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

Abstract

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.

Combining bifurcation and sensitivity analysis for ecological models

“…Bifurcation and sensitivity analysis are not commonly applied together, although there are possibilities to do this. For instance, the numerical calculation of local sensitivities has been combined with the Routh-Hurwitz criteria known from control engineering to analyse a model that combines cell signalling and cell population dynamics [35]. In fact, there are even standardized toolboxes available in which methodologies for bifurcation and sensitivity analysis are included, for example, the Systems Biology Toolbox for MATLAB [36].…”

Biochemical Systems Theory: A Review

“…While the delays are approximated, the approximation error can be made arbitrarily small [172,174,678]. It was demonstrated that the inclusion of delays is sometimes mandatory in multi-timescale models, lest the model results are quantitatively, and even qualitatively, compromised [422,599].…”

“…e strategy demonstrated how information from one step can feed into other analyses and thereby help re�ne the structure of a model [422].…”

“…As an early example of a BST analysis, Ni and Savageau developed models of the metabolic dynamics of red blood cells [370,371]. Reilly and colleagues studied renal hemodynamics [598], and Vera's group studied with a multiscale model the signaling role of erythropoietin on erythropoiesis [422,561].…”

“…For example, the article [560] successfully used simple power-law models to analyze the dynamics of feedback loops in the ERK signal transduction system. In a different, yet related line of work, Nikolov and colleagues developed a multiscale model that accounted for the effect of erythropoietin mediated JAK2-STAT5 signaling in erythropoiesis [422,561]. e group also assessed oscillations in the NF B pathway with a model that had BST components, as well as Michaelis-Menten-type functions [562].…”