In molecular dynamics (MD) simulations, free-energy differences are often calculated using free energy perturbation or thermodynamic integration (TI) methods. However, both techniques are only suited to calculate free-energy differences between two end states. Enveloping distribution sampling (EDS) presents an attractive alternative that allows to calculate multiple free-energy differences in a single simulation. In EDS, a reference state is simulated which “envelopes” the end states. The challenge of this methodology is the determination of optimal reference-state parameters to ensure equal sampling of all end states. Currently, the automatic determination of the reference-state parameters for multiple end states is an unsolved issue that limits the application of the methodology. To resolve this, we have generalised the replica-exchange EDS (RE-EDS) approach, introduced by Lee et al. [J. Chem. Theory Comput. 10, 2738 (2014)] for constant-pH MD simulations. By exchanging configurations between replicas with different reference-state parameters, the complexity of the parameter-choice problem can be substantially reduced. A new robust scheme to estimate the reference-state parameters from a short initial RE-EDS simulation with default parameters was developed, which allowed the calculation of 36 free-energy differences between nine small-molecule inhibitors of phenylethanolamine N-methyltransferase from a single simulation. The resulting free-energy differences were in excellent agreement with values obtained previously by TI and two-state EDS simulations.

1.
C.
Chipot
and
A.
Pohorille
,
Free Energy Calculations
(
Springer-Verlag
,
Berlin, Heidelberg
,
2007
).
2.
C. D.
Christ
,
A. E.
Mark
, and
W. F.
van Gunsteren
,
J. Comput. Chem.
31
,
1569
(
2010
).
3.
J. G.
Kirkwood
,
J. Chem. Phys.
3
,
300
(
1935
).
4.
R. W.
Zwanzig
,
J. Chem. Phys.
22
,
1420
(
1954
).
5.
S.
Liu
,
Y.
Wu
,
T.
Lin
,
R.
Abel
,
J. P.
Redmann
,
C. M.
Summa
,
V. R.
Jaber
,
N. M.
Lim
, and
D. L.
Mobley
,
J. Comput.-Aided Mol. Des.
27
,
755
(
2013
).
6.
C. D.
Christ
and
W. F.
van Gunsteren
,
J. Chem. Phys.
126
,
184110
(
2007
).
7.
C. D.
Christ
and
W. F.
van Gunsteren
,
J. Chem. Phys.
128
,
174112
(
2008
).
8.
C. D.
Christ
and
W. F.
van Gunsteren
,
J. Chem. Theory Comput.
5
,
276
(
2009
).
9.
C. D.
Christ
and
W. F.
Van Gunsteren
,
J. Comput. Chem.
30
,
1664
(
2009
).
10.
S.
Riniker
,
C. D.
Christ
,
N.
Hansen
,
A. E.
Mark
,
P. C.
Nair
, and
W. F.
van Gunsteren
,
J. Chem. Phys.
135
,
024105
(
2011
).
11.
U. H. E.
Hansmann
,
Chem. Phys. Lett.
281
,
140
(
1997
).
12.
Y.
Sugita
,
A.
Kitao
, and
Y.
Okamoto
,
J. Chem. Phys.
113
,
6042
(
2000
).
13.
C. J.
Woods
,
J. W.
Essex
, and
M. A.
King
,
J. Phys. Chem. B
107
,
13703
(
2003
).
14.
J.
Lee
,
B. T.
Miller
,
A.
Damjanovic
, and
B. R.
Brooks
,
J. Chem. Theory Comput.
10
,
2738
(
2014
).
15.
J.
Lee
,
B. T.
Miller
,
A.
Damjanovic
, and
B. R.
Brooks
,
J. Chem. Theory Comput.
11
,
2560
(
2015
).
16.
K.-K.
Han
,
Phys. Lett. A
165
,
28
(
1992
).
17.
Y.-G.
Chen
and
G.
Hummer
,
J. Am. Chem. Soc.
129
,
2414
(
2007
).
18.
Y.
Sugita
and
Y.
Okamoto
,
Chem. Phys. Lett.
314
,
141
(
1999
).
19.
N.
Schmid
,
C. D.
Christ
,
M.
Christen
,
A. P.
Eichenberger
, and
W. F.
van Gunsteren
,
Comput. Phys. Commun.
183
,
890
(
2012
).
20.
S.
Riniker
,
C. D.
Christ
,
H. S.
Hansen
,
P. H.
Hünenberger
,
C.
Oostenbrink
,
D.
Steiner
, and
W. F.
van Gunsteren
,
J. Phys. Chem. B
115
,
13570
(
2011
).
21.
C.
Oostenbrink
,
A.
Villa
,
A. E.
Mark
, and
W. F.
Van Gunsteren
,
J. Comput. Chem.
25
,
1656
(
2004
).
22.
H. J. C.
Berendsen
,
J. P. M.
Postma
,
W. F.
van Gunsteren
, and
J.
Hermans
, “
Interaction models for water in relation to protein hydration
,” in
Intermolecular Forces
, edited by
B.
Pullman
(
Reidel
,
Dordrecht, The Netherlands
,
1981
), pp.
331
342
.
23.
I. G.
Tironi
,
R.
Sperb
,
P. E.
Smith
, and
W. F.
van Gunsteren
,
J. Chem. Phys.
102
,
5451
(
1995
).
24.
T. N.
Heinz
,
W. F.
van Gunsteren
, and
P. H.
Hünenberger
,
J. Chem. Phys.
115
,
1125
(
2001
).
25.
H. J.
Berendsen
,
J. V.
Postma
,
W. F.
van Gunsteren
,
A.
DiNola
, and
J.
Haak
,
J. Chem. Phys.
81
,
3684
(
1984
).
26.
P. C.
Nair
,
A. K.
Malde
, and
A. E.
Mark
,
J. Chem. Theory Comput.
7
,
1458
(
2011
).
27.
A. P.
Eichenberger
,
J. R.
Allison
,
J.
Dolenc
,
D. P.
Geerke
,
B. A. C.
Horta
,
K.
Meier
,
C.
Oostenbrink
,
N.
Schmid
,
D.
Steiner
,
D.
Wang
, and
W. F.
van Gunsteren
,
J. Chem. Theory Comput.
7
,
3379
(
2011
).

Supplementary Material

You do not currently have access to this content.