Preprint Open Access

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

Filo, Maurice; Khammash, Mustafa


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    <subfield code="a">A Class of Simple Biomolecular Antithetic Proportional-Integral-Derivative Controllers</subfield>
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    <subfield code="a">&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;</subfield>
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