Sigmoidal enzyme kinetics -- two forms of the model

 Built-in to Prism 5 is an equation that describes sigmoidal enzyme kinetics. 

Y=Vmax*X^h/(Kprime + X^h)

This was adapted from equation 5.47 of R. A. Copeland, Enzymes (link below). Y is enzyme activity, X is substrate concentration (not time, despite the term 'kinetics'), and Kprime is the product of the binding constant multiplied by the cooperativity factor.  

While this is a rigorously correct treatment of the data, it is not always the most pragmatic version of the equation. An alternative version of the equation (provided by Dr. Copeland, the author of the book linked below) fits Khalf, the concentration of ligand that will afford half maximal velocity (the EC50), instead of Kprime:

Y=Vmax*X^h/(Khalf^h + X^h)

Note that Kprime=Khalf^h. The two models generate exactly the same curve, and simply have alternative methods for reporting the parameters.

Prism can report some functions of best-fit parameters, but it cannot report one parameter taken to the power of another parameter. So Prism cannot simulataneously fit both Kprime and Khalf.

This file fits a set of data twice, once to each form of the equation. To include the alternative equation in your list of user-defined equations, go to that results page, click the button to change analysis parameters for the nonlinear fit, then click the button to view the equation. Ok twice and the equation will be on your user-defined list.