Mechanistic dynamic modelling of biological systems: The road ahead

Mathematical modelling is one of the pillars of systems biology. In this review, we focus on models that are mechanistic, i.e., they explain the mechanism by which a phenomenon takes place, and dynamic, i.e., they consist of differential equations that simulate the time course of a system. Our aim is to provide an updated state of the art of mechanistic dynamic modelling in systems biology. These models, which are based on first principles, are crucial for obtaining insights about complex physiological processes. They can be used to test hypotheses, predict system behaviour, and explore and optimize intervention strategies. Since biological processes are typically nonlinear, multiscale, and subject to various sources of uncertainty, the task of building and analysing robust and reliable mechanistic models is fraught with difficulties. In this paper, we provide an overview of recent developments in key topics such as model discovery and structure selection, identifiability analysis, parameter estimation, uncertainty quantification, and model reliability. We discuss the challenges and open questions in these areas and outline perspectives for future work.