Activity Networks with Delays application to toxicity analysis

F. Delaplace, C. Di Giusto, J.-L. Giavitto, H. Klaudel and A. Spicher
Research report
ANDy, Activity Networks with Delays, is a discrete time framework aimed to the qualitative modelling of time-dependent activities such as biological networks and regulatory pathways. Activities involve entities playing the role of activators, inhibitors or products of biochemical network operation. Activities may have given duration, i.e., the time required to obtain results. An entity may represent an object (e.g., an agent, a biochemical species or a family of thereof) with a local attribute, a state denoting its level (e.g., concentration, strength). Entities levels may change as a result of an activity or may decrease gradually as time passes by. The semantics of ANDy is formally given via high-level Petri nets ensuring this way some modularity. As main results we show that ANDy systems have finite state representations even for potentially infinite processes and that ANDy's concept of time has a direct counterpart in timed automata. These results together with a modular and concise syntax make ANDy suitable for an easy and natural modelling of time-dependent (biological) systems. We conclude our paper with a general discussion on toxic behaviours, in particular we present a classification of toxicity properties and give some hints on how they can be verified with existing tools on ANDy systems.