We present the attributed $\pi$-calculus for modeling concurrent systems with interaction constraints depending on the values of attributes of processes. The $\pi$-calculus serves as a constraint language underlying the $\pi$-calculus. Interaction constraints subsume priorities, by which to express global aspects of populations. We present a nondeterministic and a stochastic semantics for the attributed $\pi$-calculus. We show how to encode the $\pi$-calculus with priorities and polyadic synchronization $\pi$@ and thus dynamic compartments, as well as the stochastic $\pi$-calculus with concurrent objects spico. We illustrate the usefulness of the attributed $\pi$-calculus for modeling biological systems at two particular examples: Euglena’s spatial movement in phototaxis, and cooperative protein binding in gene regulation of bacteriophage lambda. Furthermore, population-based model is supported beside individual-based modeling. A stochastic simulation algorithm for the attributed $\pi$-calculus is derived from its stochastic semantics. We have implemented a simulator and present experimental results, that confirm the practical relevance of our approach.