Using stationary information flows to prove kinetic uncertainty relations in biochemical control systems

TL;DR

This paper proves that in biochemical control systems, reducing fluctuations in one component inevitably involves increased variability in another, highlighting a fundamental trade-off in cellular regulation.

Contribution

It provides an exact, general proof of a conjecture linking component variability to cellular control, using stationary information flows and probability current decompositions.

Findings

Variability in cellular components is necessary for control.

Fluctuating components can help remove noise from other molecules.

The proof is based on mutual information rate decompositions.

Abstract

Many cellular components are present in such low numbers that individual stochastic production and degradation events lead to significant fluctuations in molecular abundances. Although feedback control can, in principle, suppress such low-copy-number fluctuations, general rules have emerged that suggest fundamental performance constraints on feedback control in biochemical systems. In particular, previous work has conjectured that reducing abundance fluctuations in one component requires at least one sacrificial component with increased variability in arbitrary reaction networks of any size. Here, we present an exact and general proof of this statement based on probability current decompositions of mutual information rates between molecular abundances. This suggests that variability in cellular components is necessary for cellular control and that fluctuating components do not necessarily generate cellular "noise" but may correspond to control molecules that are involved in removing "noise" from other cellular components.