Time Petri nets for modelling and analysis of biochemical networks

Biochemical networks are modelled at different abstraction levels. Basically, qualitative and quantitative models can be distinguished, which are typically treated as separate ones. In this paper, we bridge the gap between qualitative and quantitative models and apply time Petri nets for modelling and analysis of molecular biological systems. We demonstrate how to develop quantitative models of biochemical networks in a systematic manner, starting from the underlying qualitative ones. For this purpose we exploit the well-established structural Petri net analysis technique of transition invariants, which may be interpreted as a characterisation of the system's steady state behaviour. For the analysis of the derived quantitative model, given as time Petri net, we present structural techniques to decide the time-dependent realisability of a transition sequence and to calculate its shortest and longest time length. All steps of the demonstrated approach consider systems of integer linear inequalities. The crucial point is the total avoidance of any state space construction. Therefore, the presented technology may be applied also to infinite systems, i.e. unbounded Petri nets.