Accurate Calculation of Conformational Free Energy Differences in Explicit Water: The Confinement–Solvation Free Energy Approach

Abstract

The calculation of the free energy of conformation is key to understanding the function of biomolecules and has attracted significant interest in recent years. Here, we present an improvement of the confinement method that was designed for use in the context of explicit solvent MD simulations. The development involves an additional step in which the solvation free energy of the harmonically restrained conformers is accurately determined by multistage free energy perturbation simulations. As a test-case application, the newly introduced confinement/solvation free energy (CSF) approach was used to compute differences in free energy between conformers of the alanine dipeptide in explicit water. The results are in excellent agreement with reference calculations based on both converged molecular dynamics and umbrella sampling. To illustrate the general applicability of the method, conformational equilibria of met-enkephalin (5 aa) and deca-alanine (10 aa) in solution were also analyzed. In both cases, smoothly converged free-energy results were obtained in agreement with equilibrium sampling or literature calculations. These results demonstrate that the CSF method may provide conformational free-energy differences of biomolecules with small statistical errors (below 0.5 kcal/mol) and at a moderate computational cost even with a full representation of the solvent.

Computation of Hemagglutinin Free Energy Difference by the Confinement Method

“…For example, the confinement free energy method has recently been extended for use with explicit water, in which the protein might behave differently. 52 However, the current study was feasible only by the efficient acceleration of the implicit solvent model on graphical processing units (GPUs), combined with the advantage of sampling with a relatively low friction coefficient. Obtaining converged results in the relatively viscous environment of explicit water currently seems to be out of reach.…”

Balancing Accuracy and Cost of Confinement Simulations by Interpolation and Extrapolation of Confinement Energies

“…Confinement method. The confinement method [13][14][15][16][17][18][19] aims to compute the free energy of macrostate by transforming the system of interest with 3N degrees of freedom into a set of 3N non-interacting harmonic oscillators (HOs). This transformation is performed in a series of simulations by adding harmonic restraints of increasing strength to the physical potential.…”

“…This principle is exemplified by the confinement method, [13][14][15][16][17][18][19] which connects the states of interest by artificial, uncoupled harmonic oscillator states. In the confinement method, the states of interest are slowly transformed into independent harmonic oscillators using harmonic restraints of increasing strength.…”

“…[13][14] This calculation is normally carried out in an implicit solvent, but the method has recently been extended to include explicit solvation. 15 By foregoing a path in configurational space, the confinement method provides an efficient and robust way to calculate conformational free energy differences, even for states that are highly dissimilar in structure. But the method has other computational benefits that can be exploited.…”

Computational Approaches to the Chemical Equilibrium Constant in Protein‐ligand Binding

“…In practice though, the use of Eq. 6 is strongly limited in protein‐ligand problems by the evaluation of the solvation free energy of a large and flexible solute as the protein alone or the complex, which is computationally challenging, and so far this approach has been successfully applied only to small peptide systems . On the other hand, by factorizing out the kinetic energy contribution from the numerator and the denominator of Eq.…”