Markov state models (MSMs) have become the tool of choice to analyze large amounts of molecular dynamics data by approximating them as a Markov jump process between suitably predefined states. Here we investigate “Core Set MSMs,” a new type of MSMs that build on metastable core sets acting as milestones for tracing the rare event kinetics. We present a thorough analysis of Core Set MSMs based on the existing milestoning framework, Bayesian estimation methods and Transition Path Theory (TPT). We show that Core Set MSMs can be used to extract phenomenological rate constants between the metastable sets of the system and to approximate the evolution of certain key observables. The performance of Core Set MSMs in comparison to standard MSMs is analyzed and illustrated on a toy example and in the context of the torsion angle dynamics of alanine dipeptide.

1.
M.
Jäger
,
Y.
Zhang
,
J.
Bieschke
,
H.
Nguyen
,
M.
Dendle
,
M. E.
Bowman
,
J. P.
Noel
,
M.
Gruebele
, and
J. W.
Kelly
,
Proc. Natl. Acad. Sci. U.S.A.
103
,
10648
(
2006
).
2.
A. Y.
Kobitski
,
A.
Nierth
,
M.
Helm
,
A.
Jäschke
, and
G. U.
Nienhaus
,
Nucleic Acids Res.
35
,
2047
(
2007
).
3.
S.
Fischer
,
B.
Windshuegel
,
D.
Horak
,
K. C.
Holmes
, and
J. C.
Smith
,
Proc. Natl. Acad. Sci. U.S.A.
102
,
6873
(
2005
).
4.
F.
Noé
,
D.
Krachtus
,
J. C.
Smith
, and
S.
Fischer
,
J. Chem. Theo. Comp.
2
,
840
(
2006
).
5.
A.
Ostermann
,
R.
Waschipky
,
F. G.
Parak
, and
U. G.
Nienhaus
,
Nature (London)
404
,
205
(
2000
).
6.
D. D.
Schaeffer
,
A.
Fersht
, and
V.
Daggett
,
Curr. Opin. Struct. Biol.
18
,
4
(
2008
).
7.
F.
Noé
,
C.
Schütte
,
E.
Vanden-Eijnden
,
L.
Reich
, and
T. R.
Weikl
,
Proc. Natl. Acad. Sci. U.S.A.
106
,
19011
(
2009
).
8.
W.
van Gunsteren
,
J.
Dolenc
, and
A.
Mark
,
Curr. Opin. Struct. Biol.
18
,
149
(
2008
).
9.
V. A.
Voelz
,
G. R.
Bowman
,
K.
Beauchamp
, and
V. S.
Pande
,
J. Am. Chem. Soc.
132
,
1526
(
2010
).
10.
D. E.
Shaw
,
P.
Maragakis
,
K.
Lindorff-Larsen
,
S.
Piana
,
R. O.
Dror
,
M. P.
Eastwood
,
J. A.
Bank
,
J. M.
Jumper
,
J. K.
Salmon
,
Y.
Shan
, and
W.
Wriggers
,
Science
330
,
341
(
2010
).
11.
J. E.
Stone
,
J. C.
Phillips
,
P. L.
Freddolino
,
D. J.
Hardy
,
L. G.
Trabuco
, and
K.
Schulten
,
J. Comput. Chem.
28
,
2618
(
2007
).
12.
C.
Schuette
,
Conformational dynamics: modelling, theory, algorithm, and applications to biomolecules
, Habilitation thesis (
Fachbereich Mathematik und Informatik
,
FU Berlin
,
1998
).
13.
J.-H.
Prinz
,
H.
Wu
,
M.
Sarich
,
B.
Keller
,
M.
Fischbach
,
M.
Held
,
J. D.
Chodera
,
Ch.
Schütte
, and
F.
Noé
,
J. Chem. Phys.
134
,
174105
(
2011
).
14.
D. J.
Wales
,
Energy Landscapes
(
Cambridge University Press
,
Cambridge
,
2003
).
15.
F.
Noé
and
S.
Fischer
,
Curr. Opin. Struc. Biol.
18
,
154
(
2008
).
16.
M. E.
Karpen
,
D. J.
Tobias
, and
C. L.
Brooks
,
Biochemistry
32
,
412
(
1993
).
17.
I. A.
Hubner
,
E. J.
Deeds
, and
E. I.
Shakhnovich
,
Proc. Natl. Acad. Sci. U.S.A.
103
,
17747
(
2006
).
18.
M.
Weber
, ZIB Report 03-04,
2003
.
19.
N. V.
Buchete
and
G.
Hummer
,
J. Phys. Chem. B
112
,
6057
(
2008
).
20.
F.
Rao
and
A.
Caflisch
,
J. Mol. Biol.
342
,
299
(
2004
).
21.
S.
Muff
and
A.
Caflisch
,
Proteins
70
,
1185
(
2007
).
22.
B.
de Groot
,
X.
Daura
,
A.
Mark
, and
H.
Grubmüller
,
J. Mol. Biol.
301
,
299
(
2001
).
23.
V.
Schultheis
,
T.
Hirschberger
,
H.
Carstens
, and
P.
Tavan
,
J. Chem. Theory Comput.
1
,
515
(
2005
).
24.
A. C.
Pan
and
B.
Roux
,
J. Chem. Phys.
129
,
064107
(
2008
).
25.
C.
Schütte
,
A.
Fischer
,
W.
Huisinga
, and
P.
Deuflhard
,
J. Comput. Phys.
151
,
146
(
1999
).
26.
S. V.
Krivov
and
M.
Karplus
,
Proc. Nat. Acad. Sci. U.S.A.
101
,
14766
(
2004
).
27.
F.
Noé
,
I.
Horenko
,
C.
Schütte
, and
J. C.
Smith
,
J. Chem. Phys.
126
,
155102
(
2007
).
28.
J. D.
Chodera
,
K. A.
Dill
,
N.
Singhal
,
V. S.
Pande
,
W. C.
Swope
, and
J. W.
Pitera
,
J. Chem. Phys.
126
,
155101
(
2007
).
29.
W. C.
Swope
,
J. W.
Pitera
, and
F.
Suits
,
J. Phys. Chem. B
108
,
6571
(
2004
).
30.
P.
Deuflhard
,
W.
Huisinga
,
A.
Fischer
, and
C.
Schuette
,
Linear Algebra Appl.
315
,
39
(
2000
).
31.
C.
Schuette
and
W.
Huisinga
, in
Handbook of Numerical Analysis
, Vol. 10 (
Elsevier
,
Amsterdam
,
2003
), pp.
699
744
32.
P.
Deuflhard
and
M.
Weber
,
Linear Algebra Appl.
398
,
161
(
2005
) [Special issue on matrices and mathematical biology].
33.
W.
Huisinga
,
S.
Meyn
, and
C.
Schuette
,
Ann. Appl. Probab.
14
,
419
(
2004
).
34.
M.
Sarich
,
F.
Noé
, and
C.
Schütte
,
SIAM Multiscale Model. Simul.
8
,
1154
(
2010
).
35.
N.
Djurdjevac
,
M.
Sarich
, and
Ch.
Schütte
, “
Estimating the eigenvalue error of Markov State Models
,” Multiscale Model. Simul. (to be published).
36.
A. K.
Faradjian
and
R.
Elber
,
J. Chem. Phys.
120
,
10880
(
2004
).
37.
D.
Shalloway
and
A. K.
Faradijan
,
J. Chem. Phys.
124
,
054112
(
2006
).
39.
A. M. A.
West
,
R.
Elber
, and
D.
Shalloway
,
J. Chem. Phys.
126
,
145104
(
2007
).
40.
E.
Vanden-Eijnden
and
M.
Venturoli
,
J. Chem. Phys.
130
,
194101
(
2009
).
41.
W.
E
and
E.
Vanden-Eijnden
,
J. Stat. Phys.
123
,
503
(
2006
).
42.
E.
Vanden-Eijnden
, in
Computer Simulations in Condensed Matter: From Materials to Chemical Biology
, edited by
M.
Ferrario
,
G.
Ciccotti
, and
K.
Binder
(
Springer
,
Berlin
,
2006
), Vol. 1, pp.
439
478
43.
P.
Metzner
,
C.
Schütte
, and
E.
Vanden-Eijnden
,
J. Chem. Phys.
125
,
084110
(
2006
).
44.
P.
Metzner
,
C.
Schütte
, and
E.
Vanden-Eijnden
,
Multiscale Model. Simul.
7
,
1192
(
2009
).
45.
W.
E
and
E.
Vanden-Eijnden
,
Annu. Rev. Phys. Chem.
61
,
391
(
2010
).
46.
N.
Djurdjevac
,
M.
Sarich
, and
C.
Schütte
, “
On Markov state models for metastable processes
,” in
Proceeding of the ICM
2010
.
47.
D.
Chandler
,
J. Chem. Phys.
68
,
2959
(
1978
).
48.
N. G.
van Kampen
,
Stochastic Processes in Physics and Chemistry
, 4th ed. (
Elsevier
,
Amsterdam
,
2006
).
49.
E.
Vanden-Eijnden
and
F.
Tal
,
J. Chem. Phys.
123
,
184103
(
2005
).
50.
M.
Sarich
,
F.
Noé
, and
C.
Schuette
,
Multiscale Model. Simul.
8
,
1154
(
2010
).
51.
F.
Noé
,
J. Chem. Phys.
128
,
244103
(
2008
).
You do not currently have access to this content.