Contributions to mechanistic modelling in systems biologyidentifiability, symmetries and uncertainty quantification

Zusammenfassung

This thesis is framed in the context of dynamic modelling of biological systems. As dynamic models we will mainly use non-linear models in common differential equations. The objective is the development and application of computational methodologies that facilitate such modelling. These methodologies are of general purpose, applicable to biological problems in different fields (biomedicine, biotechnology industrial, food technology, ecology, etc.). Several lines of research are envisaged complementary in two respects: on the one hand, the identification of systems; on the other hand, the analysis of the uncertainty associated with model predictions. The first aspect, the identification of the system, refers to the construction and calibration of dynamic models from experimental data. These models have the capacity to make predictions about conditions not included in the experimental data. However, there is always some uncertainty associated with these predictions, which is important to quantify; this is the second aspect to consider in this thesis. The two aspects are related. In turn, within each of them we can distinguish several objectives or tasks. In this way, the objectives of this thesis can be framed in four large blocks: 1.- Analysis of the structural systemic properties of dynamic models: identifiability, observability and controllability and the relationship between them. 2.- Study of the distinction between dynamic models and their relationship with the inference of these models. 3.- Construction of sets ("ensembles") of models, and application to the analysis of uncertainty of the predictions. 4.- Machine learning of dynamic models from experimental data