Zooming out of Membrane Graph Transformation Systems

Living cells offer a rich variety of complex interactions and interesting structures to those wishing to model processes in systems biology. Of particular interest is the hierarchical nature of cell configurations, the compartmentalized reactions that can occur within individual cells, and the interaction between different levels of this hierarchy. Graph transformation systems are an intuitive and readable modelling paradigm that lends itself to representing such systems since graphs can be utilised to represent this rich structural information, while graph rewriting rules can concisely describe cell reactions. We formulate a generic graph transformation model that captures many functional properties of membrane (or P) systems that take inspiration from such cell biological processes. The main focus is then on abstraction of systems defined as instances of this metamodel, which we refer to as membrane graph transformation systems. Often, such systems are analysed by stochastic simulation, as this allows us to examine their overall, emergent behaviour, incorporating the effect that randomness may have on the results. Stochastic simulation can be resource intensive, limiting the applicability of many modelling languages to real biological systems. To improve performance and the scalability of modelling, we formalize a methodology that hides detail in the lowest level of the hierarchy, but retains any important information as attributes. We then train the parameter of the abstract model using Bayesian networks so that the local, per-rule behaviour of the original, concrete model is preserved. Consequently, trends in global properties are preserved, such as the way in which they change with respect to the stochastic parameters of certain rules. The methodology is demonstrated and evaluated against two case studies: a hypothetical immunological response and a peer-to-peer voice over IP network.