^{1}, Ganesh Kamath

^{2}, Issac Chelst

^{1}and Jeffrey J. Potoff

^{1}

### Abstract

The 1-octanol–water partition coefficient log K_{ow} of a solute is a key parameter used in the prediction of a wide variety of complex phenomena such as drug availability and bioaccumulation potential of trace contaminants. In this work, adaptive biasing force molecular dynamics simulations are used to determine absolute free energies of hydration, solvation, and 1-octanol–water partition coefficients for *n*-alkanes from methane to octane. Two approaches are evaluated; the direct transfer of the solute from 1-octanol to water phase, and separate transfers of the solute from the water or 1-octanol phase to vacuum, with both methods yielding statistically indistinguishable results. Calculations performed with the TIP4P and SPC/E water models and the TraPPE united-atom force field for *n*-alkanes show that the choice of water model has a negligible effect on predicted free energies of transfer and partition coefficients for *n*-alkanes. A comparison of calculations using wet and dry octanol phases shows that the predictions for log K_{ow} using wet octanol are 0.2–0.4 log units lower than for dry octanol, although this is within the statistical uncertainty of the calculation.

Financial support from a Thomas C. Rumble Fellowship (N.B.), University of Missouri-Columbia Post-Doctoral Fellowship (G.K.), National Science Foundation (NSF) CBET–0730768 (J.J.P.), ERDC-W9132T-06-2-0027 (J.J.P.), and the Wayne State University Research Enhancement Program are gratefully acknowledged.

I. INTRODUCTION

II. METHODS

III. SIMULATION DETAILS

IV. RESULTS AND DISCUSSION

A. Free energy of hydration

B. Free energy of solvation

C. Partition coefficients

D. Convergence and error analysis

V. CONCLUSIONS

### Key Topics

- Free energy
- 62.0
- Gibbs free energy
- 9.0
- Interface structure
- 9.0
- Molecular dynamics
- 8.0
- Transfer reactions
- 6.0

## Figures

Schematic of the system used for the calculation of ΔG via the method of direct transfer (system S3). The solute *n-*butane was placed initially at the center of water box. During the simulation, the solute diffused from the water rich phase to the 1-octanol rich phase. A, B, C, D, E, F, G, H, and I correspond to the midpoint of the 9 ABF windows along the reaction coordinate. The corresponding average free energy for each of the 9 windows is shown as filled circles on the PMF profile. Arrow shows the direction of solute transfer from water into 1-octanol.

Schematic of the system used for the calculation of ΔG via the method of direct transfer (system S3). The solute *n-*butane was placed initially at the center of water box. During the simulation, the solute diffused from the water rich phase to the 1-octanol rich phase. A, B, C, D, E, F, G, H, and I correspond to the midpoint of the 9 ABF windows along the reaction coordinate. The corresponding average free energy for each of the 9 windows is shown as filled circles on the PMF profile. Arrow shows the direction of solute transfer from water into 1-octanol.

Hydration free energy profile generated with ABF-MD method for *n-*alkane transfer from water to vacuum (system S1). Dashed line denotes the location of the interface. Data shown are from calculations performed with a 14 Å LJ cutoff.

Hydration free energy profile generated with ABF-MD method for *n-*alkane transfer from water to vacuum (system S1). Dashed line denotes the location of the interface. Data shown are from calculations performed with a 14 Å LJ cutoff.

Hydration free energy for *n*-alkanes as predicted by adaptive biasing force molecular dynamics simulations with a LJ cutoff of 14.0 Å (red diamonds); thermodynamic integration (green squares); experiment^{70,75} (black circles).

Hydration free energy for *n*-alkanes as predicted by adaptive biasing force molecular dynamics simulations with a LJ cutoff of 14.0 Å (red diamonds); thermodynamic integration (green squares); experiment^{70,75} (black circles).

Solvation free energy profile generated with ABF method for *n*-alkane transfer from 1-octanol to vacuum (system S2). Dashed line denotes the location of the interface. Data shown are from calculations performed with a 14 Å LJ cutoff.

Solvation free energy profile generated with ABF method for *n*-alkane transfer from 1-octanol to vacuum (system S2). Dashed line denotes the location of the interface. Data shown are from calculations performed with a 14 Å LJ cutoff.

Solvation free energy for transfer of *n*-alkanes from vacuum into 1-octanol predicted by adaptive biasing force molecular dynamics using a Lennard-Jones cutoff of 14 Å for the TraPPE-UA force field (red diamonds); thermodynamic integration (green squares); GEMC (blue triangles); experiment (black circles).

Solvation free energy for transfer of *n*-alkanes from vacuum into 1-octanol predicted by adaptive biasing force molecular dynamics using a Lennard-Jones cutoff of 14 Å for the TraPPE-UA force field (red diamonds); thermodynamic integration (green squares); GEMC (blue triangles); experiment (black circles).

Octanol–water partition coefficient for *n*-alkanes predicted by adaptive force bias molecular dynamics simulations using a 14 Å LJ cutoff: direct transfer for 30 Å (red diamond) and 100 Å (orange triangles) 1-octanol box; indirect transfer (blue triangles); thermodynamic integration (green squares); experiment (black circles).

Octanol–water partition coefficient for *n*-alkanes predicted by adaptive force bias molecular dynamics simulations using a 14 Å LJ cutoff: direct transfer for 30 Å (red diamond) and 100 Å (orange triangles) 1-octanol box; indirect transfer (blue triangles); thermodynamic integration (green squares); experiment (black circles).

Density profiles for system S3. The density has been normalized by average bulk density of each component: water (green), 1-octanol CH_{2} (black), 1-octanol oxygen (red). Dashed blue line represents position of the interface.

Density profiles for system S3. The density has been normalized by average bulk density of each component: water (green), 1-octanol CH_{2} (black), 1-octanol oxygen (red). Dashed blue line represents position of the interface.

Free energy profile generated with ABF method for ethane (red), butane (orange), hexane (green), and octane (blue) transfer in system S3 from water to 1-octanol (dry) phase. Data shown are from calculations performed with a 14 Å LJ cutoff. Dashed black line marks the location of the interface.

Free energy profile generated with ABF method for ethane (red), butane (orange), hexane (green), and octane (blue) transfer in system S3 from water to 1-octanol (dry) phase. Data shown are from calculations performed with a 14 Å LJ cutoff. Dashed black line marks the location of the interface.

Free energy profile generated with ABF method for *n*-alkane transfer from water to 1-octanol (dry) phase in system S4. Data shown are from calculations performed with a 14 Å LJ cutoff.

Free energy profile generated with ABF method for *n*-alkane transfer from water to 1-octanol (dry) phase in system S4. Data shown are from calculations performed with a 14 Å LJ cutoff.

(Top panel) Number integrals for interactions between CH_{2} (octane) and O (1-octanol). (Bottom panel) Number integrals for interactions between CH_{2}(octane) and CH_{2}(1-octanol). System S3 (black line), system S4 (red line).

(Top panel) Number integrals for interactions between CH_{2} (octane) and O (1-octanol). (Bottom panel) Number integrals for interactions between CH_{2}(octane) and CH_{2}(1-octanol). System S3 (black line), system S4 (red line).

Distribution of samples along the reaction coordinate from 8 ns ABF-MD simulations for the transfer of *n*-pentane from water to vacuum (red) and from 1-octanol to vacuum (black). Distribution was constructed by combining data from the 5 individual simulations.

Distribution of samples along the reaction coordinate from 8 ns ABF-MD simulations for the transfer of *n*-pentane from water to vacuum (red) and from 1-octanol to vacuum (black). Distribution was constructed by combining data from the 5 individual simulations.

Evolution of sampling histogram from 0.02 ns to 1.0 ns during 1.0 ns ABF-MD simulation.

Evolution of sampling histogram from 0.02 ns to 1.0 ns during 1.0 ns ABF-MD simulation.

Evolution of max-min ratio during 1 ns ABF MD simulation.

Evolution of max-min ratio during 1 ns ABF MD simulation.

## Tables

Hydration free energies Δ*G* _{ HYD } for *n*-alkanes predicted by TraPPE-UA force field.

Hydration free energies Δ*G* _{ HYD } for *n*-alkanes predicted by TraPPE-UA force field.

Comparison of free energies of hydration and log K_{ow} for *n*-alkanes predicted using SPC/E and TIP4P water models. Data are shown for simulations using a 14.0 Å LJ cutoff.

Comparison of free energies of hydration and log K_{ow} for *n*-alkanes predicted using SPC/E and TIP4P water models. Data are shown for simulations using a 14.0 Å LJ cutoff.

Solvation free energies (Δ*G* _{ SOLV }) for *n*-alkanes in 1-octanol predicted using TraPPE-UA force field.

Solvation free energies (Δ*G* _{ SOLV }) for *n*-alkanes in 1-octanol predicted using TraPPE-UA force field.

Effect of water saturation of the octanol phase on the free energies of solvation and partition coefficients for *n*-alkanes. Data shown are for simulations using a 14.0 Å LJ cutoff.

Effect of water saturation of the octanol phase on the free energies of solvation and partition coefficients for *n*-alkanes. Data shown are for simulations using a 14.0 Å LJ cutoff.

Octanol–water partition coefficients (log K_{OW}) predicted by the TraPPE-UA force field for *n*-alkanes.

Octanol–water partition coefficients (log K_{OW}) predicted by the TraPPE-UA force field for *n*-alkanes.

Sampling efficiency and max-min ratio at the end of ABF simulations. Data shown are for the case of *n*-pentane transfer from 1-octanol to vacuum (system S1), *n*-pentane transfer from water to vacuum (system S2), and of *n*-pentane transfer from water to 1-octanol (system S4).

Sampling efficiency and max-min ratio at the end of ABF simulations. Data shown are for the case of *n*-pentane transfer from 1-octanol to vacuum (system S1), *n*-pentane transfer from water to vacuum (system S2), and of *n*-pentane transfer from water to 1-octanol (system S4).

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