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.