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.
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:
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.
Phase 3: Formal Description of the Model SemanticsWork in progress...
Phase 4: Reasoning by Means of the Formal Model SemanticsFuture work...
ReferencesTyson, 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)