Design and Analysis of a Proportional-Integral-Derivative Controller with Biological Molecules

Chevalier, Michael; Gómez-Schiavon, Mariana; Ng, Andrew H.; El-Samad, Hana

doi:10.1016/j.cels.2019.08.010

Cited by 78 publications

(98 citation statements)

References 23 publications

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“…The application of control theory to synthetic biological controllers aims to ensure that they function robustly, in different host organisms, despite perturbations in their environments. Nevertheless, almost all sequestration feedback controllers in the current synthetic biology literature have been con-400 currently built with the process networks they control [McCardell et al, 2017,Hsiao et al, 2014,Folliard, 2017, Lillacci et al, 2017, Chevalier et al, 2018. This approach will likely limit the versatility of these biological controllers as they will be optimal with respect to a single process network, a single host organism, and its environment.…”

Section: Discussionmentioning

confidence: 99%

“…The field of synthetic biology has focused on the development of novel organisms, devices and systems for the purposes of improving industrial processes [Savage et al, 2008, Clomburg and Gonzalez, 2010, Dunlop et al, 2010, Hemme et al, 2010, Narcross et al, 2016, discovering the principles of natural biological systems [Gardner et al, 2000, Elowitz and Leibler, 2000, Guo et al, 2014, and 20 performing biomolecular computation [Qian et al, 2011, Thubagere Jagadeesh, 2017. Current applications of synthetic biology include industrial fermentation [Georgianna and Mayfield, 2012], toxin detection [McBride et al, 2003, Wang et al, 2009, biosensor development [Hsiao et al, 2016], diagnostics detection [Pardee et al, 2014], materials production [Cherny and Gazit, 2008, Moon et al, 2010, DeLoache et al, 2015, novel protein design [Dahiyat and Mayo, 1996, Arnold, 1998, Kuhlman et al, 2003, and biological computation [Moon et al, 2012, Daniel et al, 2013.…”

Section: Introductionmentioning

confidence: 99%

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Design Guidelines For Sequestration Feedback Networks

Baetica

Leong

Olsman

et al. 2018

Preprint

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Integral control is commonly used in mechanical and electrical systems to ensure perfect adaptation. A proposed design of integral control for synthetic biological systems employs the sequestration of two biochemical controller species. The unbound amount of controller species captures the integral of the error between the current and the desired state of the system. However, implementing integral control inside bacterial cells using sequestration feedback has been challenging due to the controller molecules being degraded and diluted. Furthermore, integral control can only 10 be achieved under stability conditions that not all sequestration feedback networks fulfill. In this work, we give guidelines for ensuring stability and good performance (small steady-state error) in sequestration feedback networks. Our guidelines provide simple tuning options to obtain a flexible and practical biological implementation of sequestration feedback control. Using tools and metrics from control theory, we pave the path for the systematic design of synthetic biological circuits.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Design Guidelines For Sequestration Feedback Networks

Baetica

Leong

Olsman

et al. 2018

Preprint

View full text Add to dashboard Cite

show abstract

“…Transcription of individual genes inside single cells has been shown to occur in bursts of activity, followed by periods of silence [56]- [61]. Each burst corresponds to the gene stochastically switching to a transcriptionally active state, and then becoming inactive after synthesizing a few messenger RNA (mRNA) transcripts.…”

Section: A Incorporating Bursty Dynamicsmentioning

confidence: 99%

An approximate derivate-based controller for regulating gene expression

Modi¹,

Dey²,

Singh³

2019

Preprint

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Inside individual cells, protein population counts are subject to molecular noise due to low copy numbers and the inherent probabilistic nature of biochemical processes. Such random fluctuations in the level of a protein critically impact functioning of intracellular biological networks, and not surprisingly, cells encode diverse regulatory mechanisms to buffer noise. We investigate the effectiveness of proportional and derivative-based feedback controllers to suppress protein count fluctuations originating from two noise sources: bursty expression of the protein, and external disturbance in protein synthesis. Designs of biochemical reactions that function as proportional and derivative controllers are discussed, and the corresponding closed-loop system is analyzed for stochastic controller realizations. Our results show that proportional controllers are effective in buffering protein copy number fluctuations from both noise sources, but this noise suppression comes at the cost of reduced static sensitivity of the output to the input signal. Next, we discuss the design of a coupled feedforward-feedback biochemical circuit that approximately functions as a derivate controller. Analysis using both analytical methods and Monte Carlo simulations reveals that this derivative controller effectively buffers output fluctuations from bursty stochastic expression, while maintaining the static input-output sensitivity of the open-loop system. As expected, the derivative controller performs poorly in terms of rejecting external disturbances. In summary, this study provides a systematic stochastic analysis of biochemical controllers, and paves the way for their synthetic design and implementation to minimize deleterious fluctuations in gene product levels.

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“…In fact, the antithetic integral controller is the simplest integral controller that is able to properly work in a stochastic setting. The performance analysis of the antithetic integral controller and its generalizations have also been theoretically studied in [17,42,43,47] in a deterministic and stochastic settings. In those papers, the stability and robustness properties of the antithetic integral controller is studied in various parametric regimes for both the controller and sys-tem parameters, notably in the presence of degrading controller species.…”

Section: Introductionmentioning

confidence: 99%

A Biology-Inspired Approach to the Positive Integral Control of Positive Systems: The Antithetic, Exponential, and Logistic Integral Controllers

Briat¹

2020

SIAM J. Appl. Dyn. Syst.

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The integral control of positive systems using nonnegative control input is an important problem arising, among others, in biochemistry, epidemiology and ecology. An immediate solution is to use an ON-OFF nonlinearity between the controller and the system. However, this solution is only available when controllers are implemented in computer systems. When this is not the case, like in biology, alternative approaches need to be explored. Based on recent research in the control of biological systems [7,14], we propose to develop a theory for the integral control of positive systems using nonnegative controls based on the so-called antithetic integral controller and two positively regularized integral controllers, the so-called exponential integral controller and logistic integral controller. For all these controllers, we establish several qualitative results, which we connect to standard results on integral control. We also obtain additional results which are specific to the type of controllers. For instance, we show an interesting result stipulating that if the gain of the antithetic integral controller is suitably chosen, then the local stability of the equilibrium point of the closed-loop system does not depend on the choice for the coupling parameter, an additional parameter specific to this controller. Conversely, we also show that if the coupling parameter is suitably chosen, then the equilibrium point of the closed-loop system is locally stable regardless the value of the gain. For the exponential integral controller, we can show that the local stability of the equilibrium point of the closed-loop system is independent of the gain of the controller and the gain of the system. The stability only depends on the exponential rate of the controller, again a parameter that is specific to this type of controllers. Several examples are given for illustration.

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Design and Analysis of a Proportional-Integral-Derivative Controller with Biological Molecules

Abstract: Highlights d Integral control allows perfect adaptation but can be slow or even unstable d Molecular proportional and derivative control modules improve adaptation performance d Control modules can be composed in a modular fashion to achieve design specifications

Cited by 78 publications

References 23 publications

Design Guidelines For Sequestration Feedback Networks

Design Guidelines For Sequestration Feedback Networks

An approximate derivate-based controller for regulating gene expression

A Biology-Inspired Approach to the Positive Integral Control of Positive Systems: The Antithetic, Exponential, and Logistic Integral Controllers

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