Biomolecular systems that can process information are sought for computational applications, because of their potential for parallelism and miniaturization and because their biocompatibility also makes them suitable for future biomedical applications. DNA has been used to design machines, motors, finite automata, logic gates, reaction networks and logic programs, amongst many other structures and dynamic behaviours. Here we design and program a synthetic DNA network to implement computational paradigms abstracted from cellular regulatory networks. These show information processing properties that are desirable in artificial, engineered molecular systems, including robustness of the output in relation to different sources of variation. We show the results of numerical simulations of the dynamic behaviour of the network and preliminary experimental analysis of its main components.