What does "dep" mean?
The "dep" probably stands for "depletion": read the paper you linked to for more context. Often times, subscripts on rate constants are used to refer to which reaction in a system of multiple reactions. You'll see $k_1$ and $k_2$ for rate constants of "reaction 1" and "reaction 2", etc.

I suspect in the paper, they were measuring the depletion of a substrate, and not what the substrate was converted to.  So they wouldn't know if they were measuring the rate of a single reaction $\ce{A-&gt;B}$, or the combined rates of multiple reactions such as $\ce{A-&gt;B}$ and $\ce{A-&gt;C}$.  Thus (probably) the desire to indicate $k_{depletion}$ instead of just $k$.