Hydrophobic interaction and hydrogen-bond network for a methane pair in liquid water
- Je-Luen Li*,†,‡,
- Roberto Car*,
- Chao Tang†,§, and
- Ned S. Wingreen†,¶,‖
- *Department of Chemistry, Princeton University, Princeton, NJ 08544;
- †NEC Laboratories America, Inc., 4 Independence Way, Princeton, NJ 08540;
- §California Institute for Quantitative Biomedical Research, Departments of Biopharmaceutical Sciences and Biochemistry and Biophysics, University of California, San Francisco, CA 94143; and
- ¶Department of Molecular Biology, Princeton University, Princeton, NJ 08544
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Communicated by Morrel H. Cohen, Rutgers, The State University of New Jersey, Bridgewater Township, NJ, December 19, 2006 (received for review February 3, 2006)
Abstract
We employ fully quantum-mechanical molecular dynamics simulations to evaluate the force between two methanes dissolved in water, as a model for hydrophobic association. A stable configuration is found near the methane–methane contact separation, while a shallow second potential minimum occurs for the solvent-separated configuration. The strength and shape of the potential of mean force are in conflict with earlier classical force-field simulations but agree well with a simple hydrophobic burial model which is based on solubility experiments. Examination of solvent dynamics reveals stable water cages at several specific methane–methane separations.
Footnotes
- ‖To whom correspondence should be addressed. E-mail: wingreen{at}princeton.edu
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Author contributions: R.C. and N.S.W. designed research; J.-L.L. performed research; and C.T. contributed new reagents/analytic tools.
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↵ ‡Present address: Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, Taiwan.
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The authors declare no conflict of interest.
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See Commentary on page 2557.
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This article contains supporting information online at www.pnas.org/cgi/content/full/0610945104/DC1.
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↵ ** For a linear hydrocarbon chain such as an alkane, its solvent-accessible area scales linearly with volume. Indeed, the free energy of the creation of a small cavity in water can be shown to be approximately linear in excluded volume. Therefore, the “cavity volume” free-energy contribution can be absorbed into the surface tension parameter σ in Eq. 4.
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↵ †† The value σ = 47 cal·mol−1·Å−2 is obtained by adopting Flory–Huggins theory (32), whereas Chan and Dill (6) deduced the value 34 cal·mol−1·Å−2 from “classical theory” and cyclohexane–water transfer data (see discussion in ref. 30).
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↵ ‡‡ Different surface measures may be more adequate for different thermodynamic properties (see, for example, discussions in ref. 31).
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↵ §§ Had we used σ = 34 cal·mol−1·Å−2 for the surface tension parameter (30), ΔG is ≈1.9 kcal·mol−1, still considerably larger than classical force-field MD results. The difference between the two estimated ΔG values, 1.9 and 2.7 cal·mol−1·Å−2, may well be within the uncertainties of current density-functional theory approximations.
- Abbreviations:
- FPMD,
- first-principles molecular dynamics;
- PMEF,
- potential of mean effective force;
- PMF,
- potential of mean force.
- © 2007 by The National Academy of Sciences of the USA
