Octanol-water partition coefficient K_ow is an important molecular parameter in estimating various environmental and toxicological properties of chemicals. This coefficient have been used in estimation of toxicity parameters such as LC₅₀ (lethal concentration that will kill a statistical 50% of a test population) and LD₅₀ (lethal dose that will kill a statistical 50% of a test population). It has also been found that the bio-concentration factor (BCF), describing the bioaccumulation of chemicals in an organism has a strong dependence on K_ow. In addition, octanol-water partition coefficients provide a basis to a large amount of quantitative-structure activity relationships (QSARs), which have been used to correlate or predict solute properties in biophases (membranes, fat tissue, body fluids).

The octanol-water partition coefficient, K_ow in thermodynamics is a free energy function which is directly related to the energetics of transfer between two phases. The successfulness of K_ow in predicting bioaccumulation and toxicity have been attributed to the fact that the octanol-water partitioning is a good representative of a compound going from more aqueous like-phases (extracellular phase) to organic-like phases (cellular phase) inside the body, which is the rate controlling step during the interaction of a compound and a biological system (Hansch and Fajita, 1964). 

Although, experimental data for K_ow is available for more than 18000 chemicals (Sangster, 1997), this number is far from the total number of compounds for which data is desirable. Therefore, molecular modeling simulations have been carried out for this system by various researchers. DeBolt and Kollman (1995) investigated the structure, dynamics and solvation in 1-octanol and its water saturated solution by molecular dynamics and free energy perturbation studies. Using this method they have computed the relative partition coefficients and examined the structural aspects of interaction. Similarly, Best et al. (1999) studied the relative 1-octanol/water partition coefficients by a molecular dynamics/free energy perturbation study and compared their results to a generalized Born/surface area octanol continuum solvation model. More recently, Lyubartsev et al. (2001) studied the solubility of organic compounds in water/octanol systems by molecular dynamics simulations using an expanded ensemble technique for drug compounds. Moreover, studies were performed by Chen and Siepmann (2000) where a configurational-bias Monte Carlo (CBMC) simulation was carried out in the Gibbs ensemble to calculate the partitioning of alkane and alcohol solutes in 1-octanol/water. The advantage of this latter work to free energy perturbation studies is that the Gibbs free energy of transfer can be determined directly from the ratio of solute number densities and the number density ratio can be determined very precisely from CBMC/GEMC simulations with small statistical errors.

The success of Monte Carlo and molecular dynamics methods depends on the efficient sampling of the configuration space, to generate states of low energy, enabling the calculation of properties accurately. In Monte Carlo simulations, particles are randomly selected and moved by a random extent and the energy change of the system is analyzed. For systems with large number of molecules, this task requires significant computational time. In this paper, in order to reduce the computational time and improve the efficiency of molecular simulations, we have used Hammersley Sequence Sampling (HSS) technique (Kalagnanam and Diwekar, 1997). This sampling technique uses low-discrepancy sequences (quasi-random points) which have the best uniformity or evenness in their domain of definition.  This sampling technique has been shown to require fewer samples and faster convergence properties in various applications such as off-line quality control of a CSTR (Kalagnanam and Diwekar, 1997), robust design of distillation columns (Diwekar and Kalagnanam, 1997), solvent selection (Kim and Diwekar, 2002), multi-objective optimal designs for emission reduction (Fu and Diwekar, 2004) and optimal molecular design under uncertainty (Tayal and Diwekar, 2001). Tayal and Diwekar (2000) used 3D HSS samples for efficient evaluation of 3N-dimensional property integral in molecular simulations. Up to 75% computational savings in the equilibrium phase with an overall savings of 37.5% for a 100 Lennard-Jones particle molecular system was obtained.

In this paper, quasi-random points showing k-dimensional uniformity generated by the HSS technique are used instead of pseudo-random points for various Monte Carlo moves of the molecular simulation algorithm for the prediction of octanol-water partition coefficients, to obtain faster convergence and reduce the computational requirements.  A configurational-bias Monte Carlo method based on HSS is derived for Gibbs ensemble to improve the efficiency of molecular simulations to calculate K_ow.  Using this technique we have significantly reduced the number of Monte Carlo cycles for accurate estimation of Gibbs free energies of transfer and improved the efficiency of equilibriation. 

References:      

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Chen B. & Siepmann J.I., ‘Partitioning of Alkane and Alcohol Solutes between Water and (Dry or Wet) 1-Octanol', Journal of American Chemical Society 122: 6464-6467, 2000.

DeBolt S.E. & Kollman P.A., ‘Investigation of Structure, Dynamics and Solvation in 1-Octanol and its Water-Saturated Solution: Molecular Dynamics and Free-Energy Perturbation Studies', Journal of American Chemical Society 117: 5316-5340, 1995

Diwekar U.M. & Kalagnanam J.R., ‘Robust design using an efficient sampling technique', Computers & Chemical Engineering, 20: S389-S394, 1996

Fu Y., Diwekar U.M., ‘An efficient sampling approach to multi-objective optimization', Annals of Operations Research, 132: 109-134, 2004

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Kalagnanam J.R. & Diwekar U.M., ‘An Efficient Sampling Technique for Off-line Quality Control', Technometrics 39: 308 – 319, 1997

Kim K.J. & Diwekar U.M., ‘Efficient Combinatorial Optimization Under Uncertainty. 2. Application to Stochastic Solvent Selection', Industrial & Engineering Chemistry Research 41: 1285-1296, 2002

Lyubartsev A.P., Jacobsson S.P, Sundholm G., & Laaksonen A., ‘Solubility of Organic Compouns in Water/Octanol Systems-An Expanded Ensemble Molecular Dynamics Simulation Study of log P Parameters', Journal of Physical Chemistry B 105: 7775-7782, 2001.

Sansgter J., ‘Octanol-Water Partition Coefficients: Fundamentals and Physical Chemistry', John Wiley & Sons, Chichester, 1997

Tayal M.C., & Diwekar U.M. ‘Novel Sampling Approach to Optimal Molecular Design under Uncertainty', AIChE Journal, 47: 609-628, 2001

Tayal M.C., & Diwekar U.M., ‘Improved Molecular Simulations by Efficient Sampling', AIChE Annual Meeting, Los Angeles, CA, 2000