Metastable regimes and tipping points of biochemical networks with potential applications in precision medicine

The concept of attractor of dynamic biochemical networks has been used to explain cell types and cell alterations in health and disease. We have recently proposed an extension of the notion of attractor to take into account metastable regimes, defined as long lived dynamical states of the network. These regimes correspond to slow dynamics on low dimensional invariant manifolds of the biochemical networks. Methods based on tropical geometry allow to compute the metastable regimes and represent them as polyhedra in the space of logarithms of the species concentrations. We are looking for sensitive parameters and tipping points of the networks by analyzing how these polyhedra depend on the model parameters. Using the coupled MAPK and PI3K/Akt signaling networks as an example, we test the idea that large changes of the metastable states can be associated to cancer disease specific alterations of the network. In particular, we show that for model parameters representing protein concentrations, the protein differential level between tumors of different types is reasonably reflected in the sensitivity scores, with sensitive parameters corresponding to differential proteins.