DNA strand displacement (DSD) reactions have been used to construct chemical
reaction networks in which species act catalytically at the level of the
overall stoichiometry of reactions. These effective catalytic reactions are
typically realised through one or more of the following: many-stranded gate
complexes to coordinate the catalysis, indirect interaction between the
catalyst and its substrate, and the recovery of a distinct ``catalyst'' strand
from the one that triggered the reaction. These facts make emulation of the
out-of-equilibrium catalytic circuitry of living cells more difficult. Here, we
propose a new framework for constructing catalytic DSD networks: Active
Circuits of Duplex Catalysts (ACDC). ACDC components are all double-stranded
complexes, with reactions occurring through 4-way strand exchange. Catalysts
directly bind to their substrates, and and the ``identity'' strand of the
catalyst recovered at the end of a reaction is the same molecule as the one
that initiated it. We analyse the capability of the framework to implement
catalytic circuits analogous to phosphorylation networks in living cells. We
also propose two methods of systematically introducing mismatches within DNA
strands to avoid leak reactions and introduce driving through net base pair
formation. We then combine these results into a compiler to automate the
process of designing DNA strands that realise any catalytic network allowed by
our framework.