We present a dynamic coarse-graining technique that allows one to simulate the mechanical unfolding of biomolecules or molecular complexes on experimentally relevant time scales. It is based on Markov state models (MSMs), which we construct from molecular dynamics simulations using the pulling coordinate as an order parameter. We obtain a sequence of MSMs as a function of the discretized pulling coordinate, and the pulling process is modeled by switching among the MSMs according to the protocol applied to unfold the complex. This way we cover seven orders of magnitude in pulling speed. In the region of rapid pulling, we additionally perform steered molecular dynamics simulations and find excellent agreement between the results of the fully atomistic and the dynamically coarse-grained simulations. Our technique allows the determination of the rates of mechanical unfolding in a dynamical range from approximately 10−8/ns to 1/ns thus reaching experimentally accessible time regimes without abandoning atomistic resolution.
REFERENCES
1.
E.
Evans
, Annu. Rev. Biophys. Biomol. Struct.
30
, 105
(2001
).2.
G.
Žoldák
and M.
Rief
, Curr. Opin. Struct. Biol.
23
, 48
(2013
).3.
O. K.
Dudko
, Q. Rev. Biophys.
49
, 1
(2016
).4.
C.
Hyeon
and D.
Thirumalai
, J. Phys.: Condens. Matter
19
, 113101
(2007
).5.
T.
Schmiedl
, T.
Speck
, and U.
Seifert
, J. Stat. Phys.
128
, 77
(2007
).6.
C.
Jarzynski
, Annu. Rev. Condens. Matter Phys.
2
, 329
(2011
).7.
A. N.
Gupta
et al., Nat. Phys.
7
, 631
(2011
).8.
C.
Bustamante
, J.
Liphardt
, and F.
Ritort
, Phys. Today
58
(7
), 43
(2005
).9.
A.
Alemany
and F.
Ritort
, Europhys. News
41
, 27
(2010
).10.
O. K.
Dudko
, G.
Hummer
, and A.
Szabo
, Proc. Natl. Acad. Sci. U. S. A.
105
, 15755
(2008
).11.
A.
Maitra
and G.
Arya
, Phys. Rev. Lett.
104
, 108301
(2010
).12.
Y.
Zhang
and O. K.
Dudko
, Proc. Natl. Acad. Sci. U. S. A.
110
, 16432
(2013
).13.
J. T.
Bullerjahn
, S.
Sturm
, and K.
Kroy
, Nat. Commun.
5
, 4463
(2014
).14.
G.-M.
Nam
and D. E.
Makarov
, Protein Sci.
25
, 123
(2015
).15.
P. L.
Freddolino
, C. B.
Harrison
, Y.
Liu
, and K.
Schulten
, Nat. Phys.
6
, 751
(2010
).16.
M.
Luitz
, R.
Bomblies
, K.
Ostermeir
, and M.
Zacharias
, J. Phys.: Condens. Matter
27
, 323101
(2015
).17.
Y.
Hashem
and P.
Auffinger
, Methods
47
, 187
(2009
).18.
J. R.
Perilla
et al., Curr. Opin. Struct. Biol.
31
, 64
(2015
).19.
M. G.
Saunders
and G. A.
Voth
, Annu. Rev. Biophys.
42
, 73
(2013
).20.
A. C.
Fogarty
, R.
Potestio
, and K.
Kremer
, J. Chem. Phys.
142
, 195101
(2015
).21.
J.-H.
Prinz
et al., J. Chem. Phys.
134
, 174105
(2011
).22.
C. R.
Schwantes
, R. T.
McGibbon
, and V. S.
Pande
, J. Chem. Phys.
141
, 090901
(2014
).23.
G.
Hummer
and A.
Szabo
, J. Phys. Chem. B
119
, 9029
(2015
).24.
H.
Wu
, F.
Paul
, C.
Wehmeyer
, and F.
Noé
, Proc. Natl. Acad. Sci. U. S. A.
113
, E3221
(2016
).25.
F.
Knoch
and T.
Speck
, Phys. Rev. E
95
, 012503
(2017
).26.
H.
Grubmüller
, B.
Heymann
, and P.
Tavan
, Science
271
, 997
(1996
).27.
B.
Isralewitz
, M.
Gao
, and K.
Schulten
, Curr. Opin. Struct. Biol.
11
, 224
(2001
).28.
L. Y.
Chen
, Phys. Chem. Chem. Phys.
13
, 6176
(2011
).29.
D.
de Sancho
and R. B.
Best
, J. Phys. Chem. Lett.
7
(19
), 3798
(2016
).30.
G.
Stirnemann
, S.
Kang
, R.
Zhou
, and B. J.
Berne
, Proc. Natl. Acad. Sci. U. S. A.
111
, 3413
(2014
).31.
S.
Park
and K.
Schulten
, J. Chem. Phys.
120
, 5946
(2004
).32.
E. H.
Lee
, J.
Hsin
, M.
Sotomayor
, G.
Comellas
, and K.
Schulten
, Structure
17
, 1295
(2009
).33.
M.
Habibi
, J.
Rottler
, and S. S.
Plotkin
, PLoS Comput. Biol.
12
, e1005211
(2016
).34.
F.
Rico
, L.
Gonzalez
, I.
Casuso
, M.
Puig-Vidal
, and S.
Scheuring
, Science
342
, 741
(2013
).35.
C.
Hyeon
, R. I.
Dima
, and D.
Thirumalai
, Structure
14
, 1633
(2006
).36.
R. B.
Best
and G.
Hummer
, J. Am. Chem. Soc.
130
, 3706
(2008
).37.
M. S.
Li
and M.
Kouza
, J. Chem. Phys.
130
, 145102
(2009
).38.
P.
Depa
, C.
Chen
, and J. K.
Maranas
, J. Chem. Phys.
134
, 014903
(2011
).39.
G. M.
Torrie
and J. P.
Valleau
, J. Comput. Phys.
23
, 187
(1977
).40.
B.
Roux
, Comput. Phys. Commun.
91
, 275
(1995
).41.
F.
Knoch
and T.
Speck
, “Unfolding dynamics of small peptides biased by constant mechanical forces
,” Mol. Syst. Des. Eng.
(published online).42.
M.
Janke
et al., Nat. Nanotech.
4
, 225
(2009
).43.
T.
Schlesier
, T.
Metzroth
, A.
Janshoff
, J.
Gauss
, and G.
Diezemann
, J. Phys. Chem. B
115
, 6445
(2011
).44.
T.
Schlesier
and G.
Diezemann
, J. Phys. Chem. B
117
, 1862
(2013
).45.
S.
Jaschonek
and G.
Diezemann
, J. Chem. Phys.
146
, 124901
(2017
).46.
G.
Diezemann
and A.
Janshoff
, J. Chem. Phys.
129
, 084904
(2008
).47.
R. W.
Friddle
, A.
Noy
, and J. J.
De Yoreoa
, Proc. Natl. Acad. Sci. U. S. A.
109
, 13573
(2012
).48.
G.
Diezemann
, J. Chem. Phys.
140
, 184905
(2014
).49.
G. R.
Bowman
, V. S.
Pande
, and F.
Noé
, An Introduction to Markov State Models and Their Application to Long Timescale Molecular Simulation, Volume 797
(Springer Science & Business Media
, 2013
).50.
P. I.
Zhuravlev
, M.
Hinczewski
, S.
Chakrabarti
, S.
Marqusee
, and D.
Thirumalai
, Proc. Natl. Acad. Sci. U. S. A.
113
, E715
(2016
).51.
C.
Hyeon
, M.
Hinczewski
, and D.
Thirumalai
, Phys. Rev. Lett.
112
, 138101
(2014
).52.
M. J.
Abraham
et al., SoftwareX
1–2
, 19
(2015
).53.
W. L.
Jorgensen
, D. S.
Maxwell
, and J.
Tirado-Rives
, J. Am. Chem. Soc.
118
, 11225
(1996
).54.
G.
Bussi
, D.
Donadio
, and M.
Parrinello
, J. Chem. Phys.
126
, 014101
(2007
).55.
M.
Parrinello
and A.
Rahman
, J. Appl. Phys.
52
, 7182
(1981
).56.
T.
Darden
, D.
York
, and L.
Pedersen
, J. Chem. Phys.
98
, 10089
(1993
).57.
M. P.
Allen
and D. J.
Tildesley
, Computer Simulation of Liquids
(Oxford University Press
, 1989
).58.
B.
Hess
, H.
Bekker
, H. J. C.
Berendsen
, and J. G. E. M.
Fraaije
, J. Comput. Chem.
18
, 1463
(1997
).59.
R. B.
Israel
, J. S.
Rosenthal
, and J. Z.
Wei
, Math. Finance
11
, 245
(2001
).60.
© 2018 Author(s).
2018
Author(s)
You do not currently have access to this content.
