TGF-ß and IL-6 family signalling crosstalk: an integrated model.

Mathematical models for TGF-ß and IL-6 signalling have been linked, providing a platform for analyzing the crosstalk between the systems. An integrated IL-6:TGF-ß model was developed via a reduced set of reaction equations which incorporate both feedback loops and appropriate time-delays for transcription and translation processes. The model simulates stable, robust and realistic responses to both ligands. Pulsatile (multiple pulses) inputs for both TGF-ß and IL-6 have been simulated to investigate the effects of each ligand on the sensitivity, equilibrium and dynamic responses of the integrated signalling system. In our simulations the crosstalk between constant IL-6 and TGF-ß signalling via SMAD7 does not appear to be sufficient to render the cells resistant to TGF-ß inhibition. However, the simulations predict that pulsatile IL-6 stimulation would increase SMAD7 levels substantially and consequentially, lead to resistance to TGF-ß. The model also allows the prediction of the integrated signalling pathway responses to the mutation of key components, e.g. Gp130 F/F.

Computational Modeling of the Dynamics of Spatiotemporal Rho GTPase Signaling: A Systematic Review.

The Rho family of GTPases are known to play pivotal roles in the regulation of fundamental cellular processes, ranging from cell migration and polarity to wound healing and regulation of actin cytoskeleton. Over the past decades, accumulating experimental work has increasingly mapped out the mechanistic details and interactions between members of the family and their regulators, establishing detailed interaction circuits within the Rho GTPase signaling network. These circuits have served as a vital foundation based on which a multitude of mathematical models have been developed to explain experimental data, gain deeper insights into the biological phenomenon they describe, as well as make new testable predictions and hypotheses. Due to the diverse nature and purpose of these models, they often vary greatly in size, scope, complexity, and formulation. Here, we provide a systematic, categorical, and comprehensive account of the recent modeling studies of Rho family GTPases, with an aim to offer a broad perspective of the field. The modeling limitations and possible future research directions are also discussed.

Mathematical model of TGF-ßsignalling: feedback coupling is consistent with signal switching.

BACKGROUND: Transforming growth factor ß (TGF-ß) signalling regulates the development of embryos and tissue homeostasis in adults. In conjunction with other oncogenic changes, long-term perturbation of TGF-ß signalling is associated with cancer metastasis. Although TGF-ß signalling can be complex, many of the signalling components are well defined, so it is possible to develop mathematical models of TGF-ß signalling using reduction and scaling methods. The parameterization of our TGF-ß signalling model is consistent with experimental data. RESULTS: We developed our mathematical model for the TGF-ß signalling pathway, i.e. the RF- model of TGF-ß signalling, using the "rapid equilibrium assumption" to reduce the network of TGF-ß 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-ß signalling. We were able to simulate the sigmoidal, switch-like behaviour observed for the concentration dependence of long-term (> 3 hours) TGF-ß stimulation. Computer simulations revealed the vital role of the coupling of the positive and negative feedback loops on the regulation of the TGF-ß 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-ß 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. CONCLUSIONS: Signalling feedback loops are required to model TGF-ß 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-ß signalling in cancer cells with different mutations.