Math.comput.sci. 2 (2009), 465–491 c  2009 Birkh¨auser Verlag Basel/Switzerland 1661-8270/030465-27, published online March 19, 2009 DOI 10.1007/s11786-008-0065-3 Mathematics in Computer Science Hybrid Dynamics of Stochastic π -Calculus Luca Bortolussi and Alberto Policriti Abstract. In this paper we describe a method to map stochastic π-calculus processes in chemical ground form into hybrid automata. Hybrid automata are tools widely employed to model systems characterized by both discrete and continuous evolution and their use in the context of Systems Biology al- lows us to address rather fundamental issues. Specifically, the key ingredient we use in this work is the possibility granted by hybrid automata to imple- ment a separation of control and molecular terms in biochemical systems. The computational counterpart of our analysis turns out to be related to the determination of conservation properties of the system. Mathematics Subject Classification (2000). 92C99, 68U20, 93A99. Keywords. Stochastic π-calculus, hybrid automata, conservation laws. 1. Introduction Systems biology is a fertile research area in which experimental techniques are coupled with mathematical modeling in order to understand the complex dynamics within cells [19]. In this context, both mathematical and computational tools play an important role: biological systems must be described in a precise mathematical framework, usually ordinary differential equations or stochastic processes, and the obtained models must then be analyzed. However, due to their intrinsic complexity, computational techniques (e.g. simulation) must be used. The contributions of Computer Science, on the other hand, are not just re- stricted to the computational analysis of models, but also related to the description of biological systems by means of suitable formal languages, providing such fea- tures as compositionality or model reusability [22]. These languages usually belong to the domain of stochastic process alge- bras (SPA), which have a semantics defined in terms of Continuous Time Markov Chains [17,25]. Different SPA have been used in biological modeling; here we re- call stochastic π-calculus [21], PEPA [9], and stochastic Concurrent Constraint Programming (sCCP, [7]). An important issue in using these languages is that