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How to Formalise the Meaning of a Bio-Model: A Case Study
Author(s): Christian Knüpfer, Clemens Beckstein, Peter Dittrich
Affiliations: Institute of Computer Science, Friedrich-Schiller-University Jena, Germany
Contact: Christian Knüpfer, firstname.lastname@example.org
Keywords: 'semantics of bio-models' 'meaning in systems biology' 'computer-aided modelling'
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. This is something which hampers the development of computer-aided modelling in systems biology. Here, we discuss a framework for specifying the meaning of bio-models. We show 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. We illustrate our framework by sketching what must be considered for a formal semantics of two simple numerical models of the cell cycle.
A bio-model can be seen as a binary relation between a formal (mathematical or computational) expression and the modelled biological reality. This introduces two sides of the meaning of the bio-model: The mathematical expression bears meaning by itself without referring to the biological reality. It can be interpreted, analysed, and used in computational simulations without knowing what it represents. We call this side the intrinsic meaning of the bio-model. However, a bio-model is more than a pure syntactical formal expression: it describes a piece of biological reality and thereby also exhibits an extrinsic meaning. For both meaning sides of a bio-model three pragmatic meaning levels can be identified: (1) The meaning regarding the model as a whole accounts for its intention. (2) The meaning regarding the components of the model accounts for its structure. (3) The meaning regarding the dynamics of the model accounts for its behaviour. The extrinsic/intrinsic sides of the three levels together form the six meaning facets. The meaning facets are views at the meaning of a bio-model from different perspectives. We claim that a formal semantics of a bio-model has to incorporate all of these meaning facets and the relations between them.
In order to make the notion of the meaning facets of bio-models more concrete Table 1 shows typical questions for each of the meaning facets. The answers to these questions have to be formalised in order to arrive at a semantic description of a bio-model.
|Which mathematical formalism is used? How is the formalism interpreted and executed? How is the formalism used to simulate the behaviour?||Which biological system is addressed? What does the model stand for in the biological reality? What is the aim of the model?|
|What is the structure of the mathematical expression? What are the mathematical entities of the model (equations, terms, variables)?||Which biological mechanism is proposed by the model? What are the modelled biological objects and processes? How do model entities map to biological reality?|
|Which simulation results does the model show? Which parameter settings are used therefore? What are characteristic types of dynamical behaviour (e.g. attractors)?||Which biological phenomenon correlates with which type of dynamical behaviour? Which experimental data are reproduced by simulation results?|
In order to illustrate the conceptual framework of the meaning facets we sketch the meaning of two cell cycle models by Tyson :
The following table shows the BioModels  entry for Tyson's cell cycle model (Model 1) after it has been extended according to our meanings facets (emphasised in green). In  we show how the meaning of both Tyson bio-models can be formalised.
The meaning facets suggested here can serve as a guideline to arrive at reasonable formal semantics of bio-models. We illustrate this using Tyson's cell cycle models. Our meaning facets can be seen as a methodological commitment that should be followed when modelling biological processes. They offer a set of criteria for systematically constructing bio-models and for reconstructing their meaning. Our approach also addresses aspects of the meaning that existing approaches did not, e.g. the meaning of behaviours and the meaning of aggregated abstract model variables. This can be the basis for a new class of knowledge-based modelling tools that helps the working biologist to understand bio-systems.
- Tyson, J.: Modeling the cell division cycle: cdc2 and cyclin interactions. Proc Natl Acad Sci USA 88(16) (1991), pp.7328-7332
- Le Novére, N., Bornstein, B., Broicher, A., et al.: BioModels Database: A free, centralized database of curated, published, quantitative kinetic models of biochemical and cellular systems. Nucleic Acids research 34(Database issue) (2006), pp.689-691
- Knüpfer, C., Beckstein, C., Dittrich, P.: Towards a Semantics of Bio-Models A Case Study Formalising the Meaning of Two Cell Cycle Models, submitted (2006)
- Knüpfer, C., Beckstein, C., Dittrich, P.: Towards a semantic description of biomodels: Meaning facets -- a case study. In: Proceedings of the Second International Symposium on Semantic Mining in Biomedicine (SMBM 2006), Jena, April 9th - 12th. CEUR-WS, Aachen, RWTH University (2006), pp.97-100