Modelling and robust controller design using step response data

Probing the input-output behavior of biochemical and genetic systems system identification methods from control theory

A key aspect of the behavior of any system is the timescale on which it operates: when inputs change, do responses take milliseconds, seconds, minutes, hours, days, months? Does the system respond preferentially to inputs at certain timescales? These questions are well addressed by the methods of frequency response analysis. In this review, we introduce these methods and outline a procedure for applying this analysis directly to experimental data. This procedure, known as system identification, is a well-established tool in engineering systems and control theory and allows the construction of a predictive dynamic model of a biological system in the absence of any mechanistic details. When studying biochemical and genetic systems, the required experiments are not standard laboratory practice, but with advances in both our ability to measure system outputs (e.g., using fluorescent reporters) and our ability to generate precise inputs (with microfluidic chambers capable of changing cells' environments rapidly and under fine control), these frequency response methods are now experimentally practical for a wide range of biological systems, as evidenced by a number of successful recent applications of these techniques. We use a yeast G-protein signaling cascade as a running example, illustrating both theoretical concepts and practical considerations while keeping mathematical details to a minimum. The review aims to provide the reader with the tools required to design frequency response experiments for their own biological system and the background required to analyze and interpret the resulting data.