A suite of mathematical solutions to describe ternary complex formation and their application to targeted protein degradation by heterobifunctional ligands

Small molecule–induced targeted protein degradation by heterobifunctional ligands or molecular glues represents a new modality in drug development, allowing development of therapeutic agents for targets previously considered undruggable. Successful target engagement requires the formation of a ternary complex (TC) when the ligand brings its target protein in contact with an E3 ubiquitin ligase. Unlike traditional drugs, where target engagement can be described by a simple bimolecular equilibrium equation, similar mathematical tools are currently not available to describe TC formation in a universal manner. This current limitation substantially increases the challenges of developing drugs with targeted protein degradation mechanism. In this article, I provide a full, exact, and universal mathematical description of the TC system at equilibrium for the first time. I have also constructed a comprehensive suite of mathematical tools for quantitative measurement of target engagement and equilibrium constants from experimental data. Mechanistic explanations are provided for many common challenges associated with developing this type of therapeutic agent. Insights from these analyses provide testable hypotheses and grant direction to drug development efforts in this promising area. The mathematical and analytical tools described in this article may also have broader applications in other areas of biology and chemistry in which ternary complexes are observed.