Brayden Kell | Searcharxiv

arXiv2025

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.

q-bio.MN↗

arXiv2024

Efficiency-fluctuation trade-offs in biomolecular assembly processes

Stochastic fluctuations of molecular abundances are a ubiquitous feature of cellular processes and lead to significant cell-to-cell variability. Recent theoretical work established lower bounds for stochastic fluctuations in cells for broad classes of cellular processes by analyzing the dynamics of reaction motifs that are embedded within a larger network with arbitrary interactions and dynamics. For example, a class of generalized assembly processes in which two co-regulated subunits irreversibly form a complex was shown to exhibit an unavoidable trade-off between assembly efficiency and subunit fluctuations: Regardless of rate constants and details of feedback control, subunit fluctuations were shown to diverge as the assembly efficiency approaches 100%. In contrast, other work has reported how efficient assembly processes work as stochastic noise filters or can achieve robust adaptation through integral control. While all of these results are technically correct their seemingly contradictory conclusions raise the question of how broadly applicable the previously reported efficiency-fluctuation trade-off is. Here, we show that a much broader class of assembly processes than previously considered is subject to an efficiency-fluctuation trade-off which diverges in the high efficiency regime. We find the proposed noise filtering property of efficient assembly processes corresponds to a singular limit of this class of systems. Additionally, we show that combining feedback control with distinct subunit synthesis rates is a necessary condition to overcome the generalized efficiency-fluctuation trade-off. Through numerical examples, we show that biomolecular integral controllers are one of several realizations of such control. How small a change to joint subunit control is sufficient to avoid diverging fluctuations in the high-efficiency limit remains an open question.

q-bio.MN↗