  For a paradigmatic model of chemotaxis, we analyze the effect how a nonzero
affinity driving receptors out of equilibrium affects sensitivity. This
affinity arises whenever changes in receptor activity involve ATP hydrolysis.
The sensitivity integrated over a ligand concentration range is shown to be
enhanced by the affinity, providing a measure of how much energy consumption
improves sensing. With this integrated sensitivity we can establish an
intriguing analogy between sensing with nonequilibrium receptors and kinetic
proofreading: the increase in integrated sensitivity is equivalent to the
decrease of the error in kinetic proofreading. The influence of the occupancy
of the receptor on the phosphorylation and dephosphorylation reaction rates is
shown to be crucial for the relation between integrated sensitivity and
affinity. This influence can even lead to a regime where a nonzero affinity
decreases the integrated sensitivity, which corresponds to anti-proofreading.
