Free Energies of Binding from Large-Scale First-Principles Quantum Mechanical Calculations: Application to Ligand Hydration Energies

Abstract

Schemes of increasing sophistication for obtaining free energies of binding have been developed over the years, where configurational sampling is used to include the all-important entropic contributions to the free energies. However, the quality of the results will also depend on the accuracy with which the intermolecular interactions are computed at each molecular configuration. In this context, the energy change associated with the rearrangement of electrons (electronic polarization and charge transfer) upon binding is a very important effect. Classical molecular mechanics force fields do not take this effect into account explicitly, and polarizable force fields and semiempirical quantum or hybrid quantum-classical (QM/MM) calculations are increasingly employed (at higher computational cost) to compute intermolecular interactions in free-energy schemes. In this work, we investigate the use of large-scale quantum mechanical calculations from first-principles as a way of fully taking into account electronic effects in free-energy calculations. We employ a one-step free-energy perturbation (FEP) scheme from a molecular mechanical (MM) potential to a quantum mechanical (QM) potential as a correction to thermodynamic integration calculations within the MM potential. We use this approach to calculate relative free energies of hydration of small aromatic molecules. Our quantum calculations are performed on multiple configurations from classical molecular dynamics simulations. The quantum energy of each configuration is obtained from density functional theory calculations with a near-complete psinc basis set on over 600 atoms using the ONETEP program.

Applications of large-scale density functional theory in biology

“…A very wide range of such approaches has been developed [5], with widely-used implementations including the Polarisable Continuum Model (PCM) [128], the COSMO model [129], the SMD model [130], and the unified electrostatic and cavitation model of Scherlis et al [131]. An adaptation of the latter by Dziedzic et al [132] has recently been demonstrated for application to entire proteins [133,134].…”

“…First, a hybrid Monte Carlo simulation generates a statistically-rigorous QM/MM ensemble of structures from the underlying MM ensemble [291]. Once this ensemble has been generated, a single-step free energy correction may be computed using the approach of Fox et al to transform the QM/MM hydration free energies to the full QM result [134]. The idea behind the stepping stone approach is that, in the QM/MM ensemble, the polarisation of the ligand by the surrounding solvent is accounted for and, hence, it should provide a much closer representation of the target QM ensemble.…”

Capturing the Role of Temperature and Entropy in Crystal Polymorphs Through Molecular Simulations

“…The simplest method to obtain free energy differences via Hamiltonian reweighting involves reweighting from one sampled to one unsampled state, generally referred to as exponential reweighting or the Zwanzig equation [191,238,240,[242][243][244][247][248][249][250]252], which is simply eq 6.1. This method produces asymptotically unbiased free energy differences in the limit of large sampling.…”

“…Warshel et al [238] introduced a method based on the pioneering work of Kirkwood [239] and Zwanzig [191] to calculate free energies in complex Hamiltonians indirectly by simulating in a cheap potential and calculating ensemble averages in the expensive potential using Boltzmann reweighting, thus avoiding direct simulation in the expensive potential [240][241][242][243][244][245][246][247][248][249][250][251][252][253][254][255][256][257][258]. The formula for estimating the ensemble average in a target state given samples in another state is [191]:…”

“…In previous studies employing Boltzmann reweighting, poor overlap was attributed to differences in the intramolecular interactions between the cheap and expensive potential [247,253]. This poor overlap has led researchers to using alternate reweighting strategies such as replacing the total energy difference in equation 4.1 with just the difference in intermolecular interactions, while holding the intramolecular interactions constant [247][248][249][250]. The target potential with this approach has intermolecular interactions that correspond with the expensive potential and intramolecular interactions at the cheaper level of theory.…”