Restoring circadian gene profiles in clock networks using synthetic feedback control

www.nature.com/npjsba ARTICLE OPEN Restoring circadian gene profiles in clock networks using synthetic feedback control Mathias Foo 1,4 , Ozgur E. Akman2 and Declan G. Bates 3✉ 1234567890():,; The circadian system—an organism’s built-in biological clock—is responsible for orchestrating biological processes to adapt to diurnal and seasonal variations. Perturbations to the circadian system (e.g., pathogen attack, sudden environmental change) often result in pathophysiological responses (e.g., jetlag in humans, stunted growth in plants, etc.) In view of this, synthetic biologists are progressively adapting the idea of employing synthetic feedback control circuits to alleviate the effects of perturbations on circadian systems. To facilitate the design of such controllers, suitable models are required. Here, we extend our recently developed model for the plant circadian clock—termed the extended S-System model—to model circadian systems across different kingdoms of life. We then use this modeling strategy to develop a design framework, based on an antithetic integral feedback (AIF) controller, to restore a gene’s circadian profile when it is subject to loss-of-function due to external perturbations. The use of the AIF controller is motivated by its recent successful experimental implementation. Our findings provide circadian biologists with a systematic and general modeling and design approach for implementing synthetic feedback control of circadian systems. npj Systems Biology and Applications (2022)8:7 ; https://doi.org/10.1038/s41540-022-00216-x INTRODUCTION The daily routines of most living creatures are governed by their built-in biological clock, called the circadian system1. This biological clock oscillates in a quasi-sinusoidal manner with a period close to 24 h, which enables the anticipation and coordination of biological processes cued by diurnal environmental changes to happen at the most favorable time of the day. Some examples of circadian-controlled processes across different kingdoms of life include sleep/wake cycles in mammals, spore formation and release in fungi, leaf movement in plants, pupal eclosion in insects, and valve activity in bivalves (see e.g.,2–6), all of which are important biological functions necessary for organisms to function properly. Furthermore, many studies (see e.g.,7–11) have revealed a range of pathophysiological conditions associated with the disruption of the circadian rhythm (e.g., poor metabolism, psychiatric disorders, deterioration of the immune system), thereby suggesting the importance of keeping the circadian clock in a good operating condition. The general significance of circadian systems in biology is evident from the award of the 2017 Nobel Prize in Physiology or Medicine to the pioneers of circadian research12,13. At the molecular level, the circadian rhythm is primarily generated through gene-protein feedback loops involving transcription and translation14, as well as non-transcriptional mechanisms—e.g., involving calcium15 and sucrose16 regulation. In higher organisms (e.g., mammals and plants), circadian rhythms are orchestrated by complex gene regulatory networks involving multiple clock genes. In order to gain mechanistic insights into these networks, extensive work has been undertaken by computational biologists to develop comprehensive and accurate mathematical models. These models have shown their usefulness in, for example, elucidating the effects of disruption to the plant circadian system (e.g., to plant defense17,18 and plant development19) as well as revealing the core genetic components responsible for generating oscillations in plants (e.g.,20). From the perspective of synthetic biology, a disruption to the circadian system through transcription and translation mechanisms can be potentially addressed through the use of appropriate synthetic biomolecular circuits, such as those implementing feedback control. As mitigating the effects of perturbations to a system by means of feedback is an established subject of study for control engineers, synthetic biologists have started exploring the use of controller design principles to develop synthetic feedback control circuits that can be deployed to restore a disrupted natural system (see e.g.,21–23 and references therein). To facilitate the systematic and robust design of a synthetic feedback control circuit, an accurate model describing the system of interest is essential. In the case of circadian systems, the most common approach used to describe transcription and translation mechanisms is Michaelis–Menten modeling with Hill-type nonlinearities (see e.g.,24–29). Despite the prevalence of this modeling framework in describing circadian systems, our previous work30 (see also Supplementary Methods) showed that when attempting to estimate Michaelis–Menten kinetic constants from temporal data, the estimated values are found to be inconsistent—i.e., markedly different values of the kinetic constants can reproduce the same temporal data. From the point of view of feedback control design, consistent parameter estimates are critical, since tuning of the controller design parameters for optimal performance relies heavily on these estimates. In the same work30, we found that a power law-based model, termed the extended SSystem, does not suffer from inconsistent estimates, thereby making this modeling framework suitable for control design. In ref. 31, we show that this extended S-System modeling framework has comparable accuracy to equivalent Michaelis–Menten formulations in describing the plant circadian system, but with a much simpler mathematical structure. 1 School of Mechanical, Aerospace and Automotive Engineering, Coventry University, Coventry CV1 5FB, UK. 2College of Engineering, Mathematics and Physical Science, University of Exeter, Exeter EX4 4QF, UK. 3Warwick Integrative Synthetic Biology Centre, School of Engineering, University of Warwick, Coventry CV4 7AL, UK. 4Present address: School of Engineering, University of Warwick, Coventry CV4 7AL, UK. ✉email: Published in partnership with the Systems Biology Institute M. Foo et al. 2 Here, we generalize the extended S-System modeling framework to other circadian systems—namely mammals, fungi, and insects—and show how this modeling approach can be used to facilitate the design of antithetic integral feedback (AIF) controllers32 to restore a gene’s circadian profile when it is subject to loss-of-function due to external perturbations. The AIF controller is chosen in this study due to its recent successful experimental implementation33, a result that highlights its great potential for application to circadian clocks. The application of control theory to circadian systems is not new (see e.g.,34–38). However, previous works typically focused on controlling the external light sources to readjust the phase of the circadian rhythms of plant or mammals that have been altered due to perturbations. These contro (...truncated)