Many of today’s technological applications could not get by without them: Integral feedback control systems. Such control systems maintain airplanes at a defined altitude, a vehicle at constant speed on the highway, or an industrial oven at the same temperature. Through such a control system, one can normally achieve “robust perfect adaptation” to disturbances.
Robust perfect adaptation means that the controlled system settles at the predefined reference value, independently from external perturbations or the parameters of the system to be controlled. The integral feedback control system achieves this by integrating the response of the controlled system over time, and using the resulting signal in feedback to make corrections.
Invention of biological systems
Control systems are also found in biology. They regulate the body temperature of a warm-blooded animal, or the calcium balance in mammals. At the cellular level, they are responsible for the maintenance of cellular equilibrium, the so-called homeostasis.
However, a synthetic biological control system that can integrate responses over time was still missing. The challenge is that a strong background noise dominates inside living cells. This noise arises from randomly reacting molecules that are mostly available in very small numbers. Their abundance can suddenly increase, but also drop to zero over long times – chance thereby plays a big role.
Feedback control in cells
Mustafa Khammash, professor of control theory and systems biology at the department of Biosystems Science and Engineering (D-BSSE) in Basel and his coworkers Corentin Briat and Ankit Gupta present a new approach to this problem. In the latest edition of “Cell Systems” they propose how such a control system can function inside a cell so that precisely regulated amounts of a molecule can be produced despite the strong noise. The researchers called this regulation “antithetic integral feedback control” (AIFC).
The AIFC consists of two networks: the network that needs to be controlled, and a network that acts as a control system to regulate it. The coupling between the networks allows the intended perfect adaptation.
“We have constructed the AIFC such that it satisfies three important requirements of control theory in the case of systems affected by chance: it must be stable, the reference point must be adjustable and it must allow robust perfect adaptation,” says Khammash. And this system must work flawlessly in a sea of noise.
Noise stabilizes control network
The researchers have developed a new control theory and computer models for regulation at the molecular scale. With these they disprove a misconception that noise is always bad for a control system. They show that the noise can even be advantageous for cells, allowing them to achieve the intended robust perfect adaptation. “Without the molecular noise, the system response starts to oscillate”, says the ETH-professor. When one adds the noise back, the response perfectly matches the desired reference.
To back up their theoretical approach, the researchers searched for a natural AIFC – and found one. In the bacterium Escherichia coli there exists a signaling and protein production chain, which is actually built according to the scientists’ theories.
Gene control with AIFC
In this control loop the reference value corresponds to a certain average amount of a molecular complex, which consists of a so-called sigma factor (s70) and a RNA polymerase. The complex starts transcription, i.e. the reading of genes for the production of the building instructions for proteins from RNA. The affected proteins that are activated by this complex are needed by the bacterium for its growth.
In order for the protein production to not get out of control, a protein is made as “by-product”, which binds the s70 factor as anti-s70 and pulls it out of the traffic. As a consequence, less RNAP-s70 complexes are formed. In this way the transcription rate drops and the anti-s70 level drops in the cells, so that newly produced s70 molecules can bind again into RNAP-s70 complexes. The protein production increases again.
The researchers show with their theory that this system, which exhibits their AIFC motif, drives the production of a stable amount of this complex. Thereby the average concentration of the complex will be exactly right, to be able to induce the right anti-s70 concentration.
Reconciling a paradox
According to the calculations of the scientists, the free form of s70 exists in very small amounts. How can it then act as a regulator when it is almost non-existent? “This is where randomness enter the picture”, says Khammash. “The abundance of a regulating molecule like free s70 is randomly fluctuating. However, a statistical measure of this randomness, for example their time average, can serve as a deterministic regulating signal.” Varying average temporal availability is essential to realizing a measurement system using molecules that only exist in the smallest numbers.
With this work, Khammash and his coworkers solve a paradox. “In biology, beautiful observations of robust homeostasis and adaptation demonstrate that cryptic integral feedback must be present, but the way biological systems implement it is often mysterious,” says Professor John Doyle of the California Institute of Technology in a preview of the work by Khammash and coworkers. “This mystery has been particularly confounding when the small number of molecules present guarantee that the system will be noisy, yet adaptation still occurs,” This work reconciles the paradox, says Doyle. “When bacteria are trying to control their behavior with a small number of components, noise can actually work in their favor.”
Khammash and his coworkers have also laid the groundwork for the optimization of future synthetic control networks towards integral feedback control. Such networks could for example be designed for the stable and robust production of desired amounts of medical substances, certain hormones such as insulin or biologically derived fuels.
Briat C, Gupta A, Khammash M. Antithetic Integral Feedback Ensures Robust Perfect Adaptation in Noisy Biomolecular Networks. Cell Systems 2016, 2: 15-26, doi: 10.1016/j.cels.2016.01.004
Doyle J. Even noisy responses can be perfect if integrated properly. Cell Systems 2016, 2: 73-75, doi: 10.1016/j.cels.2016.02.012