Petri Nets and Bio-Modelling - and how to benefit from their synergy

Proceedings of 5th W orkshop on Membrane Computing and Biologically Inspired Process Calculi (MeCBIC 2011) Pages 5–6, 2011. c  J. Kleijn, M. K outny and G. Rozenbe rg All the rights to the paper remain with the authors. P etri Nets and Bio-Modelling and how to b enefit fr om their synergy Jetty Kleijn LIA CS, Leiden Uni versity , 230 0 RA, The Netherlands kleijn@lia cs.nl Maciej K outny School of Computing Science,Newcastle Uni v ersity , Ne wcastle upon T yne, NE1 7R U, United Kingdo m maciej.kou tny@ncl.ac .uk Grzegorz Roze nberg Leiden Center for Natural Computing, Leiden Uni versity Niels Bohrweg 1, 2333 CA Leiden, The Netherlands rozenber@l iacs.nl Petri nets are a gene ral, well-establis hed model of concurre nt and distrib uted computation featurin g a wealth of tools for the analysis a nd ve rification of their beha viou ral pr opertie s. On the other hand, to understand specific biolog ical processes dif ferent formali sations hav e been proposed. Exampl es here are membran e systems and react ion systems which are c lose abstra ctions of the fun ctioni ng of the li ving cell. Membran e systems are a computation al model ins pired by the w ay c hemical reacti ons take pla ce in cells that are di vided by membranes into compartmen ts. The cen tral idea behind reactio n systems is that the func tionin g of a li ving cell is bas ed on intera ctions between (a lar ge number of) ind i vidual reactions , and moreo ver these intera ctions are reg ulated by two main mechani sms: facilitati on and inhib ition. In this talk we are concerned w ith the intrinsi c similaritie s and diffe rences between Petri nets on the one h and, a nd m embrane systems and reaction sys tems on the ot her h and. In particular , we ar e i nterest ed in the benefits that can result from estab lishing strong semantical links between the latter two models and Petri nets. Our aim is to e nhance the Pet ri net model in ord er to fa ithfull y model the dyn amics of the biolog ical phenomen a/proc esses represented by membrane systems and reaction systems. After introducin g P etri nets, we will outlin e ho w to und erstan d and formal ise th eir ca usality and concu rrenc y semantics. Then we turn to membrane syst ems. Like membrane syste ms, Petri ne ts are in ess ence multiset re writing syste ms. Using this ke y commonalit y we describe a fai thful translatio n from basic membrane systems to Petri nets. T o captu re the compartment alisati on of m embrane systems, the Petri net model has to be exten ded with localities which in turn leads to the idea of locall y syn chron ised ex ecuti ons. In the thus extended model the stand ard causalit y semantics is no longer sou nd, and we will discuss pos sible soluti on to this problem. Next we describ e reaction systems which are a recen tly propose d model aimed at in ve stigati ng pro- cesses carr ied by bioch emical reactions . Now , t he re sulting comp utation al model is re markably dif ferent since in reaction sy stems, b iochemica l rea ctions ar e modeled using a quali tati v e rather than a quant itati v e approa ch. As a conseq uence, counting — and henc e the multiset based calculus implemented in Petri nets — is no longer appropriat e. This insight leads to a new class of Petri nets , called set-nets, a nov el and challe nging class of nets with intrigu ing (and yet to be disco v ered) properties . W e concl ude the talk by demons trating ho w in turn set-nets with localiti es cor respon d to membrane systems with qualit ati ve ev olution rules. Altogeth er thi s talk aims to demonstrate the fruit ful two-way interactio n bet ween biolog ical models and P etri nets. Both membrane systems and react ion systems ha ve inspire d the introdu ction of ne w and rele v ant e xtensi ons to the b asic ne t model, wher eas ha ving a P etri n et semanti cs opens the way for a ne w unders tandin g, anal ysis and synthesi s techniq ues for biologic ally inspire d systems. The presentati on is essenti ally self-co ntaine d; in parti cular , all the necessary detail s concer ning the three models will be prov ided. Refer ences [1] A .Ehrenf eucht, G. Rozenberg. Reaction Systems. Fundamenta Informaticae 75, 1-18, 2007. [2] J. Kleijn, M. Koutny . Synchrony and Asynchro ny in Membran e Systems. Lectur e Notes in Computer S cience 4361, 66-8 5, 2006. [3] J. Kleijn, M. K outny . Petri Nets with Localities and T esting . Lectur e Notes in Compu ter Science 6128, 19-38 , 2010. [4] J. Kleijn, M. K outny . Petri nets and membrane computing (Chapter 15). In [10], 389-412 , 2010. [5] J. Kleijn, M. K outny . Membrane systems with Qualitati ve Ev olution R ules. to appear . [6] J. Kleijn, M. Koutny , G. Rozenberg. T ow ards a Petri Net Semantics fo r Membr ane Systems. Lectur e Notes in Computer Science 385 0, 292-309, 2006 . [7] J. Kleijn, M. K outny , G. Roz enberg. Proce ss Semantics for Me mbrane Systems. Journal of Automata, La n- guages and Combinatorics 11, 321-340 , 2006. [8] J. Kleijn, M. K outny , G. Rozenberg. Modelling Reaction Systems with Petri Nets. In: Pr oceeding s of the Internation al W orkshop on Biological Pr ocesses & P e tri Nets (BioPPN-20 11) (M. Heiner , H. Matsuno , eds.), CEUR W orkshop Pr oceedings 724, 36-52, 2011. [9] G . P ˘ aun. Membrane Computing, An Intr oduction . Springer-V erlag, 2002. [10] G. P ˘ aun , G. Rozen berg, A. Salomaa. The Oxfor d Handboo k of Membrane Computing . Oxford University Press (20 09). [11] W . Reisi g, G. Rozenbe rg (eds.) Lectures on Petri Nets I and II. Lectur e Notes in Computer Science 1491 and 1492. Springe r-V erlag, 1998. 6