Abstract
BackgroundTransforming growth factor β (TGF-β) signalling regulates the development of embryos and tissue homeostasis in adults. In conjunction with other oncogenic changes, long-term perturbation of TGF-β signalling is associated with cancer metastasis. Although TGF-β signalling can be complex, many of the signalling components are well defined, so it is possible to develop mathematical models of TGF-β signalling using reduction and scaling methods. The parameterization of our TGF-β signalling model is consistent with experimental data.ResultsWe developed our mathematical model for the TGF-β signalling pathway, i.e. the RF- model of TGF-β signalling, using the “rapid equilibrium assumption” to reduce the network of TGF-β 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-β signalling. We were able to simulate the sigmoidal, switch-like behaviour observed for the concentration dependence of long-term (> 3 hours) TGF-β stimulation. Computer simulations revealed the vital role of the coupling of the positive and negative feedback loops on the regulation of the TGF-β 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-β concentrations. We have tested the model against experimental data from MEF (mouse embryonic fibroblasts) WT, SV40-immortalized MEFs and Gp130 F/F MEFs. The predictions from the RF- model are consistent with the experimental data.ConclusionsSignalling feedback loops are required to model TGF-β 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-β signalling in cancer cells with different mutations.
Highlights
Transforming growth factor β (TGF-β) signalling regulates the development of embryos and tissue homeostasis in adults
Cancer cells: changes in response to TGF-β We propose that the time-course of the PSMAD concentration in response to TGF-β stimulation is modified in cancer cells due to the possible mutations in SMADs, mutations to TGF-β receptors and/or different receptor levels [67,68,69,70]
The importance of TGF-β signalling in the progression of cancer heralded in a new era of cancer cell biology research [73, 79,80,81]
Summary
Transforming growth factor β (TGF-β) signalling regulates the development of embryos and tissue homeostasis in adults. Recent studies indicate that TGF-β concentration, stimulation time, cell type and even the percentage of active signalling components within cells can influence the gene responses, giving a multi-functional aspect to TGF-β signaling [2, 8]. This is of particular interest in colon cancer, where SMAD signalling is a critical pathway controlling the transition of normal epithelial cells to cancerous cells [3, 8,9,10,11]. There are two opposing reactions of cancer cells to TGF-β: the proliferation of cancer cells at an early-stage is inhibited by TGF-β [13], yet at more advanced stages of malignancy, proliferation of cancer cells is stimulated by this cytokine [14]
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