Mechanistic Dissection of Entropic Penalty upon Ligand Binding and Molecular Flexibility via Molecular Dynamics Simulations and Machine Learning

Molecular flexibility governs how molecules behave, reorganize, and respond to their environment. Although experiments measure molar entropy for small molecules and molecular dynamics (MD) simulations capture molecular motions, quantifying configuration entropy and the concerted internal motions such as torsion rotations, angle bending, and their couplings are central to understanding thermodynamic behavior but remains challenging. To dissect these contributions, we used MD trajectories and developed an internal coordinate PC-entropy (iPC-entropy) method to probe the origins of entropy and reveal how specific motions shape the thermodynamic landscape. The studies accurately captured molar entropy, identified key torsional motions as major contributors, and uncovered a critical angle-torsion coupling in which angle bending was strongly correlated with torsional rotation, a coupling that increases nonlinearly with molecular size. Evaluating entropic changes upon protein-ligand binding reveals that dominant entropic penalty arises from ligand dihedral rigidification rather than protein reorganization and highlights the specific dihedral rotations that become restricted. We also suggest systematic corrections for approaches considering solely rotamers to reliably reproduce the relative entropic penalty in computer-aided drug discovery. Together, our findings elucidate the molecular origins of entropy and entropy changes. In addition, we can quantify and illustrate the internal motions that strongly shape binding thermodynamics, thereby offering mechanistic insights to guide drug development.