What is the rate law for the Eigen-Wilkins reaction mechanism?

[Amok]

Hi,

Can anyone help derive the rate law for the Eigen wilkins reaction mechanism? The derivation in the wikipedia entry (http://en.wikipedia.org/wiki/Eigen-Wilkins_Mechanism) is confusing, but the rate law is correct. I can't figure out if they make a "steady-state" approximation or a pre-equilibrium approximation, but I'm pretty sure it's both (weird).

 

[Ygggdrasil]

The equation looks very similar to the Michaelis-Menten (MM) equation used in biochemistry if you substitute [Y] for , [M]tot for [E]0, and K_E for 1/K_M (see equation 11 from the link below). The MM equation is similarly derived by assuming a mechanism whereby two molecules form an initial encounter complex that converts to product in the rate limiting step. The MM equation can be derived solely by using the steady-state approximation, for example, see the following site for a derivation: http://biofitweb.cox-thurmond.net/FittingRoom/MMderivation.htm

 

[Amok]

I tried it and it's not exactly the same. Unfortunately I don't have access to the original article that gives the derivation, but in the abstract they say they use a pre-equilbirum. But maybe I missed something, I'll try it again.