# A hierarchy of biomolecular proportional-integral-derivative feedback controllers for robust perfect adaptation and dynamic performance

Article · Filo M, Kumar S, Khammash M

- Archive id: doi:10.1038/s41467-022-29640-7
- Published: 2022-04-19
- Venue: Nature communications
- DOI: https://doi.org/10.1038/s41467-022-29640-7
- PMID: 35440114
- PMCID: PMC9018779
- Citations: 37
- Source URL: https://doi.org/10.1038/s41467-022-29640-7
- PDF: https://europepmc.org/articles/PMC9018779/pdf
- Provenance: europepmc

## Abstract

Proportional-Integral-Derivative (PID) feedback controllers are the most widely used controllers in industry. Recently, the design of molecular PID-controllers has been identified as an important goal for synthetic biology and the field of cybergenetics. In this paper, we consider the realization of PID-controllers via biomolecular reactions. We propose an array of topologies offering a compromise between simplicity and high performance. We first demonstrate that different biomolecular PI-controllers exhibit different performance-enhancing capabilities. Next, we introduce several derivative controllers based on incoherent feedforward loops acting in a feedback configuration. Alternatively, we show that differentiators can be realized by placing molecular integrators in a negative feedback loop, which can be augmented by PI-components to yield PID-controllers. We demonstrate that PID-controllers can enhance stability and dynamic performance, and can also reduce stochastic noise. Finally, we provide an experimental demonstration using a hybrid setup where in silico PID-controllers regulate a genetic circuit in single yeast cells.

_Abstract reproduced under CC-BY (article license as recorded by Europe PMC; abstract reproduced unmodified apart from markup removal)._

Topics: [Synthetic Biology & Genome Engineering](https://space-kitty.com/topics/synthetic-biology)

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