The Integrated Michaelis-Menten Model

• Activity Number: 254
• Type: Contributed
• Date/Time: Tuesday, August 13, 2002 : 2:00 PM to 3:50 PM
• Sponsor: General Methodology
• Author(s): Don Edwards*+
• Affiliation(s): University of South Carolina
• Keywords: nonlinear regression ; chemical kinetics ; curvilinear regression

Abstract

The Michaelis-Menten model is one of the oldest and most widely used nonlinear regression models. Classically, it models the velocity V of some reaction as a function of the concentration C of a substrate consumed by the reaction. Often, however, the velocity of the reaction is defined simply as the rate of consumption of the substrate, and as such is not directly measurable without the use of a finite difference approximation. Here, we consider the integrated form of the Michaelis-Menten function, which models the substrate concentration C as a function of time as the reaction proceeds. A new nonlinear function, which we call the integrated Michaelis-Menten (imm) function, arises. It is a continuous hybrid of linear and exponential forms which may have applications in other settings. We formally derive the imm function, discuss its properties, and give an example of its use in modeling Nitrogen uptake in Spartina Alterniflora (marsh grass).