Efficient Solvation Free Energy Calculations of Amino Acid Analogs by Expanded Ensemble Molecular Simulation

The Contribution of the Ion-Ion and Ion-Solvent Interactions in a Molecular Thermodynamic Treatment of Electrolyte Solutions

Developing molecular equations of state to treat electrolyte solutions is challenging due to the long-range nature of the Coulombic interactions. Seminal approaches commonly used are the mean spherical approximation (MSA) and the Debye-Hückel (DH) theory to account for ion-ion interactions and, often, the Born theory of solvation for ion-solvent interactions. We investigate the accuracy of the MSA and DH approaches using each to calculate the contribution of the ion-ion interactions to the chemical potential of NaCl in water, comparing these with newly computer-generated simulation data; the ion-ion contribution is isolated by selecting an appropriate primitive model with a Lennard-Jones force field to describe the solvent. A study of mixtures with different concentrations and ionic strengths reveals that the calculations from both MSA and DH theories are of similar accuracy, with the MSA approach resulting in marginally better agreement with the simulation data. We also demonstrate that the Born theory provides a good qualitative description of the contribution of the ion-solvent interactions; we employ an explicitly polar water model in these simulations. Quantitative agreement up to moderate salt concentrations and across the relevant range of temperature is achieved by adjusting the Born radius using simulation data of the free energy of solvation. We compute the radial and orientational distribution functions of the systems, thereby providing further insight on the differences observed between the theory and simulation. We thus provide rigorous benchmarks for use of the MSA, DH, and Born theories as perturbation approaches, which will be of value for improving existing models of electrolyte solutions, especially in the context of equations of state.

Performing solvation free energy calculations in LAMMPS using the decoupling approach

The decoupling approach to solvation free energy calculations requires scaling the interactions between the solute and the solution with all intramolecular interactions preserved. This paper reports a new procedure that makes it possible to these calculations in LAMMPS. The procedure is tested against built-in GROMACS capabilities. The model compounds chosen to test our methodology are ethanol and biphenyl. The LAMMPS and GROMACS results obtained are in good agreement with each other. This work should help perform solvation free energy calculations in LAMMPS and/or other molecular dynamics software having no built-in functions to implement the decoupling approach.

Association of Nucleobases in Hydrated Ionic Liquid from Biased Molecular Dynamics Simulations

We employed metadynamics-based classical molecular dynamics simulations to methylated adenine-thymine (mA-mT) and guanine-cytosine (mG-mC) base pairs to see favorable conformations in various concentrations of hydrated 1-ethyl, 3-methyl imidazolium acetate. We investigated various stacked and hydrogen-bonded conformations of association of base pairs through appropriately chosen collective variables. Stacked conformations more favored in water for both base pairs, whereas Watson-Crick (WC) hydrogen-bonding conformations are favored in pure and hydrated ionic liquids (ILs) except for 0.75 mol fraction IL. We observe that EMIm cations surround the base pairs in WC conformations creating a kind of hydrophobic cavity and protect the hydrogen bonds between base pairs. However, the five-membered heteroaromatic rings of cations stack with the nucleobases in the cation-base-cation (π-π-π) model, which resembles the base-base-base stacking in a DNA duplex. Interestingly, from additional simulations of 0.5 mol fraction hydrated choline dihydrogen phosphate IL, we observe that the stacked conformations become more favored than the WC conformation due to the absence of π-bonds in cations. The calculated values of relative solubility of base pairs in pure and hydrated ionic liquids compared to those in pure water correlate well with the free energy values of WC and stacked conformations.

Dissolution of cellulose in room temperature ionic liquids: anion dependence

The dissolution of cellulosic biomass in room temperature ionic liquids (RTILs) is studied through free energy calculations of its monomer, viz., cellobiose, within a molecular dynamics simulation approach. The solvation free energy (SFE) of cellobiose in ionic liquids containing any of seven different anions has been calculated. The ranking of these liquids based on SFE compares well with experimental data on the solubility of cellulose. The dissolution is shown to be enthalpically dominated, which is correlated with the strength of intermolecular hydrogen bonding between cellobiose and the anions of the IL. Large entropic changes upon solvation in [CF3SO3](-) and [OAc](-) based ionic liquids have been explained in terms of the solvent-aided conformational flexibility of cellobiose.

Practical Aspects of Free-Energy Calculations: A Review

Free-energy calculations in the framework of classical molecular dynamics simulations are nowadays used in a wide range of research areas including solvation thermodynamics, molecular recognition, and protein folding. The basic components of a free-energy calculation, that is, a suitable model Hamiltonian, a sampling protocol, and an estimator for the free energy, are independent of the specific application. However, the attention that one has to pay to these components depends considerably on the specific application. Here, we review six different areas of application and discuss the relative importance of the three main components to provide the reader with an organigram and to make nonexperts aware of the many pitfalls present in free energy calculations.

Relative free enthalpies for point mutations in two proteins with highly similar sequences but different folds

Enveloping distribution sampling was used to calculate free-enthalpy changes associated with single amino acid mutations for a pair of proteins, GA95 and GB95, that show 95% sequence identity yet fold into topologically different structures. Of the L → A, I → F, and L → Y mutations at positions 20, 30, and 45, respectively, of the 56-residue sequence, the first and the last contribute the most to the free-enthalpy difference between the native and non-native sequence-structure combinations, in agreement with the experimental findings for this protein pair. The individual free-enthalpy changes are almost sequence-independent in the four-strand/one-helix structure, the stable form of GB95, while in the three-helix bundle structure, the stable form of GA95, an interplay between residues 20 and 45 is observed.

Bennett's acceptance ratio and histogram analysis methods enhanced by umbrella sampling along a reaction coordinate in configurational space

Free energy perturbation, a method for computing the free energy difference between two states, is often combined with non-Boltzmann biased sampling techniques in order to accelerate the convergence of free energy calculations. Here we present a new extension of the Bennett acceptance ratio (BAR) method by combining it with umbrella sampling (US) along a reaction coordinate in configurational space. In this approach, which we call Bennett acceptance ratio with umbrella sampling (BAR-US), the conditional histogram of energy difference (a mapping of the 3N-dimensional configurational space via a reaction coordinate onto 1D energy difference space) is weighted for marginalization with the associated population density along a reaction coordinate computed by US. This procedure produces marginal histograms of energy difference, from forward and backward simulations, with higher overlap in energy difference space, rendering free energy difference estimations using BAR statistically more reliable. In addition to BAR-US, two histogram analysis methods, termed Bennett overlapping histograms with US (BOH-US) and Bennett-Hummer (linear) least square with US (BHLS-US), are employed as consistency and convergence checks for free energy difference estimation by BAR-US. The proposed methods (BAR-US, BOH-US, and BHLS-US) are applied to a 1-dimensional asymmetric model potential, as has been used previously to test free energy calculations from non-equilibrium processes. We then consider the more stringent test of a 1-dimensional strongly (but linearly) shifted harmonic oscillator, which exhibits no overlap between two states when sampled using unbiased Brownian dynamics. We find that the efficiency of the proposed methods is enhanced over the original Bennett's methods (BAR, BOH, and BHLS) through fast uniform sampling of energy difference space via US in configurational space. We apply the proposed methods to the calculation of the electrostatic contribution to the absolute solvation free energy (excess chemical potential) of water. We then address the controversial issue of ion selectivity in the K(+) ion channel, KcsA. We have calculated the relative binding affinity of K(+) over Na(+) within a binding site of the KcsA channel for which different, though adjacent, K(+) and Na(+) configurations exist, ideally suited to these US-enhanced methods. Our studies demonstrate that the significant improvements in free energy calculations obtained using the proposed methods can have serious consequences for elucidating biological mechanisms and for the interpretation of experimental data.

Small Molecule Solvation Free Energy: Enhanced Conformational Sampling Using Expanded Ensemble Molecular Dynamics Simulation

We present an efficient expanded ensemble molecular dynamics method to calculate the solvation free energy (or residual chemical potential) of small molecules with complex topologies. The methodology is validated by computing the solvation free energy of ibuprofen in water, methanol, and ethanol at 300 K and 1 bar and comparing to reference simulation results using Bennett's acceptance ratio method. Difficulties with ibuprofen using conventional molecular dynamics methods stem from an inadequate sampling of the carboxylic acid functional group, which, for the present study, is subject to free energy barriers of rotation of 14-20 kBT. While several advances have been made to overcome such weaknesses, we demonstrate how this shortcoming is easily overcome by using an expanded ensemble methodology to facilitate conformational sampling. Not only does the method enhance conformational sampling but it also boosts the rate of exploration of the configurational phase space and requires only a single simulation to calculate the solvation free energy. Agreement between the expanded ensemble and the reference calculations is good for all three solvents, with the reported uncertainties of the expanded ensemble being comparable to the uncertainties of the reference calculations, while requiring less simulation time; the reduced simulation time demonstrates the improved performance gained from the expanded ensemble method.