Mathias John, Hans-Jörg Schulz, Heidrun Schumann, Adelinde M Uhrmacher, and Andrea Unger (2013)

# Constructing and visualizing chemical reaction networks from pi-calculus models

Formal Aspects of Computing, 25(5):723-742.

The *π*-calculus, in particular its stochastic version the stochastic *π*-calculus, is a common modeling formalism to concisely describe the chemical reactions occurring in biochemical systems. However, it remains largely unexplored how to transform a biochemical model expressed in the stochastic *π*-calculus back into a set of meaningful reactions. To this end, we present a two step approach of first translating model states to reaction sets and then visualizing sequences of reaction sets, which are obtained from state trajectories, in terms of reaction networks. Our translation from model states to reaction sets is formally defined and shown to be correct, in the sense that it reflects the states and transitions as they are derived from the continuous time Markov chain-semantics of the stochastic*π*-calculus. Our visualization concept combines high level measures of network complexity with interactive, table-based network visualizations. It directly reflects the structures introduced in the first step and allows modelers to explore the resulting simulation traces by providing both: an overview of a network’s evolution and a detail inspection on demand.