Order parameters (OPs) characterizing the nanoscale features of macromolecules are presented. They are generated in a general fashion so that they do not need to be redesigned with each new application. They evolve on time scales much longer than 10−14 s typical for individual atomic collisions/vibrations. The list of OPs can be automatically increased, and completeness can be determined via a correlation analysis. They serve as the basis of a multiscale analysis that starts with the N-atom Liouville equation and yields rigorous Smoluchowski/Langevin equations of stochastic OP dynamics. Such OPs and the multiscale analysis imply computational algorithms that we demonstrate in an application to ribonucleic acid structural dynamics for 50 ns.

1.
J. R.
Williamson
,
Nat. Chem. Biol.
4
,
458
(
2008
).
2.
P.
Ortoleva
,
J. Phys. Chem. B
109
,
21258
(
2005
).
3.
P.
Ortoleva
,
P.
Adhangale
,
S.
Cheluvaraja
,
M. W. A.
Fontus
, and
Z.
Shreif
,
IEEE Eng. Med. Biol. Mag.
28
,
70
(
2009
).
4.
S.
Cheluvaraja
and
P.
Ortoleva
,
J. Chem. Phys.
132
,
075102
(
2010
).
5.
S.
Cheluvaraja
,
A.
Roy
, and
P.
Ortoleva
, “
Roadmap for SimNanoworld™ an all-atom nanosystem simulator
. In preparation, 2011 (unpublished).
6.
K.
Jaqaman
and
P. J.
Ortoleva
,
J. Comput. Chem.
23
,
484
(
2002
).
7.
Y.
Miao
and
P.
Ortoleva
,
J. Comput. Chem.
30
,
423
(
2009
).
8.
Y.
Miao
and
P.
Ortoleva
,
Biopolymers
93
,
61
(
2010
).
9.
S.
Pankavich
,
Y.
Miao
,
J.
Ortoleva
,
Z.
Shreif
, and
P.
Ortoleva
,
J. Chem. Phys.
128
,
234908
(
2008
).
10.
S.
Pankavich
,
Z.
Shreif
,
Y.
Miao
, and
P.
Ortoleva
,
J. Chem. Phys.
130
,
194115
(
2009
).
11.
Z.
Shreif
,
P.
Adhangale
,
S.
Cheluvaraja
,
R.
Perera
,
R. J.
Kuhn
, and
P.
Ortoleva
,
Sci. Model. Simul.
15
,
363
(
2008
).
12.
R.
Zwanzig
,
Nonequilibrium Statistical Mechanics
(
Oxford University Press
,
New York
,
2001
).
13.
C.
Chen
and
Y.
Xiao
,
Biophys. J.
88
,
3276
(
2005
).
14.
S.
Hayward
,
A.
Kitao
, and
H. J. C.
Berendsen
,
Proteins: Struct., Funct., Bioinf.
27
,
425
(
1997
).
15.
S.
Hayward
,
A.
Kitao
, and
N.
Go
,
Proteins: Struct., Funct., Genet.
23
,
177
(
1995
).
16.
A.
Altis
,
P. H.
Nguyen
,
R.
Hegger
, and
G.
Stock
,
J. Chem. Phys.
126
,
2444111
(
2007
).
17.
L.
Riccardi
,
P. H.
Nguyen
, and
G.
Stock
,
J. Phys. Chem. B
113
,
16660
(
2009
).
18.
Z.
Shreif
and
P.
Ortoleva
,
J. Stat. Phys.
130
,
669
(
2008
).
19.
A.
Arkhipov
,
P. L.
Freddolino
, and
K.
Schulten
,
Structure
14
,
1767
(
2006
).
20.
Z.
Zhang
,
J.
Pfaendtner
,
A.
Grafmüller
, and
G. A.
Voth
,
Biophys. J.
97
,
2327
(
2009
).
21.
Z.
Zhang
,
L.
Lu
,
W. G.
Noid
,
V.
Krishna
,
J.
Pfaendtner
, and
G. A.
Voth
,
Biophys. J.
95
,
5073
(
2008
).
22.
A.
Amadei
,
A. B. M.
Linssen
, and
H. J. C.
Berendsen
,
Proteins: Struct., Funct., Bioinf.
17
,
412
(
1993
).
23.
G. G.
Maisuradze
and
D. M.
Leitner
,
Proteins: Struct., Funct., Bioinf.
67
,
569
(
2007
).
24.
K.
Hinsen
,
Proteins: Struct., Funct., Bioinf.
64
,
795
(
2006
).
25.
Y.
Miao
and
P.
Ortoleva
,
J. Chem. Phys.
125
,
44901
(
2006
).
26.
Y.
Miao
and
P. J.
Ortoleva
,
J. Chem. Phys.
125
,
214901
(
2006
).
27.
P.
Das
,
M.
Moll
,
H.
Stamati
,
L. E.
Kavraki
, and
C.
Clementi
,
Proc. Natl. Acad. Sci. U.S.A.
103
,
9885
(
2006
).
28.
H.
Gohlke
and
M. F.
Thorpe
,
Biophys. J.
91
,
2115
(
2006
).
30.
Y. G.
Kevrekidis
,
C. W.
Gear
, and
G.
Hummer
,
AIChE J.
50
,
1346
(
2004
).
31.
E.
Weinan
,
B.
Engquist
,
X.
Li
,
W.
Ren
, and
E.
Vanden-Eijnden
,
Comm. Comp. Phys.
2
,
367
(
2007
).
32.
S.
Izvekov
and
G. A.
Voth
,
J. Phys. Chem. B
109
,
2469
(
2005
).
33.
S.
Izvekov
and
G. A.
Voth
,
J. Chem. Phys.
123
,
134105
(
2005
).
35.
See Supplementary Material at http://dx.doi.org/10.1063/1.3524532 for appendices SI, SII, SIII, SIV, and Figs. S1–S17.
36.
J.
Cao
and
G. J.
Martyna
,
J. Chem. Phys.
104
,
2028
(
1996
).
37.
D.
Marx
,
M. E.
Tuckerman
, and
G. J.
Martyna
,
Comput. Phys. Commun.
118
,
166
(
1999
).
38.
R.
Car
and
M.
Parrinello
,
Phys. Rev. Lett.
55
,
2471
(
1985
).
39.
S. S.
Iyengar
,
H. B.
Schlegel
,
J. M.
Millam
,
G. A.
Voth
,
G. E.
Scuseria
, and
M. J.
Frisch
,
J. Chem. Phys.
115
,
10291
(
2001
).
40.
L.
Rosso
,
P.
Minary
,
Z.
Zhu
, and
M. E.
Tuckerman
,
J. Chem. Phys.
116
,
4389
(
2002
).
41.
S.
Pankavich
and
P.
Ortoleva
,
J. Math. Phys.
51
,
063303
(
2010
).
42.
J. M.
Deutch
and
I.
Oppenheim
,
Faraday Discuss. Chem. Soc.
83
,
1
(
1987
).
43.
L.
Maragliano
and
E.
Vanden-Eijnden
,
Chem. Phys. Lett.
426
,
168
(
2006
).
44.
J. B.
Abrams
and
M. E.
Tuckerman
,
J. Phys. Chem. B
112
,
15742
(
2008
).
45.
Y.
Miao
and
P.
Ortoleva
,
J. Phys. Chem. B
114
,
11181
(
2010
).
46.
C. R.
Sweet
,
P.
Petrone
,
V. S.
Pande
, and
J. A.
Izaguirre
,
J. Chem. Phys.
128
,
145101
(
2008
).
34.
S.
Pankavich
,
Z.
Shreif
, and
P.
Ortoleva
,
Phys. A
387
,
4053
(
2008
).
47.
P. L.
Freddolino
,
A. S.
Arkhipov
,
S. B.
Larson
,
A.
McPherson
, and
K.
Schulten
,
Structure
14
,
437
(
2006
).
48.
A.
Singharoy
,
A.
Yesnik
, and
P.
Ortoleva
,
J. Chem. Phys.
132
,
174112
(
2010
).
49.
J. M.
Ginder
and
A. J.
Epstein
,
Phys. Rev. B
41
,
10674
(
1990
).
50.
M.
Severin
and
O.
Inganas
,
Europhys. Lett.
25
,
347
(
1994
).
51.
V. A.
Ivanov
,
M. R.
Stukan
,
M.
Müller
,
W.
Paul
, and
K.
Binder
,
J. Chem. Phys.
118
,
10333
(
2003
).
53.
M. M.
Lin
,
L.
Meinhold
,
D.
Shorokhov
, and
A. H.
Zewail
,
Phys. Chem. Chem. Phys.
10
,
4227
(
2008
).
54.
E. J.
Sorin
,
M. A.
Engelhardt
,
D.
Herschlag
, and
V. S.
Pande
,
J. Mol. Biol.
317
,
493
(
2002
).
55.
Y.
Sugita
and
Y.
Okamoto
,
Chem. Phys. Lett.
314
,
141
(
1999
).
56.
A.
Villa
,
E.
Widjajakusuma
, and
G.
Stock
,
J. Phys. Chem. B
112
,
134
(
2008
).
57.
J.
Day
,
Y. G.
Kuznetsov
,
S. B.
Larson
,
A.
Greenwood
, and
A.
McPherson
,
Biophys. J.
80
,
2364
(
2001
).
58.
G. M.
Torrie
and
J. P.
Valleau
,
J. Comput. Phys.
23
,
187
(
1977
).
59.
J. G.
Kirkwood
,
J. Chem. Phys.
3
,
300
(
1935
).
60.
E. A.
Carter
,
G.
Ciccotti
,
J. T.
Hynes
, and
R.
Kapral
,
Chem. Phys. Lett.
156
,
472
(
1989
).
61.
P.
Fleurat-Lessard
and
T.
Zeigler
,
J. Chem. Phys.
123
,
084101
(
2005
).
62.
A.
Laio
and
M.
Parinello
,
Proc. Natl. Acad. Sci. U.S.A.
99
,
12562
(
2002
).
63.
M.
Ianuzzi
,
A.
Laio
, and
M.
Parinello
,
Phys. Rev. Lett.
90
,
238302
(
2003
).
64.
A.
Shehu
,
L. E.
Kavraki
, and
C.
Clementi
,
Proteins: Struct., Funct., Genet.
76
,
837
(
2009
).
65.
V. S.
Pande
and
D. S.
Rokhsar
,
Proc. Natl. Acad. Sci. U.S.A.
96
,
9062
(
1999
).
66.
A. P.
Heath
,
L. E.
Kavraki
, and
C.
Clementi
,
Proteins: Struct., Funct., Genet.
68
,
646
(
2007
).
67.
Y.
Modis
,
B. L.
Trus
, and
S. C.
Harrison
,
EMBO J.
21
,
4754
(
2002
).
29.
G. S.
Ayton
and
G. A.
Voth
,
J. Struct. Biol.
157
,
570
(
2007
).

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