Integrative biological systems modeling: challenges and opportunities

Most biological systems are by nature hybrids consist of interacting discrete and continuous components, which may even operate on different time scales. Therefore, it is desirable to establish modeling frameworks that are capable of combining deterministic and stochastic, discrete and continuous, as well as multi-timescale features. In the context of molecular systems biology, an example for the need of such a combination is the investigation of integrated biological pathways that contain gene regulatory, metabolic and signaling components, which may operate on different time scales and involve on-off switches as well as stochastic effects. The implementation of integrated hybrid systems is not trivial because most software is limited to one or the other of the dichotomies above. In this study, we first review the motivation for hybrid modeling. Secondly, by using the example of a toggle switch model, we illustrate a recently developed modeling framework that is based on the combination of biochemical systems theory (BST) and hybrid functional Petri nets (HFPN). Finally, we discuss remaining challenges and future opportunities.