Integral action with time scale separation: A mechanism for modularity in biological systems

Modularity is the property according to which the input/output dynamic behavior of a system does not appreciably change after interconnection with other systems. Whether modularity is a natural property of biological systems is one of the most vexing questions in systems biology and crucial for the advancement of synthetic biology. In this paper, we recall design techniques for disturbance attenuation, which are well established in the control theory literature, and illustrate how the underlying principles are also found in biological systems as means to attain modularity. The specific system structure that we consider is the one where an integral action and the system internal dynamics occur at a much faster time scale than the reference input and external disturbances. In this case, the system displays a separation of time scales and can be taken to standard singular perturbation form to show that on the timescale of the reference input the effect of the disturbance is attenuated. We illustrate how this fast integral action structure is found in some interconnected biomolecular systems, where it allows to track time-varying input stimuli while rejecting loading disturbances due to interconnection with other systems.