Modification of the law of mass action for homotypic interactions

TL;DR

This paper revises the law of mass action for homotypic interactions, showing it overestimates interaction rates and proposing a factorial correction based on combinatorial mathematics for more accurate predictions.

Contribution

It introduces a modified law of mass action that accounts for homointeractivity, improving the accuracy of interaction rate predictions in systems with identical elements.

Findings

The traditional law overestimates homotypic interaction rates.

A factorial correction improves the law's accuracy.

The correction depends on homointeractivity and density differences.

Abstract

In its general definition, the law of mass action posits that, in systems where multiple elements move randomly, the rate by which they physically interact is proportional to the product of their densities. This law predicts the rate of elementary chemical reactions and many other phenomena in biology, physics, and social sciences. Using combinatorial mathematics, this study shows that this law inherently overestimates the rate of homotypic interactions, i.e. whereby identical elements interact with each other. This overestimation depends on how many of them interact simultaneously (homointeractivity), and on the difference between the density of interactants and homointeractivity. When this difference is large, as in most systems, the rate expression given by the law of mass action for any homotypic interaction is corrected by dividing it by the factorial of homointeractivity. This modification should yield better agreement between theoretical predictions and experimental determinations of interaction rates in a wide range of natural phenomena.