Improved Rearrangement of the Integrated Michaelis-Menten Equation for Calculating In Vivo Kinetics of Transport and Metabolism

¹ Division of Animal and Veterinary Sciences, West Virginia University, Morgantown 26506-6108
² Department of Epidemiology and Biostatistics, University of South Carolina, Columbia 29208

A multiple regression form of the integrated Michaelis-Menten equation was developed and evaluated with simulated data having controlled error. Both multiple and traditional linear regression fit errorless data perfectly, but multiple regression is much more stable with regard to accuracy and precision of estimating the Michaelis constant and maximum rate of reaction when data contain error. Bias in determining estimators of kinetic coefficients was –4 and –3% versus –56 and –35% with 10% error in the data. Multiple regression estimates for Michaelis constant and maximum rate of reaction directly as opposed to estimating 1/K_m and maximum rate of reaction/ Michaelis constant by linear regression. The difference in accuracy in estimating actual Michaelis constant, for example, is 4% versus 227% error with only 10% error in the data. Precision of estimation is approximately the same as precision of the data for multiple regression. For the 800 data sets examined, R² was always greater than .92 for multiple regression, but frequently was not significant for linear regression. The actual initial concentration was provided for linear regression but calculated by multiple regression with accuracy and precision equivalent to estimation of Michaelis constant and maximum rate of reaction. The multiple regression method has statistical power to determine treatment effects on Michaelis constant and maximum rate of reaction with a practical number of animals.

Key Words: Michaelis-Menten • in vivo kinetics • transport • clearance

Submitted on September 30, 1991
Accepted on July 24, 1992