Efficiency-noise trade-offs in biomolecular assembly processes*

Molecular abundances in single cells fluctuate due to the inherent stochasticity of chemical processes. While biochemical systems are often sparsely characterized, bounds on such fluctuations can be derived for broad classes of stochastic systems. Using such an approach, previous work established a universal trade-off between the efficiency of complex formation and subunit abundance fluctuations. Yet, perfectly efficient complex formation is central to antithetic integral feedback, a universal motif for achieving perfect adaptation of average cellular abundances. Here, we analyze the differences between antithetic integral feedback control and the previously discussed class of complex formation systems, where perfect efficiency corresponds to divergent fluctuations. We establish that dual-input feedback is a necessary but not sufficient condition to overcome the previously discussed efficiency-noise trade-off.