Preprint Open Access

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

Filo, Maurice; Khammash, Mustafa


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  <identifier identifierType="URL">https://zenodo.org/record/4835858</identifier>
  <creators>
    <creator>
      <creatorName>Filo, Maurice</creatorName>
      <givenName>Maurice</givenName>
      <familyName>Filo</familyName>
      <affiliation>ETH Zurich Department of Biosystems Science and Engineering</affiliation>
    </creator>
    <creator>
      <creatorName>Khammash, Mustafa</creatorName>
      <givenName>Mustafa</givenName>
      <familyName>Khammash</familyName>
      <affiliation>ETH Zurich Department of Biosystems Science and Engineering</affiliation>
    </creator>
  </creators>
  <titles>
    <title>A Class of Simple Biomolecular Antithetic Proportional-Integral-Derivative Controllers</title>
  </titles>
  <publisher>Zenodo</publisher>
  <publicationYear>2021</publicationYear>
  <dates>
    <date dateType="Issued">2021-03-22</date>
  </dates>
  <resourceType resourceTypeGeneral="Text">Preprint</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/4835858</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.1101/2021.03.21.436342</relatedIdentifier>
    <relatedIdentifier relatedIdentifierType="URL" relationType="IsPartOf">https://zenodo.org/communities/cosy-bio</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="https://creativecommons.org/licenses/by/4.0/legalcode">Creative Commons Attribution 4.0 International</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
  </rightsList>
  <descriptions>
    <description descriptionType="Abstract">&lt;p&gt;Abstract&lt;/p&gt;

&lt;p&gt;Proportional-Integral-Derivative (PID) feedback controllers have been the most widely used controllers in the&amp;nbsp;industry for almost a century. This is mainly due to their simplicity and intuitive operation. Recently, motivated&amp;nbsp;by their success in various engineering disciplines, PID controllers found their way into molecular biology.&amp;nbsp;In this paper, we consider the mathematical realization of (nonlinear) PID controllers via biomolecular interactions&amp;nbsp;in both the deterministic and stochastic settings. We propose several simple biomolecular PID control&amp;nbsp;architectures that take into consideration the biological implementation aspect. We verify the underlying PID&amp;nbsp;control structures by performing a linear perturbation analysis and examine their eects on the (deterministic&amp;nbsp;and stochastic) performance and stability. In fact, we demonstrate that dierent proportional controllers exhibit&amp;nbsp;dierent capabilities of enhancing the dynamics and reducing variance (cell-to-cell variability). Furthermore,&amp;nbsp;we propose a simple derivative controller that is mathematically realized by cascading the antithetic integral&amp;nbsp;controller with an incoherent feedforward loop without adding any additional species. We demonstrate that&amp;nbsp;the derivative component is capable of enhancing the transient dynamics at the cost of boosting the variance,&amp;nbsp;which agrees with the well known vulnerability of the derivative controller to noise. We also show that this can&amp;nbsp;be mitigated by carefully designing the inhibition pathway of the incoherent feedforward loop. Throughout the&amp;nbsp;paper, the stochastic analysis is carried out based on a tailored moment-closure technique and is also backed&amp;nbsp;up by simulations.&lt;/p&gt;</description>
  </descriptions>
  <fundingReferences>
    <fundingReference>
      <funderName>European Commission</funderName>
      <funderIdentifier funderIdentifierType="Crossref Funder ID">10.13039/501100000780</funderIdentifier>
      <awardNumber awardURI="info:eu-repo/grantAgreement/EC/H2020/766840/">766840</awardNumber>
      <awardTitle>Control Engineering of Biological Systems for Reliable Synthetic Biology Applications</awardTitle>
    </fundingReference>
  </fundingReferences>
</resource>
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