Correction to: Nature Communications https://doi.org/10.1038/s41467-023-38350-7, published online 12 May 2023

In Fig. 4d “Energy efficiency” data were incorrectly plotted and the arrows to indicate the corresponding y-axes were absent; the figure should have appeared as shown below.

Additionally, in Fig. 6a the arrows indicating the directionality of species fluxes across the membrane were inadvertently reversed; the figure should have appeared as shown below.

The original article has been corrected.