Incremental modelling and analysis of biological systems with fuzzy hybrid Petri nets

Modelling biological systems depends on the availability of data and components of the system at hand. As our understanding of these systems evolves, the ability to gradually refine models by adding new components of different formalisms covering stochastic, discrete, deterministic, and uncertainty without starting from scratch becomes essential. However, there remains a significant gap in the availability of methodologies and tool support for incrementally modelling and analysing complex biological systems in a flexible and intuitive manner. In this paper, we employ fuzzy hybrid Petri nets as a powerful expressive tool for presenting an incremental modelling and analysis protocol of biological systems. We demonstrate the utility of our protocol through a case study on cholesterol and lipoprotein metabolism and hypercholesterolemia therapy. Our model not only captures the underlying biochemical processes, but also quantitatively analyses how cholesterol levels are regulated, offering insights into potential therapeutic strategies for diseases associated with elevated cholesterol levels. The results confirm the validity and flexibility of our approach in representing complex biological processes and therapeutic interventions.