology reconstructs biological phenomena in order to develop explanatory models of living systems. These models are represented precisely in terms of mathematical expressions. However, the meaning of a model usually is not formally specified but only described in natural language.

In this project we develop a framework for specifying the meaning of bio-models.

So far we have shown that semantics appears on different levels: the meaning of the model as a whole, the meaning of the model's components, and the meaning of the model's behaviour. Each level has an intrinsic and extrinsic facet.

Involved Persons:


Christian Knüpfer
Artificial Intelligence Group
Department of Mathematics and Computer Science
Friedrich-Schiller-University Jena
D-07743 Jena

Case Study: Tyson's Models of the Cell Cycle

Description of the Models

We use the following two ODE-models as a case study for the formalisation of the semantics of bio-models. The models are from Tyson (1991). Both models describe the formation and activation of the maturation promoting factor (MPF), a hetero dimer made of the two proteins cyclin and cdc2. Model 1 consists of a set of ordinary differential equations (ODEs) where each equation models the temporal evolution of the concentrations of one of the involved substances wrt. the concentrations of the other substances. Involved substances are: cdc2 (C2), phosphorylated cdc2 (CP), inactive MPF (pM), active MPF (M), cyclin (Y), phosphorylated cyclin (YP), total cdc2 (CT), adenosine triphosphate (~P), and amino acids (aa). Model 2 is a mathematical abstraction of Model 1 under certain additional biological assumptions. The ki are kinetic rate coefficients.


Phase 1: Informal Characterisation of the Model Meaning

In order to get a first expression how the semantics of a bio-model may look like we investigate the meaning of Model 1 from the perspective of a human biologist. We structure the resulting information by means of our Meaning Facets. The resulting Table 1 can be seen as an extension of the corresponding entry BIOMD0000000005 in the BioModels Database wrt. the following aspects:

  1. The mathematical (intrinsic) meaning is not considered in BioModels Database at all.
  2. Tyson identifies three possible modes of behaviours of both models (cf. Tyson (1991)) and assigns biological phenomena to this modes. This very important aspect of the meaning of Model 1 is not regarded in the BioModels Database but in the behavioural facets in Table 1.

Extensions of the entry of the BioModels Database are emphasised with green background in Table 1.

Table 1. Informal Characterisation of the Meaning of Model 1.
A click on the thumbnail opens a full view of the table (pdf).

Phase 2: Semi-Formal Specification of the Model Semantics

The Table 2 represent both elementary facts of the semantics of the Tyson models and the grounding of the biological meaning by means of external references (hyperlinks). They make reference to and contribute part of a Model Ontology (MO) that formally describes concepts typically used in biological modelling. We call a fact elementary if it cannot be inferred from other facts. Thus the tables provide a minimal commitment to the semantics of both models which is necessary to account for all meaning facets and the relations among them.

Table 2 contains both the intrinsic (red IDs in the first column) and the extrinsic (black IDs) elementary facts. Because of the clean semantics of mathematical expressions most of the intrinsic structural meaning can be inferred from the given ODE systems. Therefor the intrinsic meaning structure is sparse in Table 2, especially for Model 1. Extended tables containing also important inferred facts will coming soon.

Table 2. Semi-Formal Specification of the Semantics of Model 1 and Model 2.
A click on the thumbnail opens a full view of the table (pdf).

Phase 3: Formal Description of the Model Semantics

Work in progress...

Phase 4: Reasoning by Means of the Formal Model Semantics

Future work...


Tyson, JJ. (1991)
Modeling the cell division cycle: cdc2 and cyclin interactions
In: Proc Natl Acad Sci USA, 88(16):7328-7332, Aug 1991.
online available (pdf)


  1. Christian Knüpfer. Struktur, Funktion und Verhalten dynamischer Modelle der Systembiologie: Formale Wissensrepräsentation als Grundlage für computergestützte Modellierung und Simulation, 2015. [ bib | online ]
  2. Christian Knüpfer and Clemens Beckstein. Function of dynamic models in systems biology: Linking structure to behaviour. Journal of Biomedical Semantics, 4(1):24, 2013. [ bib | DOI | online ]
  3. Christian Knüpfer, Clemens Beckstein, Peter Dittrich, and Nicolas Le Novère. Structure, function, and behaviour of computational models in systems biology. BMC Systems Biology, 7(1):43, 2013.
    bib | DOI | online ]
  4. Clemens Beckstein and Christian Knüpfer. Function of bio-models: Linking structure to behaviour. In M. Boeker, H. Herre, R. Hoehndorf, and F. Loebe, editors, Proceedings of the 4th Workshop of the GI Group "`Ontologies in Biomedicine and Life Sciences"' (OBML), 2012.
    bib | online ]
  5. Christian Knüpfer, Clemens Beckstein, and Peter Dittrich. How to formalise the meaning of a bio-model: A case study. In BioSysBio 2007: Systems Biology, Bioinformatics, Synthetic Biology, Meeting abstracts. 11.-13. January Manchester, UK, volume 1, Suppl 1 of BMC Systems Biology, page 28. BioMed Central, 2007.
    bib | DOI ]
  6. Nicolas Le Novère, Camille Laibe, Melanie Courtot, Christian Knüpfer, and Michael Hucka. Semantic annotation of kinetic models in systems biology. In The Eighth International Conference on Systems Biology (ICSB), page G28, 2007.
    bib | online ]
  7. Nicolas Le Novère, Camille Laibe, Melanie Courtot, Christian Knüpfer, and Michael Hucka. Semantic annotation of kinetic models in systems biology. In 15th Annual International Conference on Intelligent Systems for Molecular Biology, page C126, 2007.
    bib | online ]
  8. Christian Knüpfer, Clemens Beckstein, and Peter Dittrich. Towards a semantic description of bio-models: Meaning facets -- a case study. In Sophia Ananiadou and Juliane Fluck, editors, Proceedings of the Second International Symposium on Semantic Mining in Biomedicine (SMBM 2006), number 177 in CEUR Workshop Proceedings, pages 97--100. Sun SITE Central Europe, RWTH Aachen, 2006.
    bib | online ]