Ensemble-Based Thermodynamics of the Fuzzy Binding between Intrinsically Disordered Proteins and Small-Molecule Ligands.

In contrast to the "lock-and-key" model underlying the long-term success of structural biology and rational drug design, intrinsically disordered proteins (IDPs) exist in an ensemble of highly heterogeneous conformations even after binding with small-molecule ligands. It remains controversial how to characterize the thermodynamics of such fuzzy interactions. Here, we derive an ensemble-based thermodynamic framework to analyze the apparent affinity between IDPs and ligands. It is shown that the apparent affinity is related to the interaction free energy between the individual conformation and ligand in a way similar to Jarzynski's equality in nonequilibrium statistics. The oncoprotein c-Myc is adopted as an example to demonstrate the related properties, for example, the distribution of conformation-ligand interaction free energy, the entropic contribution from the ensemble, the conformation shift under ligand binding, and how to control the error under a limited number of sampled conformations.