In this paper, we first introduce port graphs as graphs with multiple edges and loops, with nodes having explicit connection points, called ports, and edges attaching to ports of nodes. We then define an abstract biochemical calculus that instantiates to a rewrite calculus on these graphs. Rules and strategies are themselves port graphs, i.e. first-class objects of the calculus. As a consequence, they can be rewritten as well, and rules can create new rules, providing a way of modeling adaptive systems. This approach also provides a formal framework to reason about computations and to verify useful properties. We show how structural properties of a modeled system can be expressed as strategies and checked for satisfiability at each step of the computation. This provides a way to ensure invariant properties of a system. This work is a contribution to the formal specification and verification of adaptive systems and to theoretical foundations ofautonomic computing.