Logic reversibility and thermodynamic irreversibility demonstrated by DNAzyme-based Toffoli and Fredkin logic gates

The Toffoli and Fredkin gates were suggested as a means to exhibit logic reversibility and thereby reduce energy dissipation associated with logic operations in dense computing circuits. We present a construction of the logically reversible Toffoli and Fredkin gates by implementing a library of predesigned Mg2+-dependent DNAzymes and their respective substrates. Although the logical reversibility, for which each set of inputs uniquely correlates to a set of outputs, is demonstrated, the systems manifest thermodynamic irreversibility originating from two quite distinct and nonrelated phenomena. (i) The physical readout of the gates is by fluorescence that depletes the population of the final state of the machine. This irreversible, heat-releasing process is needed for the generation of the output. (ii) The DNAzyme-powered logic gates are made to operate at a finite rate by invoking downhill energy-releasing processes. Even though the three bits of Toffoli's and Fredkin's logically reversible gates manifest thermodynamic irreversibility, we suggest that these gates could have important practical implication in future nanomedicine.