Developing end-point methods for absolute binding free energy calculation using the Boltzmann-quasiharmonic model

Lauren Wickstrom; Emilio Gallicchio; Lieyang Chen; Tom Kurtzman; Nanjie Deng

doi:10.1039/d1cp05075c

Developing end-point methods for absolute binding free energy calculation using the Boltzmann-quasiharmonic model

Phys Chem Chem Phys. 2022 Mar 9;24(10):6037-6052. doi: 10.1039/d1cp05075c.

Authors

Lauren Wickstrom¹, Emilio Gallicchio^{2

3

4}, Lieyang Chen^{3

4

5}, Tom Kurtzman^{3

4

5}, Nanjie Deng⁶

Affiliations

¹ Borough of Manhattan Community College, The City University of New York, Department of Science, New York, New York, USA.
² Department of Chemistry, Brooklyn College, The City University of New York, Brooklyn, New York, USA.
³ PhD Program in Chemistry, Graduate Center of the City University of New York, New York, USA.
⁴ PhD Program in Biochemistry, Graduate Center of the City University of New York, New York, USA.
⁵ Department of Chemistry, Lehman College, The City University of New York, Bronx, New York, USA.
⁶ Department of Chemistry and Physical Sciences, Pace University, New York, New York, USA. nanjie.deng@gmail.com.

Abstract

Understanding the physical forces underlying receptor-ligand binding requires robust methods for analyzing the binding thermodynamics. In end-point binding free energy methods the binding free energy is naturally decomposable into physically intuitive contributions such as the solvation free energy and configurational entropy that can provide insights. Here we present a new end-point method called EE-BQH (Effective Energy-Boltzmann-Quasiharmonic) which combines the Boltzmann-Quasiharmonic model for configurational entropy with different solvation free energy methods, such as the continuum solvent PBSA model and the integral equation-based 3D-RISM, to estimate the absolute binding free energy. We compare EE-BQH with other treatments of configurational entropy such as Quasiharmonic models in internal coordinates (QHIC) and in Cartesian coordinates (QHCC), and Normal Mode analysis (NMA), by testing them on the octa acids host-guest complexes from the SAMPL8 blind challenge. The accuracies in the calculated absolute binding free energies strongly depend on the configurational entropy and solvation free energy methods used. QHIC and BQH yield the best agreements with the established potential of mean force (PMF) estimates, with R² of ∼0.7 and mean unsigned error of ∼1.7 kcal mol^-1. These results from the end-point calculations are also in similar agreement with experiments. While 3D-RISM in combination with QHIC or BQH lead to reasonable correlations with the PMF results and experiments, the calculated absolute binding free energies are underestimated by ∼5 kcal mol^-1. While the binding is accompanied by a significant reduction in the ligand translational/rotational entropy, the change in the torsional entropy in these host-guest systems is slightly positive. Compared with BQH, QHIC underestimates the reduction of configurational entropy because of the non-Gaussian probability distributions in the ligand rotation and a small number of torsions. The study highlights the crucial role of configurational entropy in determining binding and demonstrates the potential of using the new end-point method to provide insights in more complex protein-ligand systems.

MeSH terms

Entropy
Ligands
Molecular Dynamics Simulation*
Protein Binding
Thermodynamics

Substances

Ligands

Grants and funding

R01 GM100946/GM/NIGMS NIH HHS/United States