Why nature has elected Michaelis-Menten kinetics for enzymes: a tentative rationale from variational calculus

Abstract

The kinetic performance of enzymes, the catalysts designed by nature to accelerate the chemical reactions that support life, has traditionally been described in terms of a rate expression first derived by Michaelis and Menten in the beginning of this century. Why nature has selected such kinetic behaviour remains, however, a mystery. A tentative rationale based on Euler's equation was developed and, after having eliminated functional forms due to physico-chemical unfeasibility, a final open-form objective function (written as an infinite series and including dependencies on the substrate concentration, on the reaction rate, and on the derivative thereof with respect to concentration) is found. The integral of such an objective function is maximized by Michaelis-Menten kinetics and yields its maximum value when the upper integration limit is roughly equal to the Michaelis-Menten constant.