Activity Networks with Delays An application to toxicity analysis

TL;DR

This paper introduces ANDy, a formal framework for modeling time-dependent biological activities, including toxicity analysis, using modular Petri net semantics, with finite state representations and practical case studies.

Contribution

The paper presents ANDy, a novel discrete-time modeling framework for biological systems with delays, enabling toxicity analysis and finite state verification.

Findings

ANDy systems have finite state representations.

The framework effectively models toxic behaviors.

A case study on blood glucose regulation demonstrates applicability.

Abstract

ANDy , Activity Networks with Delays, is a discrete time framework aimed at the qualitative modelling of time-dependent activities. The modular and concise syntax makes ANDy suitable for an easy and natural modelling 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 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 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 modelling of toxic behaviours. As an illustration, we present a classification of toxicity properties and give some hints on how they can be verified with existing tools on ANDy systems. A small case study on blood glucose regulation is provided to exemplify the ANDy framework and the toxicity properties.