Complex Reaction Kinetics in Chemistry: A Unified Picture Suggested by Mechanics in Physics

Abstract

Complex biochemical pathways can be reduced to chains of elementary reactions, which can be described in terms of chemical kinetics. Among the elementary reactions so far extensively investigated, we recall the Michaelis-Menten and the Hill positive-cooperative kinetics, which apply to molecular binding and are characterized by the absence and the presence, respectively, of cooperative interactions between binding sites. However, there is evidence of reactions displaying a more complex pattern: these follow the positive-cooperative scenario at small substrate concentration, yet negative-cooperative effects emerge as the substrate concentration is increased. Here, we analyze the formal analogy between the mathematical backbone of (classical) reaction kinetics in Chemistry and that of (classical) mechanics in Physics. We first show that standard cooperative kinetics can be framed in terms of classical mechanics, where the emerging phenomenology can be obtained by applying the principle of least action of classical mechanics. Further, since the saturation function plays in Chemistry the same role played by velocity in Physics, we show that a relativistic scaffold naturally accounts for the kinetics of the above-mentioned complex reactions. The proposed formalism yields to a unique, consistent picture for cooperative-like reactions and to a stronger mathematical control.