Implicit ligand theory: rigorous binding free energies and thermodynamic expectations from molecular docking

Abstract

A rigorous formalism for estimating noncovalent binding free energies and thermodynamic expectations from calculations in which receptor configurations are sampled independently from the ligand is derived. Due to this separation, receptor configurations only need to be sampled once, facilitating the use of binding free energy calculations in virtual screening. Demonstrative calculations on a host-guest system yield good agreement with previous free energy calculations and isothermal titration calorimetry measurements. Implicit ligand theory provides guidance on how to improve existing molecular docking algorithms and insight into the concepts of induced fit and conformational selection in noncovalent macromolecular recognition.

Figure 1

The mean and standard deviation of 15 independent estimates of B(r_R), B_cpl, B_RL, B_L, and min{Ψ(r_RL)} (kcal/mol) based on PBSA energies as a function of total MD simulation time for the ligand B02. Analogous plots for the other ligands in this study are available as Fig. 1 in the supplementary material.

Figure 2

(a) Histogram of binding PMF estimates $\widehat{B}\left(r_R\right)$ (kcal/mol) of B02 to 100 snapshots of CB[7] using PBSA energies. The vertical line shows the mean binding PMF for the minimized receptor structure. (b) and (c) Estimates of the binding free energy ΔG° of B02 to CB[7] (kcal/mol), using PBSA energies, as a function of the number of receptor snapshots. The line and error bars denote the mean and standard deviation from bootstrapping: the binding free energy is estimated 100 times using random selections of N out of 100 binding PMFs. Analogous plots for the other ligands in this study are available as Figs. 2 and 3 in the supplementary material.