The construction of synthetic biochemical circuits is an essential step for developing quantitative understanding
of information processing in natural organisms. Here, we report construction and analysis of an in vitro circuit with
positive autoregulation that consists of just four synthetic DNA strands and three enzymes, bacteriophage T7 RNA
polymerase, Escherichia coli ribonuclease (RNase) H, and RNase R. The modularity of the DNA switch template allowed
a rational design of a synthetic DNA switch regulated by its RNA output acting as a transcription activator. We verified
that the thermodynamic and kinetic constraints dictated by the sequence design criteria were enough to experimentally
achieve the intended dynamics: a transcription activator configured to regulate its own production. Although only
RNase H is necessary to achieve bistability of switch states, RNase R is necessary to maintain stable RNA signal levels and
to control incomplete degradation products. A simple mathematical model was used to fit ensemble parameters for the
training set of experimental results and was then directly applied to predict time-courses of switch dynamics and sensitivity
to parameter variations with reasonable agreement. The positive autoregulation switches can be used to provide constant
input signals and store outputs of biochemical networks and are potentially useful for chemical control applications
