Ligand binding free energy and kinetics calculation in 2020

Advanced Review

Vittorio Limongelli

Published Online: Jan 09 2020

DOI: 10.1002/wcms.1455

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Abstract Ligand/protein binding (LPB) is a major topic in medicine, chemistry and biology. Since the advent of computers, many scientists have put efforts in developing theoretical models that could decode the alphabet of the LPB interaction. The success of this task passes by the resolution of the molecular mechanism of LPB. In the past century, major attention was dedicated to the thermodynamics of LPB, while more recent studies have revealed that ligand (un)binding kinetics is at least as important as ligand binding thermodynamics in determining the drug in vivo efficacy. In the present review, we introduce the most widely used computational methods to study LPB thermodynamics and kinetics. It is important to say that no method outperforms another, they all have pros and cons and the choice of the user should take carefully into account the system under investigation, the available structural and experimental data, and the goal of the research. A perspective on future directions of method development and research on LPB concludes the discussion. This article is categorized under: Molecular and Statistical Mechanics > Free Energy Methods Structure and Mechanism > Computational Biochemistry and Biophysics Molecular and Statistical Mechanics > Molecular Dynamics and Monte‐Carlo Methods

(Top) Schematic representation of the LPB reaction; (Lower) Artistic representation of the free‐energy profile of LPB depicting L‐P and L+P as the lowest energy ligand binding mode and unbound state, respectively. L‐P* and L‐P** represent possible metastable (intermediate) bound states

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Application of Infrequent Metadynamics (IM) to study the benzamidine/trypsin unbinding. (a) State‐to‐state transition rates for the benzamidine unbinding from the trypsin enzyme. The lifetime of the macrostates is in s, while the rates are in s⁻¹. (b) Representation of the two rate determining ligand unbinding pathways. Both lead to state P before reaching the unbound state. State‐to‐state rates and flux calculations indicate that the dominant pathway occurs 84% of the time compared with 16% of the alternative pathway. The atomistic structure of the transition states are disclosed by further MD calculations and committor analysis. Figure adapted from PNAS Reference

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Application of Funnel‐Metadynamics (FM) to estimate LPB free‐energy. (a) (Top) The funnel restraint potential applied to the benzamidine/trypsin system. (Lower) Schematic representation of the funnel restraint potential used in FM calculations. The shape of the funnel can be customized on the protein by setting a few parameters. Specifically, given z the funnel axis defining the exit‐binding path of the ligand, z_cc is the distance at which the restraint potential switches from a cone shape into a cylinder. The angle α defines the amplitude of the cone and R_cyl is the radius of the cylindrical section (see Reference for more details). (b) The BFES of the benzamidine/trypsin system computed as a function of the projection of the ligand center of mass on the funnel axis z and a torsion angle discriminating different orientations of the ligand relative to the protein. Isosurfaces are shown every 1 kcal/mol. Insets show the lowest energy ligand binding mode and one of the isoenergetic conformations representing the unbound state

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The thermodynamic cycle used to compute the relative binding free energy ΔΔG in FEP calculations. The relative binding free energy is calculated via two distinct alchemical transformation processes: process 1 used to estimate the free energy of transforming ligand A to ligand B in the protein; and process 2 used to estimate the free energy of transforming ligand A to ligand B in the solvent. The difference between the free energies obtained from process 1 and 2 is related to the relative binding free energy difference between the two ligands (ΔG^B_bind—ΔG^A_bind). Protein is shown as gray cartoon with the binding site highlighted in orange, ligands are represented as green licorice and the water solvent as cyan surface

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