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

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.