Detalle de: Optimization-based prediction of fold bifurcations in nonlinear ODE models

A complex nonlinear system might exhibit a rich variety of dynamics. Detecting and classifying these dynamics is crucial to understand and ultimately control the system. Starting from an ODE model, this analysis can be done using standard bifurcation/continuation methods. However, when we start from measured data to infer the equations governing the dynamics (parameters and topology) we need tools to detect bifurcations in presence of parameter and even structural uncertainty. This is particularly the case in the field of systems biology, where we often deal with limited mechanistic knowledge (including potential conflicting hypotheses) and scarce experimental data. Here we present a method to efficiently predict the appearance of fold bifurcations in general systems of ordinary differential equations. The approach formulates the search of the bifurcation condition through a Mixed Integer Nonlinear Programming optimization strategy. In this way, we can simultaneously explore parameter and topology spaces searching for the desired bifurcation behaviour. We illustrate the capabilities and efficiency of our method through an example of biological relevance, the transcriptional network controlling adipogenesis, finding the conditions for an irreversible switch that causes the conversion of preadipocytes into adipocytes responsible of lipid accumulation.