Preprint Open Access

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

Filo, Maurice; Khammash, Mustafa


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{
  "DOI": "10.1101/2021.03.21.436342", 
  "author": [
    {
      "family": "Filo, Maurice"
    }, 
    {
      "family": "Khammash, Mustafa"
    }
  ], 
  "issued": {
    "date-parts": [
      [
        2021, 
        3, 
        22
      ]
    ]
  }, 
  "abstract": "<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>", 
  "title": "A Class of Simple Biomolecular Antithetic Proportional-Integral-Derivative Controllers", 
  "type": "article", 
  "id": "4835858"
}
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