Physical limits of feedback noise-suppression in biological networks

Feedback is a ubiquitous control mechanism of biological networks, and has also been identified in a variety of regulatory systems and organisms. It has been shown that, for a given gain and with negligible intrinsic noise, negative feedback impairs noise buffering whereas positive feedback enhances noise buffering. We further investigate the influence of negative and positive feedback on noise in output signals by considering both intrinsic and extrinsic noise as well as operator noise. We find that, while maintaining the system sensitivity, either there exists a minimum of the output noise intensity corresponding to a biologically feasible feedback strength, or the output noise intensity is a monotonic function of feedback strength bounded by both biological and dynamical constraints. In both cases, feedback noise-suppression is physically limited. In other words, noise suppressed by negative or positive feedback cannot be reduced without limitation even in the case of slow transcription.