Fast and precise promoter architectures in and out of equilibrium

Drosophila embryogenesis is controlled by a set of genes expressed sequentially at precise times and locations. To achieve this, the gene must make a fast and accurate readout of a given transcription factor concentration. We explore how different promoter architectures encode the speed and precision with which this readout takes place. Using the framework of sequential hypothesis testing applied to continuous-time Markov chains with concentration-dependent transition rates, we find the classes of circuits minimizing mean readout time, with and without an equilibrium constraint, and report on their properties.