On the compromise between retroactivity attenuation and noise amplification in gene regulatory networks

A bio-molecular system can be rendered insensitive to impedance-like effects, called retroactivity, at its downstream interconnections by implementing a large input amplification gain in a negative feedback loop. This type of design, however, relying on large amplifications, may have undesired effects on the internal noise of the system. We investigate this problem on a simple transcriptional component connected to downstream load by performing a stochastic analysis based on the Ω-expansion. While high gains increase the signal-to-noise ratio of the species in the upstream system and attenuate retroactivity, they also contribute to a shift toward high frequency of the internal noise of the system. We mathematically study this compromise by employing the Langevin equation and by analyzing the noise-to-state transfer function of the linearized system.