An algebraic model to determine substrate kinetic parameters by global nonlinear fit of progress curves

We propose that the time course of an enzyme reaction following the Michaelis-Menten reaction mechanism can be conveniently described by a newly derived algebraic equation, which includes the Lambert Omega function. Following Northrop's ideas [Anal. Biochem.321, 457-461, 1983], the integrated rate equation contains the Michaelis constant (K_M) and the specificity number (k_S≡k_cat/K_M) as adjustable parameters, but not the turnover number k_cat. A modification of the usual global-fit approach involves a combinatorial treatment of nominal substrate concentrations being treated as fixed or alternately optimized model parameters. The newly proposed method is compared with the standard approach based on the "initial linear region" of the reaction progress curves, followed by nonlinear fit of initial rates to the hyperbolic Michaelis-Menten equation. A representative set of three chelation-enhanced fluorescence EGFR kinase substrates is used for experimental illustration. In one case, both data analysis methods (linear and nonlinear) produced identical results. However, in another test case, the standard method incorrectly reported a finite (50-70 μM) K_M value, whereas the more rigorous global nonlinear fit shows that the K_M is immeasurably high.