Transition Path Theory (TPT) provides a rigorous framework to investigate the dynamics of rare thermally activated transitions. In this theory, a central role is played by the forward committor function q+(x), which provides the ideal reaction coordinate. Furthermore, the reactive dynamics and kinetics are fully characterized in terms of two time-independent scalar and vector distributions. In this work, we develop a scheme which enables all these ingredients of TPT to be efficiently computed using the short non-equilibrium trajectories generated by means of a specific combination of enhanced path sampling techniques. In particular, first we further extend the recently introduced self-consistent path sampling algorithm in order to compute the committor q+(x). Next, we show how this result can be exploited in order to define efficient algorithms which enable us to directly sample the transition path ensemble.
REFERENCES
1.
D.
Zuckerman
, Statistical Physics of Biomolecules: An Introduction
(CRC Press
, Boca Raton, Florida, USA
, 2010
).2.
H. S.
Chung
, K.
McHale
, J. M.
Louis
, and W. A.
Eaton
, Science
335
, 981
(2012
).3.
K.
Lindorff-Larsen
, S.
Piana
, R. O.
Dror
, and D. E.
Shaw
, Science
334
, 517
(2011
).4.
T. J.
Lane
, D.
Shukla
, K. A.
Beauchamp
, and V. S.
Pande
, Curr. Opin. Struct. Biol.
23
, 58
(2013
).5.
R.
Elber
, J. Chem. Phys.
144
, 060901
(2016
).6.
G. R.
Bowman
, V. J.
Pande
, and F.
Noé
, Advances in Experimental Medicine and Biology
(Springer
, 2013
), Vol. 797.7.
J. M.
Bello-Rivas
and R.
Elber
, J. Chem. Phys.
142
, 094102
(2015
).8.
P. G.
Bolhuis
, D.
Chandler
, C.
Dellago
, and P. L.
Geissler
, Annu. Rev. Phys. Chem.
53
, 291
(2002
).9.
T. S.
Van Erp
, D.
Moroni
, and P.
Bolhuis
, J. Chem. Phys.
118
, 7762
(2003
).10.
R. J.
Allen
, C.
Valeriani
, and P. R.
ten Wolde
, J. Phys.: Condens. Matter
21
, 463102
(2009
).11.
B.
Isralewitz
, M.
Gao
, and K.
Schulten
, Curr. Opin. Struct. Biol.
11
, 224
(2001
).12.
P.
Ferrara
, J.
Apostolakis
, and A.
Caflisch
, Proteins
39
, 252
(2000
).13.
P.
Tiwary
and M.
Parrinello
, Phys. Rev. Lett.
111
, 230602
(2013
).14.
S. a.
Beccara
, L.
Fant
, and P.
Faccioli
, Phys. Rev. Lett.
114
, 098103
(2015
).15.
E.
Paci
and M.
Karplus
, J. Mol. Biol.
288
, 441
(1999
).16.
C.
Camilloni
, R. A.
Broglia
, and G.
Tiana
, J. Chem. Phys.
134
, 045105
(2011
).17.
W.
E
and E.
Vanden-Eijnden
, J. Stat. Phys.
123
, 503
(2006
).18.
W.
E
, W.
Ren
, and E.
Vanden-Eijnden
, Chem. Phys. Lett.
413
, 242
(2005
).19.
P.
Metzner
, C.
Schütte
, and E.
Vanden-Eijnden
, J. Chem. Phys.
125
, 084110
(2006
).20.
H.
Eyring
, Chem. Rev.
17
, 65
(1935
).21.
E.
Wigner
, Trans. Faraday Soc.
34
, 29
(1938
).22.
E.
Vanden-Eijnden
and M.
Venturoli
, J. Chem. Phys.
130
, 194103
(2009
).23.
W.
E
, W.
Ren
, and E.
Vanden-Eijnden
, J. Phys. Chem. B
109
, 6688
(2005
).24.
L.
Maragliano
, A.
Fischer
, E.
Vanden-Eijnden
, and G.
Ciccotti
, J. Chem. Phys.
125
, 024106
(2006
).25.
M.
Kim
, R.
Jernigan
, and G.
Chirikjian
, Biophys. J.
83
, 1620
(2002
).26.
D. R.
Weiss
and M.
Levitt
, J. Mol. Biol.
385
, 665
(2009
).27.
H.
Jonsson
, G.
Mills
, and K. W.
Jacobsen
, “Nudged elastic band method for finding minimum energy paths of transitions
,” in Classical and Quantum Dynamics in Condensed Phase Simulations
, edited by B. J.
Berne
, G.
Ciccotti
, and D. F.
Coker
(World Scientific
, Singapore
, 1998
), Chap. 16, p. 385D404
.28.
A.
Ghosh
, R.
Elber
, and H.
Scheraga
, Proc. Natl. Acad. Sci. U. S. A.
99
, 10394
(2002
).29.
R.
Elber
and D.
Shalloway
, J. Chem. Phys.
112
, 5539
(2000
).30.
P.
Eastman
, N.
Gronbech-Jensen
, and S.
Doniach
, J. Chem. Phys.
114
, 3823
(2001
).31.
P.
Faccioli
, M.
Sega
, F.
Pederiva
, and H.
Orland
, Phys. Rev. Lett.
97
, 108101
(2006
).32.
M.
Sega
, P.
Faccioli
, F.
Pederiva
, G.
Garberoglio
, and H.
Orland
, Phys. Rev. Lett.
99
, 118102
(2007
).33.
S.
Orioli
S. a.
Beccara
and P.
Faccioli
, J. Chem. Phys.
147
, 064108
(2017
).34.
J.
Lu
and J.
Nolen
, Probab. Theory Relat. Fields
161
, 195
(2015
).35.
J. L.
Doob
, Bulletin de la S. M. F.
85
, 431
–458
(1957
).36.
R.
Elber
, J. M.
Bello-Rivas
, P.
Ma
, A. E.
Cardenas
, and A.
Fathizadeh
, Entropy
19
, 219
(2017
).37.
D.
Wales
, J. Chem. Phys.
130
, 204111
(2009
).38.
C.
Dellago
and P. G.
Bolhuis
, Atomistic Approaches in Modern Biology
, Topics in Current Chemistry (Springer
, Berlin, Heidelberg
, 2006
), Vol. 268, p. 291
.39.
G. D.
Leines
and B.
Ensing
, Phys. Rev. Lett.
109
, 020601
(2012
).40.
B.
Bonomi
, D.
Branduardi
, F. L.
Gervasio
, and M.
Parrinello
, J. Am. Chem. Soc.
130
(42
), 13938
(2008
).41.
S. a.
Beccara
, T.
Skrbic
, R.
Covino
, and P.
Faccioli
, Proc. Natl. Acad. Sci. U. S. A.
109
, 2330
(2012
).42.
G.
Cazzolli
, F.
Wang
, S. a.
Beccara
, A.
Gershenson
, P.
Faccioli
, and P. L.
Wintrode
, Proc. Natl. Acad. Sci. U. S. A.
111
, 15414
(2014
).43.
D.
Branduardi
, F. L.
Gervasio
, and M.
Parrinello
, J. Chem. Phys.
126
, 054103
(2007
).44.
G.
Mazzola
, S. a.
Beccara
, P.
Faccioli
, and H.
Orland
, J. Chem. Phys.
134
, 164109
(2011
).45.
M.
Cameron
and E.
Vanden-Eijnden
, J. Stat. Phys.
156
, 427
(2014
).46.
E.
Vanden-Eijnden
, “Transition path theory
,” in An Introduction to Markov State Models and Their Application to Long Timescale Molecular Simulation
, Volume 797 of Advances in Experimental Medicine and Biology, edited by G. R.
Bowman
, V. S.
Pande
, and F.
Noé
(Springer Science and Business Media
, 2013
), Chap. 7.47.
H.
Orland
, J. Chem. Phys.
134
, 174114
(2011
).48.
M.
Delarue
, P.
Koehl
, and H.
Orland
, J. Chem. Phys.
147
, 152703
(2017
).49.
W.
E
and E.
Vanden-Eijnden
, Annu. Rev. Phys. Chem.
61
, 391
(2010
).50.
E.
Vanden-Eijnden
, Lect. Notes Phys.
703
, 439
(2006
).51.
F.
Wang
, S.
Orioli
, A.
Ianeselli
, G.
Spagnolli
, S. a.
Beccara
, A.
Gershenson
, P.
Faccioli
, and P. L.
Wintrode
, Biophys. J.
114
, 2083
(2018
).© 2018 Author(s).
2018
Author(s)
You do not currently have access to this content.
