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 positivecooperative 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.

Symmetries and criticality of generalised van der Waals models

“…The problem of constructing suitable partial differential equations for state functions of thermodynamic systems and the study of critical properties in terms of critical asympotics of the solutions to these equations is an active field of research which brought further insights on a variety of classical systems, see e.g. [33][34][35][36][37][38], and appears to be promising for the study of complex systems [39,40]. Studies similar to the present work can be put forward therefore for other systems of physical interest.…”

On solutions to a novel non-evolutionary integrable 1 + 1 PDE

“…Other developments may be more focused on the application of equation ( 1), including those for purposes potentially different from the fluid systems considered so far, such as in the context of complex systems based on mean-field spin models. The idea of formally describing the governing behaviour of relevant statistical quantities through the solutions of PDEs is starting to be appraised even for problems in reaction kinetics [47] and artificial intelligence [48], for instance. This may raise the question about the possible need to implement the model (3) while dealing with specific problems, such as by taking into account other non-local terms in the expansion that may cure or smoothen appearing criticalities and allow for the identification of multiple scales of both mathematical and applicative relevance.…”

Symmetries and criticality of generalised van der Waals models

“…The problem of constructing suitable partial differential equations for state functions of thermodynamic systems and the study of critical properties in terms of critical asymptotics of the solutions to these equations is an active field of research which brought further insights on a variety of classical systems, see e.g. [34][35][36][37][38][39], and appears to be promising for the study of complex systems [40,41]. Studies exploiting the Lie symmetry analysis can be therefore carried out for other systems of physical interest.…”