Solving the Competitive Binding Equilibria between Many Ligands: Application to High-Throughput Screening and Affinity Optimization

Abstract

Modern small-molecule drug discovery relies on the selective targeting of biological macromolecules by low-molecular weight compounds. Therefore, the binding affinities of candidate drugs to their targets are key for pharmacological activity and clinical use. For drug discovery methods where multiple drug candidates can simultaneously bind to the same target, a competition is established, and the resulting equilibrium depends on the dissociation constants and concentration of all the species present. Such coupling between all equilibrium-governing parameters complicates analysis and development of improved mixture-based, high-throughput drug discovery techniques. In this work, we present an iterative computational algorithm to solve coupled equilibria between an arbitrary number of ligands and a biomolecular target that is efficient and robust. The algorithm does not require the estimation of initial values to rapidly converge to the solution of interest. We explored binding equilibria under ligand/receptor conditions used in mixture-based library screening by affinity selection–mass spectrometry (AS–MS). Our studies support a facile method for affinity-ranking hits. The ranking method involves varying the receptor-to-ligand concentration ratio in a pool of candidate ligands in two sequential AS–MS analyses. The ranking is based on the relative change in bound ligand concentration. The method proposed does not require a known reference ligand and produces a ranking that is insensitive to variations in the concentration of individual compounds, thereby enabling the use of unpurified compounds generated by mixture-based combinatorial synthesis techniques.

Binding Curve Viewer: Visualizing the Equilibrium and Kinetics of Protein–Ligand Binding and Competitive Binding

“…Therefore, we term the equilibrium concentration calculated by the Wang equation the “theoretical equilibrium concentration” in the second-order binding process. It should be emphasized that the consistent unit of concentration used in our program was nanomolar, we did not encounter the round-off errors in the Wang equation shown in the work of Blay et al…”

“…It should be emphasized that the consistent unit of concentration used in our program was nanomolar, we did not encounter the round-off errors in the Wang equation shown in the work of Blay et al 36 To describe the kinetic process of competitive binding (eqs 11 and 12), we used the Motulsky−Mahan equation 37 to calculate the relationship of [PL] and time in the association process. By association, we mean that the binding is initiated by mixing an arbitrary volume of protein with an arbitrary volume of the mixture of ligand and inhibitor.…”

Linking Transthyretin-Binding Chemicals and Free Thyroid Hormones: In Vitro to In Vivo Extrapolation Based on a Competitive Binding Model

“…If n + m > 3, there are no available mathematical expressions for L i, f , P j, f , or [ P j L i ], and we have to rely on nonlinear system solvers to get the solutions. Alternatively, an iterative algorithm proposed by Blay et al can be used to solve the competitive binding models, which was more efficient and robust . Consequently, the concentrations of free ligands, free proteins, and bound ligands can be obtained as long as [ P ], [ L ], K , and B ns are available.…”

“…Alternatively, an iterative algorithm proposed by Blay et al can be used to solve the competitive binding models, which was more efficient and robust. 41 Consequently, the concentrations of free ligands, free proteins, and bound ligands can be obtained as long as [P], [L], K, and B ns are available. Detailed information about the computational algorithm is presented in Text S2 and Figure S1.…”