Trade-offs and limits in feedback-driven noise suppression

Johan Paulsson (Harvard Medical School)

Abstract

Negative feedback control is thought to check spontaneous fluctuations and provide homeostasis to external changes. However, most control theory has focused on macroscopically large systems subject to external perturbations – like airplanes in random gusts of wind – while other principles can arise in discrete molecular-scale probabilistic processes. Many biological control loops are also strongly nonlinear, and crucial aspects are often unknown. Such systems are typically considered impossible to analyze: how can we make quantitative statements about strongly nonlinear stochastic systems if we do not even know the nature of the nonlinearities? By combining exact analytical tools from functional analysis, information theory and statistical physics, we show that seemingly mild constraints, such as short delays or finite numbers of control molecules, can place fundamental limits on noise suppression that no arbitrarily elaborate feedback system could overcome – hard physical bounds that can be derived explicitly. Using approximate methods for families of feedback systems, we also show how the limits can arise because different types of noise are suppressed according to incompatible principles, generating frustration trade-offs where reducing one type of variation inevitably amplifies another. Finally we identify partial loopholes in the general laws where counterintuitive mechanisms can circumvent the trade-offs to some extent. The general results are illustrated by bacterial plasmids, where large fluctuations promote extinction and where numerous mechanisms have evolved to approach the physical limits.

Back to The First q-bio Conference.