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. 2020 Jun 4;22(21):12044-12057.
doi: 10.1039/d0cp00376j.

On the polarization of ligands by proteins

Soohaeng Yoo Willow  1 , Bing Xie  1 , Jason Lawrence  2 , Robert S Eisenberg  3 , David D L Minh  1
Affiliations

On the polarization of ligands by proteins

Soohaeng Yoo Willow et al. Phys Chem Chem Phys. .

Abstract

Although ligand-binding sites in many proteins contain a high number density of charged side chains that can polarize small organic molecules and influence binding, the magnitude of this effect has not been studied in many systems. Here, we use a quantum mechanics/molecular mechanics (QM/MM) approach, in which the ligand is the QM region, to compute the ligand polarization energy of 286 protein-ligand complexes from the PDBBind Core Set (release 2016). Calculations were performed both with and without implicit solvent based on the domain decomposition Conductor-like Screening Model. We observe that the ligand polarization energy is linearly correlated with the magnitude of the electric field acting on the ligand, the magnitude of the induced dipole moment, and the classical polarization energy. The influence of protein and cation charges on the ligand polarization diminishes with the distance and is below 2 kcal mol-1 at 9 Å and 1 kcal mol-1 at 12 Å. Compared to these embedding field charges, implicit solvent has a relatively minor effect on ligand polarization. Considering both polarization and solvation appears essential to computing negative binding energies in some crystallographic complexes. Solvation, but not polarization, is essential for achieving moderate correlation with experimental binding free energies.

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Conflict of interest statement

Conflicts of interest

There are no conflicts to declare.

Figures

Fig. 1
Fig. 1
Schematic illustrating the decomposition of binding energy, Ψbind, into desolvation free energy of the protein, −W(P), the desolvation free energy of the ligand, −W(L), the intermolecular pairwise interaction energy, Epair, the ligand polarization energy, Ξpol, and the solvation free energy of the complex, W(PL).
Fig. 2
Fig. 2
Histograms of the ligand polarization (top, Ξpol), distortion (middle, Ξdist), and stabilization (bottom, Ξstab) energies in the PDBBind Core Set. The three quantities are related by Ξpol =Ξdist + Ξstab.
Fig. 3
Fig. 3
Scatter plot of the ligand polarization energy Ξpol as a function of the minimum distance between a ligand and cation atom, Rmin, for (a) the entire range of Rmin and (b) Rmin < 6 Å.
Fig. 4
Fig. 4
(a) The molecular structure of the ligand with one Zinc cation Zn2+ in the complex 3dx1. Hydrogen, carbon, nitrogen, oxygen, and zinc atoms are colored with white, gray, blue, red, and green, respectively. (b) The difference in the electronic probability density is plotted. Blue and red contours illustrate the gain and loss of the electronic probability density due to the embedding field.
Fig. 5
Fig. 5
Dependence of the Coulomb interaction ECoul, the ligand polarization energy Ξpol, and the distortion energy Ξdist on the cutoff distance Rcut. Here, the deviation and the gradient are defined as ΔF(Rcut)=F(Rcut)−F(∞) and G=dF(Rcut)/dRcut, respectively, where F is either E or Ξ. In these violin plots, the width of the shaded area is proportional to the frequency of observations. Large blue points are placed at mean values. In the plot of ΔΞpol as a function of Rcut, the green line is a function that was fitted to the mean values, 80.778Rcut−2+0.177.
Fig. 6
Fig. 6
The ligand polarization energy, Ξpol, as a function of the magnitude of the electric field |EL0| (top), the magnitude of the induced dipole moment |μLind,QM | (middle), and the classical polarization energy Ξpol,cL (bottom), where EL0, μLind,QM , and Ξpol,cL are from Eq. 29, Eq. 30, and Eq. 28, respectively. The range of Ξpol is either Ξpol < 0 kcal/mol (left) or −50 kcal/mol < Ξpol < 0 kcal/mol (right).
Fig. 7
Fig. 7
Histograms of ratio of the polarization energy of the ligand to (a) the electrostatic interaction (Ξelec = ECoul +Ξpol), (b) the intermolecular pairwise potential energy with the ligand polarization energy (Epair +Ξpol), (c) the binding energy without considering ligand polarization in the solvation free energy (ΨOBC2bind,np+Ξpol), and (d) the binding energy with considering ligand polarization in the solvation free energy (ΨOBC2bind ). The histograms are truncated at a ratio of 1.25. Data are only included for complexes where Ξpol < 0 kcal/mol (left) or −50 kcal/mol < Ξpol < 0 kcal/mol. For analogous histograms including all data, see Fig. S11 in the ESI.
Fig. 8
Fig. 8
The molecular structure of the ligand with two Magnesium cations Mg2+ in the complex, 2zcq. Hydrogen, carbon, oxygen, magnesium, phosphorus, and sulfur atoms are colored with white, gray, red, pink, orange, and yellow, respectively.
Fig. 9
Fig. 9
Solvent effect on the ligand polarization energies of the ligand-protein complexes. The axes are limited to a range of −40 kcal/mol < Ξpol < 0 kcal/mol.
Fig. 10
Fig. 10
Comparison of solvation free energy estimates (in kcal/mol) based on OBC2 (x-axis) and ddCOSMO (y-axis). Solvation free energy estimates are of the (a) ligand, (b) protein, (c) complex, and (d) the binding energy.
Fig. 11
Fig. 11
Histograms of intermolecular potential energies and binding energies. The intermolecular potential energies are (a) the permanent Coulomb interaction (ECoul), (b) the electrostatic interaction (Ξelec = ECoul +Ξpol), (c) the intermolecular pairwise potential energy (Epair =EvdW +ECoul), and (d) the intermolecular pairwise potential energy with the polarization energy of the ligand (Epair +Ξpol) in the gas phase. The OBC2 binding energies are (e) without considering ligand polarization at all, ΨOBC2bind,np, (f) considering ligand polarization for electrostatic interactions but not in the solvation free energy, ΨOBC2bind,np+Ξpol, (g) considering ligand polarization in the solvation free energy but not for electrostatic interactions, ΨOBC2bind −Ξpol, (h) considering ligand polarization both in the electrostatic interactions and the solvation free energy. The ddCOSMO binding energies are (i) without and (j) with the ligand polarization energy. A similar plot that only considers systems for which −50 < Ξpol < 0 kcal/mol is available as Fig. S13 in the ESI.
Fig. 12
Fig. 12
Comparison of interaction energies (in kcal/mol) to experimentally measured binding free energies (in kcal/mol) for complexes with −50 kcal/mol < Ξpol < 0 kcal/mol. Interaction energies are according to (a) the intermolecular pairwise potential energy (Epair =EvdW +ECoul) and (b) the intermolecular pairwise potential energy with the polarization energy of the ligand (Epair +Ξpol) in the gas phase. Panels (c-h) are binding energies, with (c-f) based on the OBC2 and (g-h) based on the ddCOSMO implicit solvent models. The OBC2-based binding energies are: (c) without considering ligand polarization at all, ΨOBC2bind,np; (d) considering ligand polarization for electrostatic interactions but not in the solvation free energy, Ψbind,np +Ξpol; (e) considering ligand polarization in the solvation free energy but not for electrostatic interactions, Ψbind −Ξpol; or (f) considering ligand polarization both in the electrostatic interactions and the solvation free energy. The ddCOSMO-based binding energies are (g) without and (h) with considering the ligand polarization energy. A similar plot for all complexes is available as Fig. S15 in the ESI.
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