Integration of sensitivity and bifurcation analysis to detect critical processes in a model combining signalling and cell population dynamics

In this article we present and test a strategy to integrate, in a sequential manner, sensitivity analysis, bifurcation analysis and predictive simulations. Our strategy uses some of these methods in a coordinated way such that information, generated in one step, feeds into the definition of further analyses and helps refining the structure of the mathematical model. The aim of the method is to help in the designing of more informative predictive simulations, which focus on critical model parameters and the biological effects of their modulation. We tested our methodology with a multilevel model, accounting for the effect of erythropoietin (Epo)-mediated JAK2-STAT5 signalling in erythropoiesis. Our analysis revealed that time-delays associated with the proliferation-differentiation process are critical to induce pathological sustained oscillations, whereas the modulation of time-delays related to intracellular signalling and hypoxia-controlled physiological dynamics is not enough to induce self-oscillations in the system. Furthermore, our results suggest that the system is able to compensate (through the physiological-level feedback loop on hypoxia) the partial impairment of intracellular signalling processes (downregulation or overexpression of Epo receptor complex and STAT5), but cannot control impairment in some critical physiological-level processes, which provoke the emergence of pathological oscillations.