Foundational aspects of multiscale modeling of biological systems with process algebras

We propose a variant of the CCS process algebra with new features aiming at allowing multiscale modeling of biological systems. In the usual semantics of process algebras for modeling biological systems actions are instantaneous. When different scale levels of biological systems are considered in a single model, one should take into account that actions at a level may take much more time than actions at a lower level. Moreover, it might happen that while a component is involved in one long lasting high level action, it is involved also in several faster lower level actions. Hence, we propose a process algebra with operations and with a semantics aimed at dealing with these aspects of multiscale modeling. We give both a reduction semantics and an SOS semantics for our new algebra with a result of operational correspondence between the two. Moreover, we study behavioral equivalences for such an algebra and give some examples.