Transient response characteristics in a biomolecular integral controller.

The cellular behaviour of perfect adaptation is achieved through the use of an integral control element in the underlying biomolecular circuit. It is generally unclear how integral action affects the important aspect of transient response in these biomolecular systems, especially in light of the fact that it typically deteriorates the transient response in engineering contexts. To address this issue, the authors investigated the transient response in a computational model of a simple biomolecular integral control system involved in bacterial signalling. They find that the transient response can actually speed up as the integral gain parameter increases. On further analysis, they find that the underlying dynamics are composed of slow and fast modes and the speed-up of the transient response is because of the speed-up of the slow-mode dynamics. Finally, they note how an increase in the integral gain parameter also leads to a decrease in the amplitude of the transient response, consistent with the overall improvement in the transient response. These results should be useful in understanding the overall effect of integral action on system dynamics, particularly for biomolecular systems.