Many methods to accelerate sampling of molecular configurations are based on the idea that temperature can be used to accelerate rare transitions. These methods typically compute equilibrium properties at a target temperature using reweighting or through Monte Carlo exchanges between replicas at higher temperatures. A recent paper [G. M. Rotskoff and E. Vanden-Eijnden, Phys. Rev. Lett. 122, 150602 (2019)] demonstrated that accurate equilibrium densities of states can also be computed through a nonequilibrium “quench” process, where sampling is performed at a higher temperature to encourage rapid mixing and then quenched to lower energy states with dissipative dynamics. Here, we provide an implementation of the quench dynamics in LAMMPS and evaluate a new formulation of nonequilibrium estimators for the computation of partition functions or free energy surfaces (FESs) of molecular systems. We show that the method is exact for a minimal model of N-independent harmonic springs and use these analytical results to develop heuristics for the amount of quenching required to obtain accurate sampling. We then test the quench approach on alanine dipeptide, where we show that it gives an FES that is accurate near the most stable configurations using the quench approach but disagrees with a reference umbrella sampling calculation in high FE regions. We then show that combining quenching with umbrella sampling allows the efficient calculation of the free energy in all regions. Moreover, by using this combined scheme, we obtain the FES across a range of temperatures at no additional cost, making it much more efficient than standard umbrella sampling if this information is required. Finally, we discuss how this approach can be extended to solute tempering and demonstrate that it is highly accurate for the case of solvated alanine dipeptide without any additional modifications.

1.
G. M.
Rotskoff
and
E.
Vanden-Eijnden
,
Phys. Rev. Lett.
122
,
150602
(
2019
).
2.
D.
Frenkel
and
B.
Smit
,
Understanding Molecular Simulation: From Algorithms to Applications
(
Elsevier
,
2001
), Vol.
1
.
3.
M.
Tuckerman
,
Statistical Mechanics: Theory and Molecular Simulation
(
Oxford University Press
,
2010
).
4.
J.
Hénin
,
T.
Lelièvre
,
M.
Shirts
,
O.
Valsson
, and
L.
Delemotte
,
Living J. Comput. Mol. Sci.
4
,
1583
(
2022
).
5.
G. M.
Torrie
and
J. P.
Valleau
,
J. Comput. Phys.
23
,
187
(
1977
).
6.
A.
Barducci
,
G.
Bussi
, and
M.
Parrinello
,
Phys. Rev. Lett.
100
,
020603
(
2008
).
7.
Y.
Sugita
and
Y.
Okamoto
,
Chem. Phys. Lett.
314
,
141
(
1999
).
8.
P.
Liu
,
B.
Kim
,
R. A.
Friesner
, and
B.
Berne
,
Proc. Natl. Acad. Sci. U. S. A.
102
,
13749
(
2005
).
10.
S.
Vaikuntanathan
and
C.
Jarzynski
,
Phys. Rev. Lett.
100
,
190601
(
2008
).
11.
J. P.
Nilmeier
,
G. E.
Crooks
,
D. D.
Minh
, and
J. D.
Chodera
,
Proc. Natl. Acad. Sci. U. S. A.
108
,
E1009
(
2011
).
12.
S.
Martiniani
, “
On the complexity of energy landscapes: Algorithms and a direct test of the Edwards conjecture
,” Ph.D. thesis,
University of Cambridge
,
2017
.
13.
A.
Thin
,
Y.
Janati El Idrissi
,
S.
Le Corff
,
C.
Ollion
,
E.
Moulines
,
A.
Doucet
,
A.
Durmus
, and
C. X.
Robert
, in
Advances in Neural Information Processing Systems 34
, edited by
M.
Ranzato
,
A.
Beygelzimer
,
Y.
Dauphin
,
P.
Liang
, and
J. W.
Vaughan
(
Curran Associates, Inc.
,
2021
), Vol.
34
, pp.
17060
17071
.
14.
Y.
Cao
and
E.
Vanden-Eijnden
, in
Advances in Neural Information Processing Systems 35
, edited by
A. H.
Oh
,
A.
Agarwal
,
D.
Belgrave
, and
K.
Cho
, (Curran Associates, Inc.,
2022
).
16.
17.
A. P.
Thompson
,
H. M.
Aktulga
,
R.
Berger
,
D. S.
Bolintineanu
,
W. M.
Brown
,
P. S.
Crozier
,
P. J.
in ’t Veld
,
A.
Kohlmeyer
,
S. G.
Moore
,
T. D.
Nguyen
et al,
Comput. Phys. Commun.
271
,
108171
(
2022
).
18.
B.
Leimkuhler
and
C.
Matthews
,
J. Chem. Phys.
138
,
174102
(
2013
).
19.
S.
Kirkpatrick
,
C. D.
Gelatt
, Jr.
, and
M. P.
Vecchi
,
Science
220
,
671
(
1983
).
20.
F.
Aluffi-Pentini
,
V.
Parisi
, and
F.
Zirilli
,
J. Optim. Theory Appl.
47
,
1
(
1985
).
21.
E.
Marinari
and
G.
Parisi
,
Europhys. Lett.
19
,
451
(
1992
).
22.

In real MD simulations, it is impossible to compute free energy at any particular s. Rather, we use a block function (integrating delta function over windows), and we show in  Appendix C that free energy computed in this way has an error with magnitude O(Δs2), where Δs is the width of windows.

23.
Y.
Babuji
,
A.
Woodard
,
Z.
Li
,
D. S.
Katz
,
B.
Clifford
,
R.
Kumar
,
L.
Lacinski
,
R.
Chard
,
J. M.
Wozniak
,
I.
Foster
et al, in
Proceedings of the 28th International Symposium on High-Performance Parallel and Distributed Computing
(
Association for Computing Machinery
,
2019
), pp.
25
36
.
24.
L. F. G.
Jensen
and
N.
Grønbech-Jensen
,
Mol. Phys.
117
,
2511
(
2019
).
25.
A. D.
MacKerell
, Jr.
,
N.
Banavali
, and
N.
Foloppe
,
Biopolymers
56
,
257
(
2000
).
26.
E.
Gallicchio
,
M.
Andrec
,
A. K.
Felts
, and
R. M.
Levy
,
J. Phys. Chem. B
109
,
6722
(
2005
).
27.
E. H.
Thiede
,
B.
Van Koten
,
J.
Weare
, and
A. R.
Dinner
,
J. Chem. Phys.
145
,
084115
(
2016
).
28.
G. A.
Tribello
,
M.
Bonomi
,
D.
Branduardi
,
C.
Camilloni
, and
G.
Bussi
,
Comput. Phys. Commun.
185
,
604
(
2014
).
29.
M.
Bonomi
,
G.
Bussi
,
C.
Camilloni
,
G. A.
Tribello
,
P.
Banas
,
A.
Barducci
,
M.
Bernetti
,
P. G.
Bolhuis
,
S.
Bottaro
,
D.
Branduardi
,
R.
Capelli
,
P.
Carloni
,
M.
Ceriotti
,
A.
Cesari
,
H.
Chen
,
W.
Chen
,
F.
Colizzi
,
S.
De
,
M. D. L.
Pierre
,
D.
Donadio
,
V.
Drobot
,
B.
Ensing
,
A. L.
Ferguson
,
M.
Filizola
,
J. S.
Fraser
,
H.
Fu
,
P.
Gasparotto
,
F. L.
Gervasio
,
F.
Giberti
,
A.
Gil-Ley
,
T.
Giorgino
,
G. T.
Heller
,
G. M.
Hocky
,
M.
Iannuzzi
,
M.
Invernizzi
,
K. E.
Jelfs
,
A.
Jussupow
,
E.
Kirilin
,
A.
Laio
,
V.
Limongelli
,
K.
Lindorff-Larsen
,
T.
Lohr
,
F.
Marinelli
,
L.
Martin-Samos
,
M.
Masetti
,
R.
Meyer
,
A.
Michaelides
,
C.
Molteni
,
T.
Morishita
,
M.
Nava
,
C.
Paissoni
,
E.
Papaleo
,
M.
Parrinello
,
J.
Pfaendtner
,
P.
Piaggi
,
G. M.
Piccini
,
A.
Pietropaolo
,
F.
Pietrucci
,
S.
Pipolo
,
D.
Provasi
,
D.
Quigley
,
P.
Raiteri
,
S.
Raniolo
,
J.
Rydzewski
,
M.
Salvalaglio
,
G. C.
Sosso
,
V.
Spiwok
,
J.
Sponer
,
D. W. H.
Swenson
,
P.
Tiwary
,
O.
Valsson
,
M.
Vendruscolo
,
G. A.
Voth
, and
A.
White
,
Nat. Methods
16
,
670
(
2019
).
30.
31.
M. R.
Shirts
and
J. D.
Chodera
,
J. Chem. Phys.
129
,
124105
(
2008
).
32.
X.
Ding
,
J. Z.
Vilseck
, and
C. L.
Brooks
III
,
J. Chem. Theory Comput.
15
,
799
(
2019
).
33.
S.
Jo
,
T.
Kim
,
V. G.
Iyer
, and
W.
Im
,
J. Comput. Chem.
29
,
1859
(
2008
).
34.
J.
Lee
,
X.
Cheng
,
J. M.
Swails
,
M. S.
Yeom
,
P. K.
Eastman
,
J. A.
Lemkul
,
S.
Wei
,
J.
Buckner
,
J. C.
Jeong
,
Y.
Qi
et al,
J. Chem. Theory Comput.
12
,
405
(
2016
).
35.
J.
Lee
,
M.
Hitzenberger
,
M.
Rieger
,
N. R.
Kern
,
M.
Zacharias
, and
W.
Im
,
J. Chem. Phys.
153
,
035103
(
2020
).
36.
M.
Kardar
,
Statistical Physics of Particles
(
Cambridge University Press
,
2007
).
37.
S.
Kumar
,
J. M.
Rosenberg
,
D.
Bouzida
,
R. H.
Swendsen
, and
P. A.
Kollman
,
J. Comput. Chem.
13
,
1011
(
1992
).

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