How Molecular Conformational Changes Affect Changes in Free Energy

Relative Principal Components Analysis: Application to Analyzing Biomolecular Conformational Changes

A new method termed “Relative Principal Components Analysis” (RPCA) is introduced that extracts optimal relevant principal components to describe the change between two data samples representing two macroscopic states. The method is widely applicable in data-driven science. Calculating the components is based on a physical framework that introduces the objective function (the Kullback–Leibler divergence) appropriate for quantifying the change of the macroscopic state affected by the changes in the microscopic features. To demonstrate the applicability of RPCA, we analyze the thermodynamically relevant conformational changes of the protein HIV-1 protease upon binding to different drug molecules. In this case, the RPCA method provides a sound thermodynamic foundation for analyzing the binding process and thus characterizing both the collective and the locally relevant conformational changes. Moreover, the relevant collective conformational changes can be reconstructed from the informative latent variables to exhibit both the enhanced and the restricted conformational fluctuations upon ligand association.

Elucidating the energetic contributions to the binding free energy

New exact equations are derived for the terms contributing to the binding free energy (ΔG⁰) of a ligand-receptor pair using our recently introduced formalism which we here call perturbation-divergence formalism (PDF). Specifically, ΔG⁰ equals the sum of the average of the perturbation (pertaining to new interactions) and additional dissipative terms. The average of the perturbation includes the sum of the average receptor-ligand interactions and the average of the change of solvation energies upon association. The Kullback-Leibler (KL) divergence quantifies the energetically dissipative terms, which are due to the configurational changes and, using the chain rule of KL divergence, can be decomposed into (i) dissipation due to limiting the external liberation (translation and rotation) of the ligand relative to the receptor and (ii) dissipation due to conformational (internal) changes inside the receptor and the ligand. We also identify all exactly canceling energetic terms which do not contribute to ΔG⁰. Furthermore, the PDF provides a new approach towards dimensionality reduction in the representation of the association process and towards relating the dynamic (high dimensional) with the thermodynamic (one-dimensional) changes.

The Role of Conformational Changes in Molecular Recognition

Conformational changes of molecules are crucial elements in many biochemical processes, and also in molecular recognition. Here, we present a novel exact mathematical equation for the binding free energy of a receptor-ligand pair. It shows that the energetic contribution due to conformational changes upon molecular recognition is defined by the so-called Kullback-Leibler (KL) divergence between the probability distributions of the conformational ensemble of the biomolecule in the bound and free states. We show that conformational changes always contribute positively to the change in free energy and therefore disfavor the association process. Using the example of ligands binding to a flexible cavity of T4 lysozyme, we illustrate that, due to enthalpy-entropy compensation, the conformational entropy is a misleading quantity for assessing the conformational contribution to the binding free energy, in contrast to the KL divergence, which is the correct quantity to use in this context.