If Kd=1/Ka and Ka=1/M, then the units would be Kd=1/[1/M]=M. So yeah, Kd would then be M, not 1/M. The dimensional analysis wouldn't make sense otherwise.
Sorry for my old gchem knowledge, but I wonder if you are really talking about equilibria (specifically acid-base), not kinetics. Are you sure the "K" is capitalized?
I was gonna say the same thing. I'm not exactly sure what you're talking about, but in no case that I can think of would you have a situation in which M=1/M unless M were a unitless 1, in which case it would be pretty pointless and could just be treated as a constant.
Yeah, it's probably equlibria then. AFAIK/BTW, Ka is reserved for acids. You can use plain Kc for the foward reaction. K' can be the reverse. It actually makes sense if you figure out the units for each reaction... the stoichiometry changes with reactions. However, I remember not even bothering to use units for K and just treating it as an unitless quantity.
In your notation, does Kd denote the reverse reaction away from the protein-DNA complex?