Fundamental limits on the suppression of molecular fluctuations

Negative feedback is common in biological processes and can increase a system’s stability to internal and external perturbations. But at the molecular level, control loops always involve signaling steps with finite rates for random births and deaths of individual molecules. By developing mathematical tools that merge control and information theory with physical chemistry we show that seemingly mild constraints on these rates place severe limits on the ability to suppress molecular fluctuations. Specifically, the minimum standard deviation in abundances decreases with the quartic root of the number of signaling events, making it extraordinarily expensive to increase accuracy. Our results are formulated in terms of experimental observables, and existing data show that cells use brute force when noise suppression is essential, e.g. transcribing regulatory genes 10,000s of times per cell cycle. The theory challenges conventional beliefs about biochemical accuracy and presents an approach to rigorously analyze poorly characterized biological systems.