Accurate and efficient integration of the equations of motion is indispensable for molecular dynamics (MD) simulations. Despite the massive use of the conventional leapfrog (LF) integrator in modern computational tools within the framework of MD propagation, further development for better performance is still possible. The alternative version of LF in the middle thermostat scheme (LF-middle) achieves a higher order of accuracy and efficiency and maintains stable dynamics even with the integration time stepsize extended by several folds. In this work, we perform a benchmark test of the two integrators (LF and LF-middle) in extensive conventional and enhanced sampling simulations, aiming at quantifying the time-stepsize-induced variations of global properties (e.g., detailed potential energy terms) as well as of local observables (e.g., free energy changes or bondlengths) in practical simulations of complex systems. The test set is composed of six chemically and biologically relevant systems, including the conformational change of dihedral flipping in the N-methylacetamide and an AT (Adenine-Thymine) tract, the intra-molecular proton transfer inside malonaldehyde, the binding free energy calculations of benzene and phenol targeting T4 lysozyme L99A, the hydroxyl bond variations in ethaline deep eutectic solvent, and the potential energy of the blue-light using flavin photoreceptor. It is observed that the time-step-induced error is smaller for the LF-middle scheme. The outperformance of LF-middle over the conventional LF integrator is much more significant for global properties than local observables. Overall, the current work demonstrates that the LF-middle scheme should be preferably applied to obtain accurate thermodynamics in the simulation of practical chemical and biological systems.
References
[1]
B. J.
Alder
and T. E.
Wainwright
, J. Chem. Phys.
27
, 1208
(1957
).[2]
E.
Fermi
, J.
Pasta
, and S.
Ulam
, Studies of Non Linear Problems
, Los Alamos Report LA-1940
, (1955
).[3]
M. P.
Allen
and D. J.
Tildesley
, Computer Simulation of Liquids
, Oxford
: Clarendon Press
, 385
(1987
).[4]
D.
Frenkel
and B.
Smit
, Understanding Molecular Simulation: from Algorithms to Applications
, 2nd Edn, San Diego
: Academic Press
, (2002
).[5]
Y.
Xiang
, L. L.
Duan
, and J. Z. H.
Zhang
, Phys. Chem. Chem. Phys.
12
, 15681
(2010
).[6]
B.
Wang
, Y. F.
Qi
, Y.
Gao
, and J. Z. H.
Zhang
, Phys. Chem. Chem. Phys.
22
, 8461
(2020
).[7]
J. Z.
Chen
, L. X.
Pang
, W.
Wang
, L. F.
Wang
, J. Z. H.
Zhang
, and T.
Zhu
, J. Biomol. Struct. Dyn.
38
, 985
(2020
).[8]
J.
Liu
, D. Z.
Li
, and X. J.
Liu
, J. Chem. Phys.
145
, 024103
(2016
).[9]
Z. J.
Zhang
, X. Z. J.
Liu
, Z. F.
Chen
, H. F.
Zheng
, K. Y.
Yan
, and J.
Liu
, J. Chem. Phys.
147
, 034109
(2017
).[10]
Z. J.
Zhang
, X. Z. J.
Liu
, K. Y.
Yan
, M. E.
Tuckerman
, and J.
Liu
, J. Phys. Chem. A
123
, 6056
(2019
).[11]
J. Z.
Chen
, S. L.
Zhang
, W.
Wang
, L. X.
Pang
, Q. G.
Zhang
, and X. G.
Liu
, J. Chem. Inf. Model.
61
, 1954
(2021
).[12]
Z. X.
Sun
, Z. H.
Gong
, F.
Xia
, and X.
He
, Chem. Phys.
548
, 111245
(2021
).[13]
H.
Fukunishi
, O.
Watanabe
, and S.
Takada
, J. Chem. Phys.
116
, 9058
(2002
).[14]
R. W. W.
Hooft
, B. P.
van Eijck
, and J.
Kroon
, J. Chem. Phys.
97
, 6690
(1992
).[15]
G. H.
Paine
and H. A.
Scheraga
, Biopolymers
24
, 1391
(1985
).[16]
C.
Jarzynski
, Phys. Rev. Lett.
78
, 2690
(1997
).[17]
R.
Chelli
, C.
Gellini
, G.
Pietraperzia
, E.
Giovannelli
, and G.
Cardini
, J. Chem. Phys.
138
, 214109
(2013
).[18]
E.
Giovannelli
, P.
Procacci
, G.
Cardini
, M.
Pagliai
, V.
Volkov
, and R.
Chelli
, J. Chem. Theory Comput.
13
, 5874
(2017
).[19]
V.
Lindahl
, J.
Lidmar
, and B.
Hess
, Phys. Rev. E
98
, 023312
(2018
).[20]
Z. X.
Sun
, Q. L.
He
, X.
Li
, and Z. D.
Zhu
, J. Comput. Aided Mol. Des.
34
, 589
(2020
).[21]
Z. X.
Sun
, J. Comput. Aided Mol. Des.
35
, 105
(2021
).[22]
D. A.
Case
, T. E.
Cheatham
III, T.
Darden
, H.
Gohlke
, R.
Luo
, K. M.
Merz
Jr., A.
Onufriev
, C.
Simmerling
, B.
Wang
, and R. J.
Woods
, J. Comput. Chem.
26
, 1668
(2005
).[23]
[24]
B.
Leimkuhler
and C.
Matthews
, J. Chem. Phys.
138
, 174102
(2013
).[25]
N.
Grønbech-Jensen
and O.
Farago
, Mol. Phys.
111
, 983
(2013
).[26]
D. Z.
Li
, X.
Han
, Y. C.
Chai
, C.
Wang
, Z. J.
Zhang
, Z. F.
Chen
, J.
Liu
, and J. S.
Shao
, J. Chem. Phys.
147
, 184104
(2017
).[27]
D. Z.
Li
, Z. F.
Chen
, Z. J.
Zhang
, and J.
Liu
, Chin. J. Chem. Phys.
30
, 735
(2017
).[28]
Z. J.
Zhang
, K. Y.
Yan
, X. Z. J.
Liu
, and J.
Liu
, Chin. Sci. Bull.
63
, 3467
(2018
).[29]
M.
Marchi
and P.
Procacci
, J. Chem. Phys.
109
, 5194
(1998
).[30]
P.
Procacci
and M.
Marchi
, J. Chem. Phys.
104
, 3003
(1996
).[31]
P.
Procacci
and B. J.
Berne
, J. Chem. Phys.
101
, 2421
(1994
).[32]
B.
Leimkuhler
and C.
Matthews
, Proc. Roy. Soc. A: Math., Phys. Eng. Sci.
472
, 20160138
(2016
).[33]
X. H.
Wang
, Q. L.
He
, and Z. X.
Sun
, Phys. Chem. Chem. Phys.
21
, 6672
(2019
).[34]
X. H.
Wang
, X. Z.
Tu
, B. M.
Deng
, J. Z. H.
Zhang
, and Z. X.
Sun
, J. Comput. Chem.
40
, 1270
(2019
).[35]
V.
Hornak
, R.
Abel
, A.
Okur
, B.
Strockbine
, A.
Roitberg
, and C.
Simmerling
, Proteins
65
, 712
(2006
).[36]
W. L.
Jorgensen
, J.
Chandrasekhar
, J. D.
Madura
, R. W.
Impey
, and M. L.
Klein
, J. Chem. Phys.
79
, 926
(1983
).[37]
D. J.
Price
and C. L.
Brooks
III, J. Chem. Phys.
121
, 10096
(2004
).[38]
U.
Essmann
, L.
Perera
, M. L.
Berkowitz
, T.
Darden
, H.
Lee
, and L. G.
Pedersen
, J. Chem. Phys.
103
, 8577
(1995
).[39]
R. W. W.
Hooft
, B. P.
van Eijck
, and J.
Kroon
, J. Chem. Phys.
97
, 6690
(1992
).[40]
M.
Mezei
, J. Comput. Phys.
68
, 237
(1987
).[41]
[42]
Z. X.
Sun
, Phys. Chem. Chem. Phys.
21
, 21942
(2019
).[43]
J. P.
Ryckaert
, G.
Ciccotti
, and H. J. C.
Berendsen
, J. Comput. Phys.
23
, 327
(1977
).[44]
S.
Miyamoto
and P. A.
Kollman
, J. Comput. Chem.
13
, 952
(1992
).[45]
Z. X.
Sun
, X. H.
Wang
, and J. Z. H.
Zhang
, Chem. Phys. Lett.
684
, 239
(2017
).[46]
J. A.
Lemkul
, A.
Savelyev
, and A. D.
MacKerell
Jr., J. Phys. Chem. Lett.
5
, 2077
(2014
).[47]
H.
Zheng
, Y. Q.
Cai
, S.
Ding
, Y. J.
Tang
, K.
Kropachev
, Y. Z.
Zhou
, L. H.
Wang
, S. L.
Wang
, N. E.
Geacintov
, Y. K.
Zhang
, and S.
Broyde
, Chem. Res. Toxicol.
23
, 1868
(2010
).[48]
T. S.
Lee
, B. K.
Radak
, A.
Pabis
, and D. M.
York
, J. Chem. Theory Comput.
9
, 153
(2013
).[49]
J. J. P.
Stewart
, J. Mol. Model.
13
, 1173
(2007
).[50]
N. K.
Banavali
and A. D.
MacKerell
Jr., J. Mol. Biol.
319
, 141
(2002
).[51]
Y. S.
Lazurkin
, M. D.
Frank-Kamenetskii
, and E. N.
Trifonov
, Biopolymers
9
, 1253
(1970
).[52]
N. A.
Špačková
, E.
Cubero
, J.
Šponer
, and M.
Orozco
, J. Am. Chem. Soc.
126
, 14642
(2004
).[53]
M.
O’Gara
, R. J.
Roberts
, and X. D.
Cheng
, J. Mol. Biol.
263
, 597
(1996
).[54]
K. A.
Velizhanin
, C. C.
Chien
, Y.
Dubi
, and M.
Zwolak
, Phys. Rev. E
83
, 050906(R
) (2011
).[55]
B. H.
Zimm
, J. Chem. Phys.
33
, 1349
(1960
).[56]
A.
Travers
, Curr. Biol.
15
, R377
(2005
).[57]
A.
Zeida
, M. R.
Machado
, P. D.
Dans
, and S.
Pantano
, Phys. Rev. E
86
, 021903
(2012
).[58]
M.
Peyrard
, S.
Cuesta-López
, and G.
James
, J. Biol. Phys.
35
, 73
(2009
).[59]
C. I.
Duduiala
, J. A. D.
Wattis
, I. L.
Dryden
, and C. A.
Laughton
, Phys. Rev. E
80
, 061906
(2009
).[60]
N.
Huang
, N. K.
Banavali
, and A. D.
MacKerell
Jr., Proc. Natl. Acad. Sci. USA
100
, 68
(2003
).[61]
X. H.
Wang
and Z. X.
Sun
, J. Chem. Inf. Model.
59
, 2980
(2019
).[62]
R.
Galindo-Murillo
, J. C.
Robertson
, M.
Zgarbová
, J.
Šponer
, M.
Otyepka
, P.
Jurečka
, and T. E.
Cheatham
III, J. Chem. Theory Comput.
12
, 4114
(2016
).[63]
P. D.
Dans
, I.
Ivani
, A.
Hospital
, G.
Portella
, C.
González
, and M.
Orozco
, Nucl. Acids Res.
45
, 4217
(2017
).[64]
I.
Ivani
, P. D.
Dans
, A.
Noy
, A.
Pérez
, I.
Faustino
, A.
Hospital
, J.
Walther
, P.
Andrio
, R.
Goñi
, A.
Balaceanu
, G.
Portella
, F.
Battistini
, J. L.
Gelpí
, C.
González
, M.
Vendruscolo
, C. A.
Laughton
, S. A.
Harris
, D. A.
Case
, and M.
Orozco
, Nat. Methods
13
, 55
(2016
).[65]
I. S.
Joung
and T. E.
Cheatham
III, J. Phys. Chem. B
112
, 9020
(2008
).[66]
I. S.
Joung
and T. E.
Cheatham
III, J. Phys. Chem. B
113
, 13279
(2009
).[67]
Z. X.
Sun
and J. Z. H.
Zhang
, CCS Chem.
3
, 1026
(2021
).[68]
Z. X.
Sun
, X. H.
Wang
, J. Z. H.
Zhang
, and Q. L.
He
, Phys. Chem. Chem. Phys.
21
, 14923
(2019
).[69]
X. H.
Wang
, X. Z.
Tu
, J. Z. H.
Zhang
, and Z. X.
Sun
, Phys. Chem. Chem. Phys.
20
, 2009
(2018
).[70]
M.
Muñoz
and C.
Cárdenas
, Phys. Chem. Chem. Phys.
19
, 16003
(2017
).[71]
F.
Nerattini
, R.
Chelli
, and P.
Procacci
, Phys. Chem. Chem. Phys.
18
, 15005
(2016
).[72]
Z. X.
Sun
, X. H.
Wang
, and J. N.
Song
, J. Chem. Inf. Model.
57
, 1621
(2017
).[73]
P.
Mikulskis
, D.
Cioloboc
, M.
Andrejić
, S.
Khare
, J.
Brorsson
, S.
Genheden
, R. A.
Mata
, P.
Söderhjelm
, and U.
Ryde
, J. Comput. Aided Mol. Des.
28
, 375
(2014
).[74]
J.
Michel
and J. W.
Essex
, J. Comput. Aided Mol. Des.
24
, 639
(2010
).[75]
Z. X.
Sun
, X. H.
Wang
, and J. Z. H.
Zhang
, Phys. Chem. Chem. Phys.
19
, 15005
(2017
).[76]
Z.
Huai
, Z. X.
Shen
, and Z. X.
Sun
, J. Chem. Inf. Model.
61
, 284
(2021
).[77]
Z.
Huai
, H. Y.
Yang
, X.
Li
, and Z. X.
Sun
, J. Comput. Aided Mol. Des.
35
, 117
(2021
).[78]
A. E.
Eriksson
, W. A.
Baase
, J. A.
Wozniak
, and B. W.
Matthews
, Nature
355
, 371
(1992
).[79]
A.
Morton
and B. W.
Matthews
, Biochemistry
34
, 8576
(1995
).[80]
T.
Steinbrecher
, D. L.
Mobley
, and D. A.
Case
, J. Chem. Phys.
127
, 214108
(2007
).[81]
M.
Zacharias
, T. P.
Straatsma
, and J. A.
McCammon
, J. Chem. Phys.
100
, 9025
(1994
).[82]
T. C.
Beutler
, A. E.
Mark
, R. C.
van Schaik
, P. R.
Gerber
, and W. F.
van Gunsteren
, Chem. Phys. Lett.
222
, 529
(1994
).[83]
D. A.
Pearlman
and P. A.
Kollman
, J. Chem. Phys.
91
, 7831
(1989
).[84]
M.
Levitt
, J. Mol. Biol.
170
, 723
(1983
).[85]
Bruckner
and S.
Boresch
, J. Comput. Chem.
32
, 1320
(2011
).[86]
H.
Resat
and M.
Mezei
, J. Chem. Phys.
99
, 6052
(1993
).[87]
H.
Resat
and M.
Mezei
, J. Chem. Phys.
101
, 6126
(1994
).[88]
A. P.
Abbott
, G.
Capper
, D. L.
Davies
, R. K.
Rasheed
, and V.
Tambyrajah
, Chem. Commun.
1
, 70
(2003
).[89]
P.
Kalhor
and K.
Ghandi
, Catalysts
11
, 178
(2021
).[90]
P.
Kalhor
and K.
Ghandi
, Molecules
24
, 4012
(2019
).[91]
T.
El Achkar
, H.
Greige-Gerges
, and S.
Fourmentin
, Environ. Chem. Lett.
19
, 3397
(2021
).[92]
E. L.
Smith
, A. P.
Abbott
, and K. S.
Ryder
, Chem. Rev.
114
, 11060
(2014
).[93]
P.
Kalhor
, J.
Xu
, H.
Ashraf
, B. B.
Cao
, and Z. W.
Yu
, J. Phys. Chem. B
124
, 1229
(2020
).[94]
P.
Kalhor
, Y. Z.
Zheng
, H.
Ashraf
, B. B.
Cao
, and Z. W.
Yu
, ChemPhysChem
21
, 995
(2020
).[95]
K.
Shahbaz
, F. S.
Mjalli
, M. A.
Hashim
, and I. M.
ALNashef
, J. Appl. Sci.
10
, 3349
(2010
).[96]
S. Y.
Park
and J. R. H.
Tame
, Biophys. Rev.
9
, 169
(2017
).[97]
J. J.
Goings
and S.
Hammes-Schiffer
, J. Am. Chem. Soc.
141
, 20470
(2019
).[98]
A.
Losi
and W.
Gärtner
, Photochem. Photobiol.
93
, 141
(2017
).[99]
J. J.
Goings
, P. F.
Li
, Q. W.
Zhu
, and S.
Hammes-Schiffer
, Proc. Natl. Acad. Sci. USA
117
, 26626
(2020
).[100]
S.
Anderson
, V.
Dragnea
, S.
Masuda
, J.
Ybe
, K.
Moffat
, and C.
Bauer
, Biochemistry
44
, 7998
(2005
).
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