How Symmetry and Order Affect Logic Operations and Computation in Catalytic Chemical Networks

We discuss here the recent progress in design, construction and kinetic analysis of logic gates and computational modules within small chemical networks. We show how small artificial networks of replicating and catalyzed molecules, when manipulated properly by enabling or disabling specific catalytic pathways, may yield all two-input Boolean logic operations, as well as the half-adder and half-subtractor arithmetic units. We then discuss experiments where actual networks of synthetic peptides are employed. Finally, we show mathematically that while all logic gates may be constructed in principle even from low-order catalytic systems, symmetry constraints and reasonable chemical assumptions require higher catalytic order, a conclusion with far-reaching implications for molecular self-organization and Systems Chemistry.