We present a coarse-grained lattice model of solvation thermodynamics and the hydrophobic effect that implements the ideas of Lum–Chandler–Weeks theory [J. Phys. Chem. B134, 4570 (1999)] and improves upon previous lattice models based on it. Through comparison with molecular simulation, we show that our model captures the length-scale and curvature dependence of solvation free energies with near-quantitative accuracy and 2–3 orders of magnitude less computational effort, and further, correctly describes the large but rare solvent fluctuations that are involved in dewetting, vapor tube formation, and hydrophobic assembly. Our model is intermediate in detail and complexity between implicit-solvent models and explicit-water simulations.

2.
C.
Tanford
,
The Hydrophobic Effect: Formation of Micelles and Biological Membranes
(
Wiley
,
New York
,
1973
).
3.
B.
Alberts
,
A.
Johnson
,
J.
Lewis
,
M.
Raff
,
K.
Roberts
, and
P.
Walter
,
Molecular Biology of the Cell
, 5th ed. (
Garland Science
,
New York
,
2007
).
4.
D.
Chandler
,
Nature (London)
437
,
640
(
2005
).
5.
N.
Chennamsetty
,
V.
Voynov
,
V.
Kayser
,
B.
Helk
, and
B. L.
Trout
,
Proc. Natl. Acad. Sci. U.S.A.
106
,
11937
(
2009
).
6.
N.
Chennamsetty
,
V.
Voynov
,
V.
Kayser
,
B.
Helk
, and
B. L.
Trout
,
J. Phys. Chem. B
114
,
6614
(
2010
).
7.
H.
Acharya
,
S.
Vembanur
,
S. N.
Jamadagni
, and
S.
Garde
,
Faraday Discuss.
146
,
1
(
2010
).
8.
M. R.
Shirts
,
J. W.
Pitera
,
W. C.
Swope
, and
V. S.
Pande
,
J. Chem. Phys.
119
,
5740
(
2003
).
9.
M. R.
Shirts
and
V. S.
Pande
,
J. Chem. Phys.
122
,
134508
(
2005
).
10.
W. C.
Still
,
A.
Tempczyk
,
R. C.
Hawley
, and
T.
Hendrickson
,
J. Am. Chem. Soc.
112
,
6127
(
1990
).
11.
D.
Qiu
,
P. S.
Shenkin
,
F. P.
Hollinger
, and
W. C.
Still
,
J. Phys. Chem. A
101
,
3005
(
1997
).
12.
K.
Lum
,
D.
Chandler
, and
J. D.
Weeks
,
J. Phys. Chem. B
103
,
4570
(
1999
).
13.
P. R.
ten Wolde
,
S. X.
Sun
, and
D.
Chandler
,
Phys. Rev. E
65
,
011201
(
2001
).
14.
P. R.
ten Wolde
and
D.
Chandler
,
Proc. Natl. Acad. Sci. U.S.A.
99
,
6539
(
2002
).
15.
D.
Chandler
,
Introduction to Modern Statistical Mechanics
(
Oxford University Press
,
New York, 1987
).
16.
B.
Roux
and
T.
Simonson
,
Biophys. Chem.
78
,
1
(
1999
).
17.
For reduced classes of solutes, such as linear alkanes, surface-area scaling is nonetheless observed. These molecules are properly in the small length-scale regime, where solvation free energy scales as volume. However, for linear molecules, surface area also scales as volume, leading to the misleading scaling behavior (Ref. 4). Moreover, the resulting empirical surface tension is almost negligibly small. Typical values are in the 5–10 cal/mol/Å2 ≈ 1 kBT/nm2 range (Refs. 11 and 40), in contrast to the water-air surface tension of about 17 kBT/nm2 and the water-oil surface tension of about 12 kBT/nm2: see Ref. 18.
18.
C.
Tanford
,
Proc. Natl. Acad. Sci. U.S.A.
76
,
4175
(
1979
).
19.
D.
Huang
,
P. L.
Geissler
, and
D.
Chandler
,
J. Phys. Chem. B
105
,
6704
(
2001
).
20.
R. M.
Levy
,
L. Y.
Zhang
,
E.
Gallicchio
, and
A. K.
Felts
,
J. Am. Chem. Soc.
125
,
9523
(
2003
).
21.
H. S.
Ashbaugh
and
L. R.
Pratt
,
Rev. Mod. Phys.
78
,
159
(
2006
).
22.
J.
Chen
and
C. L.
Brooks
,
J. Am. Chem. Soc.
129
,
2444
(
2007
).
23.
A.
Wallqvist
and
B. J.
Berne
,
J. Phys. Chem.
99
,
2893
(
1995
).
24.
K.
Lum
and
A.
Luzar
,
Phys. Rev. E
56
,
R6283
(
1997
).
25.
P. G.
Bolhuis
and
D.
Chandler
,
J. Chem. Phys.
113
,
8154
(
2000
).
26.
A.
Anishkin
and
S.
Sukharev
,
Biophys. J.
86
,
2883
(
2004
).
27.
P.
Liu
,
X.
Huang
,
R.
Zhou
, and
B. J.
Berne
,
Nature (London)
437
,
159
(
2005
).
28.
T. F.
Miller
,
E.
Vanden-Eijnden
, and
D.
Chandler
,
Proc. Natl. Acad. Sci. U.S.A.
104
,
14559
(
2007
).
29.
M. V.
Athawale
,
G.
Goel
,
T.
Ghosh
,
T. M.
Truskett
, and
S.
Garde
,
Proc. Natl. Acad. Sci. U.S.A.
104
,
733
(
2007
).
30.
J. C.
Rasaiah
,
S.
Garde
, and
G.
Hummer
,
Annu. Rev. Phys. Chem.
59
,
713
(
2008
).
31.
S. N.
Jamadagni
,
R.
Godawat
,
J. S.
Dordick
, and
S.
Garde
,
J. Phys. Chem. B
113
,
4093
(
2009
).
32.
B. J.
Berne
,
J. D.
Weeks
, and
R.
Zhou
,
Annu. Rev. Phys. Chem.
60
,
85
(
2009
).
33.
A. J.
Patel
,
P.
Varilly
, and
D.
Chandler
,
J. Phys. Chem. B
114
,
1632
(
2010
).
34.
G.
Hummer
,
S.
Garde
,
A. E.
García
,
A.
Pohorille
, and
L. R.
Pratt
,
Proc. Natl. Acad. Sci. U.S.A.
93
,
8951
(
1996
)
35.
D.
Huang
and
D.
Chandler
,
Phys. Rev. E
61
,
1501
(
2000
).
36.
S.
Garde
,
R.
Khare
, and
G.
Hummer
,
J. Chem. Phys.
112
,
1574
(
2000
).
37.
L.
Xu
and
V.
Molinero
,
J. Phys. Chem. B
114
,
7320
(
2010
).
39.
I.
Daidone
,
M. B.
Ulmschneider
,
A.
Di Nola
,
A.
Amadei
, and
J. C.
Smith
,
Proc. Natl. Acad. Sci. U.S.A.
104
,
15230
(
2007
).
40.
J.
Chen
,
C. L.
Brooks
 III
, and
J.
Khandogin
,
Curr. Opin. Struct. Biol.
18
,
140
(
2008
).
41.
C. Y.
Janda
,
J.
Li
,
C.
Oubridge
,
H.
Hernandez
,
C. V.
Robinson
, and
K.
Nagai
,
Nature (London)
465
,
507
(
2010
).
42.
S. F.
Harris
,
A. K.
Shiau
, and
D. A.
Agard
,
Structure (London)
12
,
1087
(
2004
).
43.
D.
Chandler
,
Phys. Rev. E
48
,
2898
(
1993
).
44.
G.
Crooks
and
D.
Chandler
,
Phys. Rev. E
56
,
4217
(
1997
).
45.
K.
Lum
, “
Hydrophobicity at small and large length scales
,” Ph.D. thesis (University of California, Berkeley,
1998
), Fig. (3.6), p.
61
.
47.
J. D.
Weeks
,
R. L. B.
Selinger
, and
J. Q.
Broughton
,
Phys. Rev. Lett.
75
,
2694
(
1995
).
48.
J. D.
Weeks
,
K.
Vollmayr
, and
K.
Katsov
,
Physica A
244
,
461
(
1997
).
49.
J. D.
Weeks
,
K.
Katsov
, and
K.
Vollmayr
,
Phys. Rev. Lett.
81
,
4400
(
1998
).
50.
K.
Katsov
and
J. D.
Weeks
,
J. Phys. Chem. B
105
,
6738
(
2001
).
51.
A. P.
Willard
and
D.
Chandler
,
J. Phys. Chem. B
112
,
6187
(
2008
).
52.
H.
Berendsen
,
J.
Grigera
, and
T.
Straatsma
,
J. Phys. Chem.
91
,
6269
(
1987
).
53.
D. M.
Huang
and
D.
Chandler
,
J. Phys. Chem. B
106
,
2047
(
2002
).
54.
E.
Lemmon
,
M.
McLinden
, and
D.
Friend
, in
NIST Chemistry WebBook, NIST Standard Reference Database Number 69
, edited by
P.
Linstrom
and
W.
Mallard
(
National Institute of Standards and Technology
,
Gaithersburg MD
,
2009
); See http://webbook.nist.gov (retrieved Oct. 25, 2009).
55.
A. H.
Narten
and
H. A.
Levy
,
J. Chem. Phys.
55
,
2263
(
1971
).
56.
D. M.
Huang
and
D.
Chandler
,
Proc. Natl. Acad. Sci. U.S.A.
97
,
8324
(
2000
).
57.
A.
Pohorille
,
C.
Jarzynski
, and
C.
Chipot
,
J. Phys. Chem. B
114
,
10235
(
2010
).
58.
C. H.
Bennett
,
J. Comput. Phys.
22
,
245
(
1976
).
59.
B.
Hess
,
C.
Kutzner
,
D.
van der Spoel
, and
E.
Lindahl
,
J. Chem. Theory Comput.
4
,
435
(
2008
).
60.
C. G.
Sztrum-Vartash
and
E.
Rabani
,
J. Phys. Chem. C
114
,
11040
(
2010
).
61.
J.
Chen
and
C. L.
Brooks
 III
,
Phys. Chem. Chem. Phys.
10
,
471
(
2008
).
62.
W.
Humphrey
,
A.
Dalke
, and
K.
Schulten
,
J. Mol. Graphics
14
,
33
(
1996
). VMD was developed by the Theoretical and Computational Biophysics Group in the Beckman Institute for Advanced Science and Technology at the University of Illinois at Urbana-Champaign.
63.
The parameters of the solute-solute Lennard-Jones potential are those of Ref. 64: σ = 3.905 Å and ε = 0.118 kcal/mol. Lorentz–Berthelot mixing rules were used to obtain the water-solute interaction parameters.
64.
W. L.
Jorgensen
,
J. D.
Madura
, and
C. J.
Swenson
,
J. Am. Chem. Soc.
106
,
6638
(
1984
).
65.
J. D.
Weeks
,
D.
Chandler
, and
H. C.
Andersen
,
J. Chem. Phys.
54
,
5237
(
1971
).
66.
J.-P.
Hansen
and
I. R.
McDonald
,
Theory of Simple Liquids
, 3rd ed. (
Academic
,
New York
,
2006
).
67.
L.
Verlet
and
J.-J.
Weis
,
Phys. Rev. A
5
,
939
(
1972
).
68.
F.
Wang
and
D.
Landau
,
Phys. Rev. Lett.
86
,
2050
(
2001
).
69.
D.
Earl
and
M.
Deem
,
Phys. Chem. Chem. Phys.
7
,
3910
(
2005
).
70.
M. R.
Shirts
and
J. D.
Chodera
,
J. Chem. Phys.
129
,
124105
(
2008
).
71.
S.
Plimpton
,
J. Comput. Phys.
117
,
1
(
1995
), available at http://lammps.sandia.gov.
72.
See supplementary material at http://dx.doi.org/10.1063/1.3532939 for a listing of the model plate's coordinates, tabulated values of χab for water at ambient conditions, and additional PV(N) distributions.
73.
J.
Mittal
and
G.
Hummer
,
Proc. Natl. Acad. Sci. U.S.A.
105
,
20130
(
2008
).
74.
R.
Godawat
,
S. N.
Jamadagni
, and
S.
Garde
,
Proc. Natl. Acad. Sci. U.S.A.
106
,
15119
(
2009
).
75.
S.
Sarupria
and
S.
Garde
,
Phys. Rev. Lett.
103
,
037803
(
2009
).
76.
J.
Mittal
and
G.
Hummer
,
Faraday Discuss.
146
,
341
(
2010
).
77.
P.
Setny
and
M.
Zacharias
,
J. Phys. Chem. B
114
,
8667
(
2010
).
78.
V.
Molinero
and
E. B.
Moore
,
J. Phys. Chem. B
113
,
4008
(
2009
).
79.
J.
Dzubiella
,
J. M. J.
Swanson
, and
J. A.
McCammon
,
Phys. Rev. Lett.
96
,
087802
(
2006
).
80.
M.
Marchi
,
D.
Borgis
,
N.
Levy
, and
P.
Ballone
,
J. Chem. Phys.
114
,
4377
(
2001
).
81.
R. A.
Marcus
,
J. Chem. Phys.
24
,
966
(
1956
).
82.
B. U.
Felderhof
,
J. Chem. Phys.
67
,
493
(
1977
).
83.
X.
Song
,
D.
Chandler
, and
R. A.
Marcus
,
J. Phys. Chem.
100
,
11954
(
1996
).
84.
X.
Song
and
D.
Chandler
,
J. Chem. Phys.
108
,
2594
(
1998
).
85.
M.
Doi
and
S. F.
Edwards
,
The Theory of Polymer Dynamics
(
Oxford University Press
,
New York
,
1988
).
86.
N.
Kikuchi
,
A.
Gent
, and
J.
Yeomans
,
Eur. Phys. J. E
9
,
63
(
2002
).
87.
S.
Whitelam
,
E. H.
Feng
,
M. F.
Hagan
, and
P. L.
Geissler
,
Soft Matter
5
,
1251
(
2009
).
88.
A.
Malevanets
and
R.
Kapral
,
Europhys. Lett.
44
,
552
(
1998
).
89.
N. K.
Voulgarakis
and
J.-W.
Chu
,
J. Chem. Phys.
130
,
134111
(
2009
).
90.
S.
Chen
and
G. D.
Doolen
,
Annu. Rev. Fluid Mech.
30
,
329
(
1998
).
91.
In Ref. 13, the term proportional to ni is omitted. Since
$\phi ({\protect {\bf r}})$
φ(r)
only acts on cells with ni = 1, this omission is inconsequential, and shows up as an extra factor of 2 in their value of a.
92.
J. S.
Rowlinson
and
B.
Widom
,
Molecule Theory of Capillarity
(
Dover
,
New York
,
1982
), Chap. 3.
93.
J. D.
Weeks
,
J. Chem. Phys.
67
,
3106
(
1977
).
94.
C.
Vega
and
E.
de Miguel
,
J. Chem. Phys.
126
,
54707
(
2007
).
95.
W. E.
Lorensen
and
H. E.
Cline
,
SIGGRAPH Comput. Graph.
21
,
163
(
1987
).
96.
97.
H.
Conroy
,
J. Chem. Phys.
47
,
5307
(
1967
).

Supplementary Material

You do not currently have access to this content.