Mean-field cooperativity in chemical kinetics

TL;DR

This paper uses mean-field statistical mechanics models to analyze cooperative reactions, linking microscopic interactions to macroscopic reaction rates, and introduces criteria to distinguish weak and strong cooperativity.

Contribution

It develops a unified mean-field framework for cooperative reactions, including criteria for weak and strong cooperativity and extension to p-body interactions.

Findings

Model recovers all cooperative measures with positive coupling

Introduces susceptibility-based criterion for cooperativity strength

Extends to p-body interactions for multiple attachments phenomena

Abstract

We consider cooperative reactions and we study the effects of the interaction strength among the system components on the reaction rate, hence realizing a connection between microscopic and macroscopic observables. Our approach is based on statistical mechanics models and it is developed analytically via mean-field techniques. First of all, we show that, when the coupling strength is set positive, the model is able to consistently recover all the various cooperative measures previously introduced, hence obtaining a single unifying framework. Furthermore, we introduce a criterion to discriminate between weak and strong cooperativity, based on a measure of "susceptibility". We also properly extend the model in order to account for multiple attachments phenomena: this is realized by incorporating within the model $p$-body interactions, whose non-trivial cooperative capability is investigated too.