 ATPase dwell-time inference from concentration dependence

A rotary ATP synthase subunit can exhibit an ATP-dependent exponential distribution of binding waits with rate $k_{1}c$ and an ATP-independent sum of two first-order waits. Convolution gives the latter density $k_a{k}_b(e^{-k_{b}t}-e^{-k_{a}t})/(k_a-k_b)$. The equal-rate limit is the Erlang distribution $k^{2}t{e}^{-kt}$. These fits support one concentration-dependent binding event and two kinetically resolved transitions, but do not uniquely assign the latter to hydrolysis, product release or conformational change. Their rates cannot be ordered from this symmetric density alone.