5th Workshop on Membrane Computing and Biologically Inspired Process Calculi

In this paper we are interested in situations of biochemical reaction systems(BioRSs) in which all species have constant concentrations and all reactions haveconstant rates. Such a situation is called steady state and usually achieved aftersome time has elapsed since the system’s beginning.We start with a model of a BioRS presented as a stochastic Petri net (SPN).This is originally obtained from a system of ordinary differential equations(ODEs) achieved using simulation and interpolation.The concentrations and rates modeling the steady state in the BioRS canbe established by simulation of the SPN-model. A steady state in the BioRSsignifies also that on the model level only a subset of all possible reachablestates is relevant to this situation. It would be of interest to isolate formally andconstructively this subset of states.Considering the SPN model we propose an approach to calculate the part ofthe state space corresponding to a steady state in the BioRS. To do so, we mapthe SPN-model onto a Time Petri Net-model (TPN) with the same behaviouras that formerly observed one during the simulation of the SPN attaining thesteady state. Finally, the TPN can be analyzed qualitatively and quantitatively.Notably, the time length of the cycle(s) representing the steady state can now becomputed. To our knowledge there is no way to achieve this using the SPN-modelor the ODE-model.In addition, this approach helps for validating the correctness of the calcu-lated (and used) rates in the steady state in the BioRS and of the parametersused in the original ODEs, fixed by experiments in the wet labs, both being -apriorisubject to a certain degree of uncertainty.We thank the PC for inviting us to present our work at this workshop so thatwe can help to build a bridge between traditionnal MecBIC themes and PetriNets. All details of this work can be found in http://ceur-ws.org/Vol-724.