The Attributed Pi Calculus

The attributed pi calculus (π(L)) forms an extension of the pi calculus with attributed processes and attribute dependent synchronization. To ensure flexibility, the calculus is parametrized with the language L which defines possible values of attributes. π(L) can express polyadic synchronization as in pi@ and thus diverse compartment organizations. A non-deterministic and a stochastic semantics, where rates may depend on attribute values, is introduced. The stochastic semantics is based on continuous time Markov chains. A simulation algorithm is developed which is firmly rooted in this stochastic semantics. Two examples underline the applicability of π(L) to systems biology: Euglena’s movement in phototaxis, and cooperative protein binding in gene regulation of bacteriophage lambda.