Taming the mathematical beast of ternary complex for targeted protein degradation

Protein degradation is a normal process of protein turnover within the cell. It provides a mechanism of quality control during protein folding, an ability to rapidly respond to changing cellular signals, and a mechanism to modulate the pool of available amino acids. Due to extensive research in the area, small molecule-induced targeted protein degradation has been identified as a promising method for developing conventional drugs for traditionally undruggable targets. Specifically, targeted protein degradation removes the entire protein with the assurance to reproduce gene knock out or knock down phenotypes. Consequently, this approach enhances the in vivo efficacy of therapeutic agents for their targets. However, achieving specific protein degradation requires the ligand-induced formation of a ternary complex that brings an E3 ubiquitin ligase into a contact with the target protein with a resulting polyubiquitination and subsequent degradation by proteasome complex. Two main types of ligands widely used for targeted protein degradation are heterobifunctional ligands and molecular glues. In addition to their modular nature, heterobifunctional ligands can be constructed from existing ligands, making them a preferred choice for drug development in this mechanism.

Ternary complex formation is analogous to target engagement associated with traditional drug action. As such, measurements and quantification of ternary complex formation are considered critical in the screening and characterization of ligands. For most traditional drugs, the dose-response curve of the target engagement is sigmoid in shape reaching 100% target occupancy at sufficiently high ligand concentrations, and this relationship can be described by a simple mathematical equation. On the other hand, the dose-response behavior for the ternary complex by heterobifunctional ligands exhibit a hook effect engaging only a fraction of the target protein population even at the height of the bell-shaped curve. Higher ligand concentrations are inhibitory. Due to this, careful dose titrations are deemed necessary for successful target protein degradation using heterobifunctional ligands.

Despite the extensive research in this area, there had been no reliable mathematical tools to describe the ternary complex formation. Besides, developing effective therapeutic agents for such mechanisms is made difficult by the lack of easily measurable biochemical properties predictive of efficacy and potency of the drug molecules. These challenges present a great obstacle to developing drugs with efficient targeted protein degradation mechanisms. To address these challenges, Dr. Bomie Han from Lilly Research Laboratories developed a universal mathematical description of the ternary complex system at equilibrium and its variations in biological systems. In this work published in the Journal of Biological Chemistry, he also provided discussions on its implications in biological systems and drug development for targeted protein degradation.

Dr. Han first solved different mathematical equations describing various system components based on free ligand concentrations at equilibrium. Next, mathematical modeling of the systems allowed the author to understand the underlying causes for several challenges in developing reagents for targeted protein degradation, leading to alternative solutions. He also developed analytical tools for extracting required information on the efficacy and potency of target engagement and equilibrium constants from the dose response data. Finally, the applicability of the mathematic solutions to target protein degradation by heterobifunctional ligands was discussed.

Results proved that the presented mathematical and analytical solutions were indeed exact, viable and universal. They enabled a mechanistic understanding and provided a solution to many challenges experienced with such systems. As such, this type of therapeutic agent could be developed efficiently. Additionally, it was worth noting that the mathematical and analytical tools were versatile and could be potentially applied to other fields in which ternary complex systems are involved.

In summary, Dr. Bomie Han, for the first time, successfully developed comprehensive mathematical solutions for ternary complex systems induced by heterobifunctional ligands.  The insights gained from mathematical understanding of the complex biological system provided testable hypotheses that are useful in troubleshooting problems and finding solutions and making informed decisions on the direction of future drug development efforts. In a statement to Medicine Innovates, the author explained that the proposed mathematical principles can be applied to solve challenges in various biomedical fields that involve ternary complexes.