Raising the level of abstraction for synthetic biology design requires solving several challenging problems, including mapping abstract designs to DNA sequences. In this paper we present the first formalism and algorithms to address this problem. The key steps of this transformation are feature matching, signal matching, and part matching. Feature matching ensures that the mapping satisfies the regulatory relationships in the abstract design. Signal matching ensures that the expression levels of functional units are compatible. Finally, part matching finds a DNA part sequence that can implement the design. Our software tool MatchMaker implements these three steps.