Bigraphical models for protein and membrane interactions

We present a bigraphical framework suited for modeling biological systems both at protein level and at membrane level. We characterize formally bigraphs corresponding to biologically meaningful systems, and bigraphic rewriting rules representing biologically admissible interactions. At the protein level, these bigraphic reactive systems correspond exactly to systems of kappa-calculus. Membrane-level interactions are represented by just two general rules, whose application can be triggered by protein-level interactions in a well-de\"ined and precise way. This framework can be used to compare and merge models at different abstraction levels; in particular, higher-level (e.g. mobility) activities can be given a formal biological justification in terms of low-level (i.e., protein) interactions. As examples, we formalize in our framework the vesiculation and the phagocytosis processes.