A new validated mathematical model of the Wnt signalling pathway predicts effective combinational therapy by sFRP and Dkk.

The Wnt signalling pathway controls cell proliferation and differentiation, and its deregulation is implicated in different diseases including cancer. Learning how to manipulate this pathway could substantially contribute to the development of therapies. We developed a mathematical model describing the initial sequence of events in the Wnt pathway, from ligand binding to β-catenin accumulation, and the effects of inhibitors, such as sFRPs (secreted Frizzled-related proteins) and Dkk (Dickkopf). Model parameters were retrieved from experimental data reported previously. The model was retrospectively validated by accurately predicting the effects of Wnt3a and sFRP1 on β-catenin levels in two independent published experiments (R(2) between 0.63 and 0.91). Prospective validation was obtained by testing the model's accuracy in predicting the effect of Dkk1 on Wnt-induced β-catenin accumulation (R(2)≈0.94). Model simulations under different combinations of sFRP1 and Dkk1 predicted a clear synergistic effect of these two inhibitors on β-catenin accumulation, which may point towards a new treatment avenue. Our model allows precise calculation of the effect of inhibitors applied alone or in combination, and provides a flexible framework for identifying potential targets for intervention in the Wnt signalling pathway.