We present a novel and efficient method for performing free energy calculations. Treating the conventional λ variables associated with the ‘‘progress’’ in the chemical coordinates dynamically, our approach transforms free energy calculations into calculating potentials of mean force in the λ‐space with molecular dynamics. This extended Hamiltonian formalism utilizes the full power of umbrella sampling techniques and the weighted histogram analysis method. Applications to free energies of hydration and a model illustrating competitive binding calculations are presented. These calculations demonstrate the robustness and flexibility of the new λ‐dynamics approach.

1.
C. L. Brooks III, M. Karplus, and B. M. Pettitt, in Advances in Chemical Physics, edited by I. Prigogine and S. A. Rice (Wiley, New York, 1988), Vol. LXXI.
2.
J. A. McCammon and S. Harvey, Dynamics of Proteins and Nuclei Acids (Cambridge University Press, Cambridge, 1987).
3.
M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Clarendon, Oxford, 1989).
4.
S. F.
Sneddon
,
D. J.
Tobias
, and
C. L.
Brooks
III
,
J. Mol. Biol.
209
,
817
(
1989
).
5.
D. J.
Tobias
and
C. L.
Brooks
III
,
Biochemistry
30
,
6059
(
1991
).
6.
D. J.
Tobias
and
C. L.
Brooks
III
,
J. Mol. Biol.
216
,
783
(
1991
).
7.
D. J. Tobias, S. F. Sneddon, and C. L. Brooks III, in Advances in Bimolecular Simulations, AIP Conference Proceedings No. 238, edited by R. Lavery, J.-L. Rivail, and J. Smith (Obernai, France, 1991).
8.
M. L.
Smythe
,
S. E.
Huston
, and
G. R.
Marshall
,
J. Am. Chem. Soc.
115
,
11594
(
1993
).
9.
S. E.
Huston
and
G. R.
Marshall
,
Biopolymers
34
,
75
(
1994
).
10.
P. A.
Bash
,
U. C.
Singh
,
R.
Langridge
, and
P. A.
Kollman
,
Science
236
,
564
(
1987
).
11.
J. P. M.
Postma
,
H. J. C.
Berendsen
, and
J. R.
Haak
,
Faraday Symp. Chem. Soc.
17
,
55
(
1982
).
12.
W. L.
Jorgensen
and
C.
Ravimohan
,
J. Chem. Phys.
83
,
3050
(
1985
).
13.
S. H.
Fleischman
and
C. L.
Brooks
III
,
J. Chem. Phys.
87
,
3029
(
1987
).
14.
T. P.
Lybrand
,
I.
Ghosh
, and
J. A.
McCammon
,
J. Am. Chem. Soc.
107
,
7793
(
1985
).
15.
T. P.
Lybrand
,
J. A.
McCammon
, and
G.
Wipff
,
Proc. Natl. Acad. Sci. U.S.A.
83
,
833
(
1986
).
16.
C. F.
Wong
and
J. A.
McCammon
,
J. Am. Chem. Soc.
108
,
3830
(
1986
).
17.
D. A.
Pearlman
,
J. Phys. Chem.
98
,
1487
(
1994
).
18.
D. A. Pearlman and P. A. Kollman, in Computer Simulation of Bimolecular Systems: Theoretical and Experimental Applications, edited by W. F. van Gunsteren and P. K. Weiner (Escom Science, The Netherlands, 1989), Vol. 1.
19.
D. A.
Pearlman
,
J. Phys. Chem.
98
,
1487
(
1993
).
20.
J.
Tirado-River
,
D. S.
Maxwell
, and
W. L.
Jorgensen
,
J. Am. Chem. Soc.
115
,
11590
(
1993
).
21.
W. R.
Fiori
,
S. M.
Miick
, and
G. L.
Millhauser
,
Biochemistry
32
,
11957
(
1993
).
22.
S.
Yun-yu
,
A. E.
Mark
,
W.
Cun-xin
,
H.
Fuhua
,
H.
Berendsen
, and
W. F.
van Gunsteren
,
Protein Eng.
6
,
289
(
1993
).
23.
G. M.
Torrie
and
J. P.
Valleau
,
Chem. Phys. Lett.
28
,
578
(
1974
).
24.
D. L.
Beveridge
and
F. M.
DiCapua
,
Annu. Rev. Biophys. Biophys. Chem.
18
,
431
(
1989
).
25.
L. D. Landau and E. M. Lifschitz, Statistical Physics, 2nd ed. (Pergamon, New York, 1960).
26.
S. H.
Northrup
,
M. R.
Pear
,
C.-Y.
Lee
,
J. A.
McCammon
, and
M.
Karplus
,
Proc. Natl. Acad. Sci. U.S.A.
79
,
4035
(
1982
).
27.
G. N.
Patey
and
J. P.
Valleau
,
J. Chem. Phys.
63
,
2334
(
1975
).
28.
C.
Pangali
,
M.
Rao
, and
B. J.
Berne
,
J. Chem. Phys.
71
,
2975
(
1979
).
29.
J. P.
Valleau
and
D. N.
Card
,
J. Chem. Phys.
57
,
5457
(
1972
).
30.
Z.
Liu
and
B. J.
Berne
,
J. Chem. Phys.
99
,
6071
(
1993
).
31.
S.
Nose
,
J. Chem. Phys.
81
,
511
(
1984
).
32.
J.
Ji
,
T.
Cagin
, and
B. M.
Pettitt
,
J. Chem. Phys.
96
,
1333
(
1992
).
33.
J. Ji and B. M. Pettitt, in Computer Simulation of Bimolecular Systems: Theoretical and Experimental Applications, edited by W. F. van Gunsteren, P. W. Weiner, and A. J. Wilkinson (ESCOM, Leiden, 1993), Vol. 2.
34.
A. M.
Ferrenberg
and
R. H.
Swendsen
,
Phys. Rev. Lett.
63
,
1195
(
1989
).
35.
A. M. Ferrenberg, Ph.D. thesis, Carnegie Mellon University, 1989.
36.
S.
Kumar
,
D.
Bouzida
,
R. H.
Swendsen
,
P. A.
Kollman
, and
J.
Rosenberg
,
J. Comput. Chem.
13
,
1011
(
1992
).
37.
E. M.
Boczko
and
C. L.
Brooks
III
,
J. Phys. Chem.
97
,
4509
(
1993
).
38.
D. A.
Pearlman
and
P. A.
Kollman
,
J. Chem. Phys.
90
,
2460
(
1989
).
39.
B.
Tidor
,
J. Phys. Chem.
97
,
1069
(
1993
).
40.
W. L.
Jorgensen
,
J. Phys. Chem.
87
,
5304
(
1983
).
41.
W. L.
Jorgensen
,
J. Chem. Phys.
77
,
5757
(
1982
).
42.
B. R.
Brooks
,
R. E.
Bruccoleri
,
B. D.
Olafson
,
D. J.
States
,
S.
Swaminathan
, and
M.
Karplus
,
J. Comput. Chem.
4
,
187
(
1983
).
43.
W. L.
Jorgensen
,
J.
Chandrasekhar
,
J. D.
Madura
,
R. W.
Impey
, and
M. L.
Klein
,
J. Chem. Phys.
79
,
926
(
1983
).
44.
H. A.
Carlson
,
T. B.
Nyuyen
,
M.
Orozco
, and
W. L.
Jorgensen
,
J. Comput. Chem.
14
,
1240
(
1993
).
45.
G. L.
Martyna
and
M. L.
Klein
,
J. Chem. Phys.
97
,
2635
(
1992
).
46.
W. C.
Swope
,
H. C.
Andersen
,
P. H.
Berens
, and
K. R.
Wilson
,
J. Chem. Phys.
76
,
637
(
1982
).
47.
W. F.
van Gunsteren
and
H. J. C.
Berendsen
,
Mol. Phys.
34
,
1311
(
1977
).
48.
A.
Ben-Naim
and
Y.
Marcus
,
J. Chem. Phys.
81
,
2016
(
1984
).
49.
W. L.
Jorgensen
,
J. M.
Briggs
, and
M. L.
Contreras
,
J. Phys. Chem.
94
,
1683
(
1990
).
50.
H. A.
Carlson
and
W. J.
Jorgensen
,
J. Phys. Chem.
99
,
10667
(
1995
).
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