Abstract
Proportional-Integral-Derivative (PID) feedback controllers have been the most widely used controllers in industry for almost a century due to their good performance, simplicity, and ease of tuning. Motivated by their success in various engineering disciplines, PID controllers recently found their way into synthetic biology, where the design of feedback molecular control systems has been identified as an important goal. In this paper, we consider the mathematical realization of PID controllers via biomolecular interactions. We propose an array of topologies that offer a compromise between simplicity and high performance. We first demonstrate that different Proportional-Integral (PI) controllers exhibit different capabilities for enhancing the dynamics and reducing variance (cell-to-cell variability). Next, we introduce several derivative controllers that are realized based on incoherent feedforward loops acting in a feedback configuration. Alternatively, we show that differentiators can be realized by placing molecular integrators in a negative feedback loop—an arrangement that can then be augmented by PI components to yield PID feedback controllers. We demonstrate that the derivative component can be exploited for enhancing system stability, dramatically increasing the molecular control system’s dynamic performance, and for reducing the noise effect on the output of interest. The PID controller features are established through various deterministic and stochastic analyses as well as numerical simulations. Finally, we provide an experimental demonstration using a recently developed hybrid setup, the cyberloop, where the controller is implemented in silico to control a biological genetic circuit in vivo. The large array of novel biomolecular PID controllers introduced here forms a basis for the design and construction of advanced high-performance biomolecular control systems that robustly regulate the dynamics of living systems.
Competing Interest Statement
ETH Zurich has filed a patent application on behalf of the inventors T.F., C.H.C., M.F. and M.K. that includes the designs described (application no. EP21187316.1).
Footnotes
Firstly, we have proposed genetic designs in E.coli with specific biological parts that are capable of realizing two of our PID controllers. The biological parts detail the various choices of transcription factors, promoters and sequestration mechanisms that are capable of realizing the reaction-network control topologies which we propose in the manuscript. Furthermore, we carried out a careful literature review to extract biologically realistic values of the various parameters in the designed circuits. This allowed us to perform numerical simulations that demonstrate the effectiveness of our controllers in more realistic settings. Secondly, we have demonstrated the effectiveness of one of our more complex PID controllers in the Cyberloop, a hybrid experimental setup that we have recently developed. The Cyberloop serves as an ideal rapid prototyping platform for testing biomolecular controllers. In this hybrid setup, the controller is implemented in silico by carrying out a stochastic simulation of the controller topology in the computer, while the network to be controlled is a real biological genetic circuit. The in silico controller actuates the in vivo genetic circuit through light (exploiting light-responsive biological parts) and senses it using fluorescence microscopy. In the new version of our manuscript, we included experiments that clearly demonstrate the performance enhancements gained by one of our biomolecular PID controllers.