How to steer a living cell like a ship

We present a roadmap for realizing proportional-integral-derivative (PID) cybergenetic controllers in living cells.

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In 1922, Nicolas Minorsky wrote for the first time the mathematical law for what we now refer to as proportional-integral-derivative (PID) control. This ubiquitous scheme is at the heart of a three-part feedback regulation strategy that was first developed by Minorsky while working on automatic ship steering systems. Today, more than 95% of all industrial feedback control systems employ this PID control strategy.

One hundred years later, control theorists working in the field of synthetic biology are attempting to genetically engineer PID control systems inside living cells [1-5]. Such systems promise to achieve robust and precise regulation of cellular processes, with many potential applications in industrial biotechnology and medical therapy. But why PID, you may ask, and how is it different from the more familiar negative feedback strategies? The integral term of a PID controller gives robust perfect adaptation, a highly desirable property when regulating key variables of interest (e.g. species concentrations). The proportional and derivative terms, add to perfect adaptation enhanced dynamical stability, good transient dynamic performance, and noise rejection properties.

There is no shortage of challenges engineering PID control systems in living cells: Unlike their electronic/mechanical counterparts, genetic PID control systems must contend with the unique environment of the cell. In such an environment, the variables one works with are concentrations or reaction rates, and therefore they can only be positive. In addition, all mathematical operations must be achieved through biochemical reactions, which aside from being nonlinear exhibit noisy dynamics. Parameters are difficult to design and measure, and cellular resources are scarce and must be shared. In spite of these challenges early progress has shown that integral [1,2] and proportional-integral [3,4] genetic control systems can be successfully engineered in living cells. To date, no synthetic genetic PID control system has been built and demonstrated.

In this article [6], we put forth a framework for designing and implementing genetic PID controllers. We present a hierarchy of such controllers that go from the simple to the more complex. We show how biochemical reactions can be coaxed to realize the three key mathematical operations of scaling, integration, and differentiation. The genetic PID controllers are tested in a cyberloop environment, where the genetic controllers are simulated in a computer that is interfaced with living cells.

Synthetic PID controllers aside, one wonders if nature has evolved PID control in natural biological systems. While PI control systems have been observed in several biological regulatory mechanisms, I suspect that the answer is ‘Yes’ also for PID controllers. After all, when Minorsky set out to write the mathematical laws of PID control, he was just putting into equations his observations of an experienced helmsman steering a ship!


[1] Briat, C., Gupta, A., & Khammash, M. (2016). Antithetic integral feedback ensures robust perfect adaptation in noisy biomolecular networks. Cell systems, 2(1), 15-26.

[2] Briat, C., Gupta, A., & Khammash, M. (2018). Antithetic proportional-integral feedback for reduced variance and improved control performance of stochastic reaction networks. Journal of The Royal Society Interface, 15(143), 20180079.

[3] Aoki, S. K., Lillacci, G., Gupta, A., Baumschlager, A., Schweingruber, D., & Khammash, M. (2019). A universal biomolecular integral feedback controller for robust perfect adaptation. Nature, 570(7762), 533-537.

[4] Frei, T., Chang, C. H., Filo, M., & Khammash, M. (in press). A genetic mammalian proportional-integral feedback control circuit for robust and precise gene regulation. Proc. Nat. Acad. Sci.

[5] Chevalier, M., Gómez-Schiavon, M., Ng, A. H., & El-Samad, H. (2019). Design and analysis of a proportional-integral-derivative controller with biological molecules. Cell Systems, 9(4), 338-353.

[6] Filo, M., Kumar, S., & Khammash, M. (2022). A Hierarchy of Biomolecular Proportional-Integral-Derivative Feedback Controllers for Robust Perfect Adaptation and Dynamic Performance. Nature Communications.

Mustafa Khammash

Professor, ETH Zurich