A Comprehensive Mathematical Model for Three-Body Binding Equilibria

Three-component
systems are often more complex than their two-component
counterparts. Although the reversible association of three components
in solution is critical for a vast array of chemical and biological
processes, no general physical picture of such systems has emerged.
Here we have developed a general, comprehensive framework for understanding
ternary complex equilibria, which relates directly to familiar concepts
such as EC50 and IC50 from simpler (binary complex)
equilibria. Importantly, application of our model to data from the
published literature has enabled us to achieve new insights into complex
systems ranging from coagulation to therapeutic dosing regimens for
monoclonal antibodies. We also provide an Excel spreadsheet to assist
readers in both conceptualizing and applying our models. Overall,
our analysis has the potential to render complex three-component systemswhich
have previously been characterized as “analytically intractable”readily
comprehensible to theoreticians and experimentalists alike.