Net charge changes in the calculation of relative ligand-binding free energies via classical atomistic molecular dynamics simulation

Abstract

The calculation of binding free energies of charged species to a target molecule is a frequently encountered problem in molecular dynamics studies of (bio-)chemical thermodynamics. Many important endogenous receptor-binding molecules, enzyme substrates, or drug molecules have a nonzero net charge. Absolute binding free energies, as well as binding free energies relative to another molecule with a different net charge will be affected by artifacts due to the used effective electrostatic interaction function and associated parameters (e.g., size of the computational box). In the present study, charging contributions to binding free energies of small oligoatomic ions to a series of model host cavities functionalized with different chemical groups are calculated with classical atomistic molecular dynamics simulation. Electrostatic interactions are treated using a lattice-summation scheme or a cutoff-truncation scheme with Barker–Watts reaction-field correction, and the simulations are conducted in boxes of different edge lengths. It is illustrated that the charging free energies of the guest molecules in water and in the host strongly depend on the applied methodology and that neglect of correction terms for the artifacts introduced by the finite size of the simulated system and the use of an effective electrostatic interaction function considerably impairs the thermodynamic interpretation of guest-host interactions. Application of correction terms for the various artifacts yields consistent results for the charging contribution to binding free energies and is thus a prerequisite for the valid interpretation or prediction of experimental data via molecular dynamics simulation. Analysis and correction of electrostatic artifacts according to the scheme proposed in the present study should therefore be considered an integral part of careful free-energy calculation studies if changes in the net charge are involved. © 2013 The Authors Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Free Energy Perturbation Calculation of Relative Binding Free Energy between Broadly Neutralizing Antibodies and the gp120 Glycoprotein of HIV-1

“…As noted previously, mutations in which the net charge of the system is changed present significantly greater difficulties for FEP simulations due to periodic boundary condition artifacts, as has been investigated by Parameswaran et al and Rocklin et al [27], [28], Lin and coworkers [41], and Reif and Oostenbrink [42]. These authors have suggested a posteriori corrections using Poisson–Boltzmann (PB) electrostatics to ameliorate these problems, a technique that appears to be promising.…”

Blinded predictions of distribution coefficients in the SAMPL5 challenge

“…This is based on the work by Reif and Oostenbrink [21], Rocklin et al [22], and earlier work from Kastenholz and Hünenberger [23, 24]. Here corrections on the free energy estimation for a BWRF atom based cutoff for the discharging step were derived.…”

“…Here corrections on the free energy estimation for a BWRF atom based cutoff for the discharging step were derived. Net charge free energy calculations are affected by several finite size artefacts [21, 22]. To be computationally efficient periodic boundary conditions along with an effective Coulombic potential are employed, which introduces artefacts that can be sizable for simulations of charged species [25, 26].…”

“…A second source of error occurs in the present molecular simulations due to the use of an atom-based cutoff to compute solute-solvent interactions. This summation scheme causes an apparent solvation of negatively charged species and a de-solvation of positively charged molecules [21, 23, 24]. For atom-based BWRF conditions a correction term was evaluated as:where is Avogadro number, is the experimental permittivity for the solvent, is the dielectric constant of the water model used, is the trace of the quadrupole-moment tensor of the solvent model, where the sum is over all N atoms in a solvent molecule, is the charge of the i -th atom in a solvent molecule, is the coordinate vector, is the net charge of the solute, is the reaction field cutoff length and is the average number of solvent molecules within .…”

Toward the correction of effective electrostatic forces in explicit-solvent molecular dynamics simulations: restraints on solvent-generated electrostatic potential and solvent polarization

“…It is a widely known and well-understood problem of simulations with a lattice-sum electrostatic interaction function [18, 35, 58, 63, 65, 67, 69, 70, 81, 82]. There is a second issue that is not reflected in structural properties but only in thermodynamic properties.…”