Efficiency-fluctuation trade-offs in biomolecular assembly processes

TL;DR

This paper explores the fundamental trade-off between efficiency and fluctuations in biomolecular assembly processes, revealing that most such processes inherently face diverging fluctuations at high efficiency unless specific feedback controls are implemented.

Contribution

It broadens the understanding of the efficiency-fluctuation trade-off in biomolecular assemblies and identifies feedback control as a key to overcoming divergence in fluctuations.

Findings

Most assembly processes exhibit an efficiency-fluctuation trade-off.

Feedback control, especially with distinct subunit synthesis rates, can prevent divergence.

Biomolecular integral controllers are one example of such feedback mechanisms.

Abstract

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.