Dwell time equations for ATP-sythase?
ATP Binding dwell time

Here is a very dodgy derivation of the binding dwell time (note I am the OP). For this we have $$E+S\rightarrow ES$$
Where $E$ is the enzyme and $S$ is the substrate (keeping this general). We can write our rate equation as: 
$$rate=k[E][S]$$
But we can also write the rate as:
$$rate=-\frac{d[E]}{dt}$$
so that:
$$\frac{d[E]}{dt}=-k[E][S]$$
Now here is the bit that I think is a bit dodgy, we are going to assume that $[S]$ is approximately constant. So that:
$$[E]=Ae^{-k[S]t}$$
We can take $n=[E]V$ to represent the number of enzymes left, where $V$ is the volume, then letting $n_0=VA=constant$:
$$n=n_0e^{-k[S]t}$$
The probability of been within the time $t$ is then given by:
$$F(t)=1-e^{-k[S]t}$$
Which is our commutative distribution function. Differentiating this gives our probability density function:
$$f(t)=k[S]e^{-k[s]t}$$

Interim dwell time

The interim dwell time (also called the catalytic dwell time) involves two steps[7]:
1. The cleavage of the enzyme bound ATP.
2. The release of the hydrolysed products.

Each of which is going to follow the distribution (analogous to the above) of:

$$p_i(t)=k_i e^{-k_i t_i}$$
For $i=1,2$ respectively. The joint probability distribution is found by the convolution of these two [8]:
$$p_T(t)=\int^{\tau}_0 p_1(t) p_2(\tau-t)dt$$
Which gives:
$$p_T(t)=\frac{k_1 k_2}{k_1-k_2} (e^{-k_2 \tau}-e^{-k_1\tau})$$

Edit

Although starting from deterministic equations (which actually doesn't really matter), this method does hold and is simple. The type of reaction is called a pseudo-1st-order reaction (or 2nd order class 2) which explains my approximation for $[S]$ been constant. See [9] and [10] 

Sources for additional info


https://youtu.be/X_YXTWU2maY?list=PLbKSbFnKYVY3j6ubaW1zgTXj5C4443v8s
http://www.nature.com/articles/srep08773
http://www.ks.uiuc.edu/Research/atp_hydrolysis/
http://www.pnas.org/content/85/17/6314.full.pdf
https://books.google.co.uk/books?id=uIxwICNmLKEC&amp;pg=PA199&amp;lpg=PA199&amp;dq=catalytic+dwell+time+distribution+%5Batp%5D&amp;source=bl&amp;ots=u8oBcVNCDc&amp;sig=PKvdVAwT0WxdqTuVwMxhU3RfSwM&amp;hl=en&amp;sa=X&amp;ved=0CCAQ6AEwADgKahUKEwiGhKDalufHAhXkadsKHc54ADs#v=onepage&amp;q=catalytic%20dwell%20time%20distribution%20%5Batp%5D&amp;f=false
http://crystal.harvard.edu/PDFs/floyd_biophysj.2010.pdf
http://www.ncbi.nlm.nih.gov/pubmed/16258036
http://crystal.harvard.edu/PDFs/floyd_biophysj.2010.pdf
http://glutxi.umassmed.edu/grad/GradKinetics.pdf
http://chemwiki.ucdavis.edu/Physical_Chemistry/Kinetics/Reaction_Rates/Second-Order_Reactions/Pseudo-1st-order_reactions