(569e) Molecular Simulations for Environmental Property Predictions: an Efficient Sampling Approach

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:      

Best
S.A., Merz
K.M., Reynolds
C.H., Free Energy Perturbation Study Of Octanol/Water Partition
Coefficients: Comparison With Continuum GB/SA Calculations, Journal of
Physical Chemistry B 103: 714-726, 1999

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

Hansch
C. & Fujita T., ?p-- Analysis. A
Method for the Correlation of Biological Activity and Chemical Structure',
Journal of American Chemical Society 86: 1616-1626, 1964

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