An ATP-binding step with pseudo-first-order rate k1c has survival probabilityS1=e−k1ct and waiting densityP1=−S1′=k1ce−k1ct. It decreases from a finite value at zero, integrates to one and has mean 1/(k1c). Its concentration dependence suggests binding-limited waiting before the large 80-degree substep.
Two independent sequential exponential steps of rates ka,kb give the convolution
It begins at zero, rises to a maximum at log(ka/kb)/(ka−kb) and decays; its mean is ka−1+kb−1. At equal rates it becomes k2te−kt. This supports at least two kinetic events during the waiting associated with the 40-degree substep, plausibly chemical transformation/product release and conformational changes. It does not uniquely identify which rate belongs to hydrolysis or a particular product: different hidden-state networks can have the same waiting distribution. Three 120-degree catalytic cycles per revolution, partitioned into 80 and 40 degrees in the assay, are consistent with three catalytic sites.
