Mathematical model of TGF-β signalling: feedback coupling is consistent with signal switching

Background: Transforming growth factor beta (TGF-beta) signalling regulates the development of embryos and tissue homeostasis in adults. In conjunction with other oncogenic changes, long-term perturbation of TGF-beta signalling is associated with cancer metastasis. Although TGF-beta signalling can be complex, many of the signalling components are well defined, so it is possible to develop mathematical models of TGF-beta signalling using reduction and scaling methods. The parameterization of our TGF-beta signalling model is consistent with experimental data. Results: We developed our mathematical model for the TGF-beta signalling pathway, i.e. the RF-model of TGF-beta signalling, using the rapid equilibrium assumption to reduce the network of TGF-beta signalling reactions based on the time scales of the individual reactions. By adding time-delayed positive feedback to the inherent time-delayed negative feedback for TGF-beta signalling. We were able to simulate the sigmoidal, switch-like behaviour observed for the concentration dependence of long-term (>3 hours) TGF-beta stimulation. Computer simulations revealed the vital role of the coupling of the positive and negative feedback loops on the regulation of the TGF-beta signalling system. The incorporation of time-delays for the negative feedback loop improved the accuracy, stability and robustness of the model. This model reproduces both the short-term and long-term switching responses for the intracellular signalling pathways at different TGF-beta concentrations. We have tested the model against experimental data from MEF (mouse embryonic fibroblasts) WT, SV40-immortalized MEFs and Gp130F/F MEFs. The predictions from the RF-model are consistent with the experimental data. Conclusions: Signalling feedback loops are required to model TGF-beta signal transduction and its effects on normal and cancer cells. We focus on the effects of time-delayed feedback loops and their coupling to ligand stimulation in this system. The model was simplified and reduced to its key components using standard methods and the rapid equilibrium assumption. We detected differences in short-term and long-term signal switching. The results from the RF-model compare well with experimental data and predict the dynamics of TGF-beta signalling in cancer cells with different mutations.