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A Comprehensive Mathematical Model for Three-Body Binding Equilibria

Douglass, Eugene F., Miller, Chad J., Sparer, Gerson, Shapiro, Harold, Spiegel, David A.
Journal of the American Chemical Society 2013 v.135 no.16 pp. 6092-6099
coagulation, inhibitory concentration 50, mathematical models, median effective concentration, monoclonal antibodies
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.