Accurate kinetic parameter estimation during progress curve analysis of systems with endogenous substrate production

We have identified an error in the published integral form of the modified Michaelis–Menten equation that accounts for endogenous substrate production. The correct solution is presented and the error in both the substrate concentration, S, and the kinetic parameters V_m, K_m, and R resulting from the incorrect solution was characterized. The incorrect integral form resulted in substrate concentration errors as high as 50% resulting in 7–50% error in kinetic parameter estimates. To better reflect experimental scenarios, noise containing substrate depletion data were analyzed by both the incorrect and correct integral equations. While both equations resulted in identical fits to substrate depletion data, the final estimates of V_m, K_m, and R were different and K_m and R estimates from the incorrect integral equation deviated substantially from the actual values. Another observation was that at R = 0, the incorrect integral equation reduced to the correct form of the Michaelis–Menten equation. We believe this combination of excellent fits to experimental data, albeit with incorrect kinetic parameter estimates, and the reduction to the Michaelis–Menten equation at R = 0 is primarily responsible for the incorrectness to go unnoticed. However, the resulting error in kinetic parameter estimates will lead to incorrect biological interpretation and we urge the use of the correct integral form presented in this study. Biotechnol. Bioeng. 2011;108: 2499–2503. © 2011 Wiley Periodicals, Inc.