Bigraphical models for protein and membrane interactions

TL;DR

This paper introduces a bigraphical modeling framework for biological systems, capturing protein and membrane interactions, enabling formal comparison and integration of models at different biological abstraction levels.

Contribution

It formalizes bigraphs for biological systems, linking protein-level and membrane-level interactions with precise rewriting rules, and demonstrates applications to vesiculation and phagocytosis.

Findings

Bigraphical models accurately represent protein and membrane interactions.

The framework aligns with kappa-calculus at the protein level.

It formalizes complex biological processes like vesiculation and phagocytosis.

Abstract

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.