On the Lambert W function and its utility in biochemical kinetics

This article presents closed-form analytic solutions to three illustrative problems in biochemical kinetics that have usually been considered solvable only by various numerical methods. The problems solved concern two enzyme-catalyzed reaction systems that obey diversely modified Michaelis–Menten rate equations, and biomolecule surface binding that is limited by mass transport. These problems involve the solutions of transcendental equations that include products of variables and their logarithms. Such equations are solvable by the use of the Lambert W(x) function. Thus, these standard kinetics examples are solved in terms of W(x) to show the applicability of this commonly unknown function to the biochemical community. Hence, this review first of all describes the mathematical definition and properties of the W(x) function and its numerical evaluations, together with analytical approximations, and then it describes the use of the W(x) function in biochemical kinetics. Other applications of the function in various engineering sciences are also cited, although not described.

► This review describes the Lambert W function, and its use in biochemical kinetics.
► Numerical evaluations of W, together with analytical approximations, are presented.
► Three illustrative problems that are solvable by the use of W are demonstrated.
► The utility of W in various engineering sciences are also cited but not described.