Introduction: BMP and Wnt pathways are crucial for bone formation [Eyckmans, 2009]. However, the dynamic details of how the BMP and Wnt pathways influence each other are not fully elucidated.

Mathematical models are interesting tools to study pathways and their interactions. In the proposed model  we focus on the dynamical interaction between  the BMP and Wnt pathways and the way they determine the switch in osteogenic precursor cells between the Sox9 (proliferation) and Runx2 (hypertrophy) program via β-catenin [Zou, 2006].

Materials and Methods: Figure 1 shows a schematic representation of the proposed model, clearly showing the role of β-catenin as switch between the Runx2 and Sox9 program.  The model consists of two main parts.  The first submodel is based on a previously developed model of the crosstalk between BMP and Wnt which will regulate the amount of β-catenin in the nucleus [Geris, 2010]. The second submodel focusses on the switch between the Runx2 and the Sox9 and has been mathematically designed to demonstrate bistable behaviour for specific parameter sets [Yao, 2011 ]. Both submodels are systems of ordinary differential equations, based on the law of mass action and rate kinetics, and have been implemented in Matlab. An extensive screening [Yao, 2011 ] of the parameter space has been carried out to define those parameters sets for which submodel 2 exhibits bistable behaviour.

Results and discussion: Figure 2 shows the influence of BMP and Wnt on the transition from the proliferative program (Sox9 positive) to the hypertrophy program (Runx2 positive).  Upon activation of the Wnt pathway, β catenin is upregulated and as a result the switch towards hypertrophy will take place, in agreement with experimental results available in the literature.  Further activation of BMP will inhibit the transition of β-catenin to the nucleus (only mutual inhibition between Wnt and BMP was incorporated in submodel 1) but the switch is irreversible.  Additional simulations are being carried out and experimental work is underway to corroborate these preliminary results and to further investigate the model’s parameter space.

Acknowledgement: This study was supported by the Belgian National Fund for Scientific Research (FNRS) and the European Research Council. This work is part of Prometheus, the Leuven R&D Division of Skeletal Tissue Engineering of the KU Leuven: http://www.kuleuven.be/prometheus.

References: Eyckmans et all, 2009, Journal of Cellular and Molecular Medecine, 14:1845-1856; Geris et al, 2010, Termis-EU Galway; Yao et al, 2011, Molecular Systems Biology, 7:485 ; Zou et al, 2006, Adv Exp Med Biol. 585:431-41 ;