AC-BioSD : A biomolecular signal differentiator module with enhanced performance (extended version)

Temporal gradient estimation is a pervasive phenomenon in natural biological systems and holds great promise for synthetic counterparts with broad-reaching applications. Here, we advance the concept of BioSD (Biomolecular Signal Differentiators) by introducing a novel biomolecular topology, termed Autocatalytic-BioSD or AC-BioSD. Its structure allows for insensitivity to input signal changes and high precision in terms of signal differentiation, even when operating far from nominal conditions. Concurrently, disruptive high-frequency signal components are effectively attenuated. In addition, the usefulness of our topology in biological regulation is highlighted via a PID (Proportional-Integral-Derivative) bio-control scheme with set point weighting and filtered derivative action in both the deterministic and stochastic domains.