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# A Class of Simple Biomolecular Antithetic Proportional-Integral-Derivative Controllers

Filo, Maurice; Khammash, Mustafa

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{
"description": "<p>Abstract</p>\n\n<p>Proportional-Integral-Derivative (PID) feedback controllers have been the most widely used controllers in the&nbsp;industry for almost a century. This is mainly due to their simplicity and intuitive operation. Recently, motivated&nbsp;by their success in various engineering disciplines, PID controllers found their way into molecular biology.&nbsp;In this paper, we consider the mathematical realization of (nonlinear) PID controllers via biomolecular interactions&nbsp;in both the deterministic and stochastic settings. We propose several simple biomolecular PID control&nbsp;architectures that take into consideration the biological implementation aspect. We verify the underlying PID&nbsp;control structures by performing a linear perturbation analysis and examine their eects on the (deterministic&nbsp;and stochastic) performance and stability. In fact, we demonstrate that dierent proportional controllers exhibit&nbsp;dierent capabilities of enhancing the dynamics and reducing variance (cell-to-cell variability). Furthermore,&nbsp;we propose a simple derivative controller that is mathematically realized by cascading the antithetic integral&nbsp;controller with an incoherent feedforward loop without adding any additional species. We demonstrate that&nbsp;the derivative component is capable of enhancing the transient dynamics at the cost of boosting the variance,&nbsp;which agrees with the well known vulnerability of the derivative controller to noise. We also show that this can&nbsp;be mitigated by carefully designing the inhibition pathway of the incoherent feedforward loop. Throughout the&nbsp;paper, the stochastic analysis is carried out based on a tailored moment-closure technique and is also backed&nbsp;up by simulations.</p>",
"creator": [
{
"affiliation": "ETH Zurich Department of Biosystems Science and Engineering",
"@type": "Person",
"name": "Filo, Maurice"
},
{
"affiliation": "ETH Zurich Department of Biosystems Science and Engineering",
"@type": "Person",
"name": "Khammash, Mustafa"
}
],
"headline": "A Class of Simple Biomolecular Antithetic Proportional-Integral-Derivative Controllers",
"datePublished": "2021-03-22",
"url": "https://zenodo.org/record/4835858",
"@context": "https://schema.org/",
"identifier": "https://doi.org/10.1101/2021.03.21.436342",
"@id": "https://doi.org/10.1101/2021.03.21.436342",
"@type": "ScholarlyArticle",
"name": "A Class of Simple Biomolecular Antithetic Proportional-Integral-Derivative Controllers"
}
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