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Activity Networks with Delays an Application to Toxicity Analysis

Delaplace F., Di Giusto C., Giavitto J. -L, Klaudel H., Spicher A.

Fundamenta Informaticae

2018

Vol. 160, nr 1/2

119--142

ANDy, Activity Networks with Delays, is a discrete framework aiming at the qualitative modeling of time-dependent activities. The modular and expressive syntax makes ANDy suitable for a concise and natural modeling of time-dependent biological systems (i.e., regulatory pathways). Activities involve entities playing the role of activators, inhibitors or products of biochemical network operation. Activities may have a 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). Entity levels may change as a result of an activity or may decay 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 it well adapts to the modeling of toxic behaviors. As an illustration, we present a classification of toxicity properties and give some hints on how they can be verified on ANDy systems with existing tools. A case study on blood glucose regulation is provided to exemplify the ANDy framework and the toxicity properties.