Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Exploiting stochastic focusing for noise reduction through feedback
Andreas Milias-Argeitis, Pavol Bauer, Stefan Engblom, Mustafa Khammash

Last modified: 2014-03-31


Stochastic focusing [Paulsson et al., PNAS 97(13), 2000] has been proposed as a mechanism of sensitivity amplification: due to random fluctuations, changes in the mean level of a “signal” species can result in disproportionally large changes in the mean abundance of a “product” molecule. However, systems with the capability of stochastic focusing can also display extreme product fluctuations, when signal fluctuations are slow relatively to the lifetime of product molecules. Increased sensitivity to changes in the signal may thus be obtained at the cost of an extreme (and probably undesirable) noise in system output.

In the world of analog electronics, a system with similar properties is the operational amplifier (op-amp), a ubiquitous device that serves as a building block for many analog circuits. Op-amps are hardly usable in open loop, due to the fact that they tend to amplify both internal and input noise, while their open-loop gain is highly variable from one part to another and sensitive to temperature variations. However, redirecting a part of the op-amp output to its inverting input results in a very robust, noise-free and predictable circuit element, thanks to the properties of negative feedback and the high open-loop gain of the op-amp.

In this work we consider a simple stochastically focused system, where a low-copy signal molecule controls the degradation of a substrate with a high production rate. Following the op-amp idea, we explore the behavior of the system operating under feedback from the product to the signal molecule. Interestingly, this negative feedback configuration generates a dramatic reduction of output fluctuations, as demonstrated by our extensive simulation analysis. The resulting system also displays increased robustness to variations in reaction rates that is almost identical to its deterministic counterpart, despite the fact that the numbers of molecules involved are still very small.

Similarly low output noise levels (for the same output mean) in the open-loop system can be alternatively achieved by increasing the number of signal molecules, while simultaneously decreasing the coupling strength between signal and product. This, however, is a wasteful control scheme, as it requires many signal molecules to control a small amount of product. On the other hand, a decrease in the signal mean and increase in coupling generates the conditions for stochastic focusing and the accompanying large output fluctuations. The feedback mechanism studied in this work allows maintaining both species at low copies while keeping output noise low.

Our results could assist the construction of synthetic biochemical networks with low-copy components and good noise properties. On the other hand, they present another possible noise suppression mechanism for natural biochemical systems.


stochastic focusing; feedback control; stochastic chemical kinetics