The integrated Michaelis-Menten rate equation: déjà vu or vu jàdé?
A recent article of Johnson and Goody (Biochemistry, 2011;50:8264-8269) described the almost-100-years-old paper of Michaelis and Menten. Johnson and Goody translated this classic article and presented the historical perspective to one of incipient enzyme-reaction data analysis, including a pioneering global fit of the integrated rate equation in its implicit form to the experimental time-course data. They reanalyzed these data, although only numerical techniques were used to solve the model equations. However, there is also the still little known algebraic rate-integration equation in a closed form that enables direct fitting of the data. Therefore, in this commentary, I briefly present the integral solution of the Michaelis-Menten rate equation, which has been largely overlooked for three decades. This solution is expressed in terms of the Lambert W function, and I demonstrate here its use for global nonlinear regression curve fitting, as carried out with the original time-course dataset of Michaelis and Menten.
Institute of Biochemistry, Faculty of Medicine, University of Ljubljana, Vrazov trg 2, Ljubljana, Slovenia. marko.golicnik@mf.uni-lj.si
Marko
M
Goličnik
D055162:Biocatalysis; D004798:Enzymes / Q000737:chemistry / Q000378:metabolism*; D005632:Fructose / Q000737:chemistry / Q000378:metabolism; D005947:Glucose / Q000737:chemistry / Q000378:metabolism; D006868:Hydrolysis; D007700:Kinetics; D012996:Solutions; D013395:Sucrose / Q000737:chemistry / Q000378:metabolism
D004798:Enzymes; D012996:Solutions; D005632:Fructose; D013395:Sucrose; D005947:Glucose