Performance metrics for a biomolecular step response

Establishing performance metrics is a key part of a systematic design process. In particular, specifying metrics useful for quantifying performance in the ongoing efforts towards biomolecular circuit design is an important problem. Here we address this issue for the design of a fast biomolecular step response that is uniform across different cells and widely different environmental conditions using a combination of simple mathematical models and experimental measurements using single-cell time-lapse microscopy. We evaluate two metrics, the difference of the step response from an ideal step and the relative difference between multiple realizations of the step response, that can provide a single number to measure performance. We use a model of protein productiondegradation to show that these performance metrics correlate with response features of speed and noise. Finally, we work through an experimental methodology to estimate these metrics for step responses that have been acquired for inducible protein expression circuits in E. coli. These metrics will be useful to evaluate biomolecular step responses, as well as for setting similar performance measures for other design goals.