The process of RNA base fraying (i.e., the transient opening of the termini of a helix) is involved in many aspects of RNA dynamics. We here use molecular dynamics simulations and Markov state models to characterize the kinetics of RNA fraying and its sequence and direction dependence. In particular, we first introduce a method for determining biomolecular dynamics employing core-set Markov state models constructed using an advanced clustering technique. The method is validated on previously reported simulations. We then use the method to analyze extensive trajectories for four different RNA model duplexes. Results obtained using D. E. Shaw research and AMBER force fields are compared and discussed in detail and show a non-trivial interplay between the stability of intermediate states and the overall fraying kinetics.

1.
K. V.
Morris
and
J. S.
Mattick
, “
The rise of regulatory RNA
,”
Nat. Rev. Genet.
15
,
423
(
2014
).
2.
H. M.
Al-Hashimi
and
N. G.
Walter
, “
RNA dynamics: It is about time
,”
Curr. Opin. Struct. Biol.
18
,
321
329
(
2008
).
3.
G. R.
Bowman
,
V. S.
Pande
, and
F.
Noé
,
An Introduction to Markov State Models and Their Application to Long Timescale Molecular Simulation
(
Springer Science & Business Media
,
2013
), Vol. 797.
4.
D. E.
Shaw
,
J. P.
Grossman
,
J. A.
Bank
,
B.
Batson
,
J. A.
Butts
,
J. C.
Chao
,
M. M.
Deneroff
,
R. O.
Dror
,
A.
Even
,
C. H.
Fenton
,
A.
Forte
,
J.
Gagliardo
,
G.
Gill
,
B.
Greskamp
,
C. R.
Ho
,
D. J.
Ierardi
,
L.
Iserovich
,
J. S.
Kuskin
,
R. H.
Larson
,
T.
Layman
,
L.-S.
Lee
,
A. K.
Lerer
,
C.
Li
,
D.
Killebrew
,
K. M.
Mackenzie
,
S. Y.-H.
Mok
,
M. A.
Moraes
,
R.
Mueller
,
L. J.
Nociolo
,
J. L.
Peticolas
,
T.
Quan
,
D.
Ramot
,
J. K.
Salmon
,
D. P.
Scarpazza
,
U.
Ben Schafer
,
N.
Siddique
,
C. W.
Snyder
,
J.
Spengler
,
P. T. P.
Tang
,
M.
Theobald
,
H.
Toma
,
B.
Towles
,
B.
Vitale
,
S. C.
Wang
, and
C.
Young
, “
Anton 2: Raising the bar for performance and programmability in a special-purpose molecular dynamics supercomputer
,” in
Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, SC’14
(
IEEE Press
,
Piscataway, NJ, USA
,
2014
), pp.
41
53
.
5.
O.
Valsson
,
P.
Tiwary
, and
M.
Parrinello
, “
Enhancing important fluctuations: Rare events and metadynamics from a conceptual viewpoint
,”
Annu. Rev. Phys. Chem.
67
,
159
184
(
2016
).
6.
V.
Mlỳnskỳ
and
G.
Bussi
, “
Exploring RNA structure and dynamics through enhanced sampling simulations
,”
Curr. Opin. Struct. Biol.
49
,
63
71
(
2018
).
7.
C.
Camilloni
and
F.
Pietrucci
, “
Advanced simulation techniques for the thermodynamic and kinetic characterization of biological systems
,”
Adv. Phys.: X
3
,
1477531
(
2018
).
8.
J. L.
Klepeis
,
K.
Lindorff-Larsen
,
R. O.
Dror
, and
D. E.
Shaw
, “
Long-timescale molecular dynamics simulations of protein structure and function
,”
Curr. Opin. Struct. Biol.
19
,
120
127
(
2009
).
9.
T. J.
Lane
,
D.
Shukla
,
K. A.
Beauchamp
, and
V. S.
Pande
, “
To milliseconds and beyond: Challenges in the simulation of protein folding
,”
Curr. Opin. Struct. Biol.
23
,
58
65
(
2013
).
10.
J.
Preto
and
C.
Clementi
, “
Fast recovery of free energy landscapes via diffusion-map-directed molecular dynamics
,”
Phys. Chem. Chem. Phys.
16
,
19181
19191
(
2014
).
11.
N.
Plattner
,
S.
Doerr
,
G.
De Fabritiis
, and
F.
Noé
, “
Complete protein–protein association kinetics in atomic detail revealed by molecular dynamics simulations and Markov modelling
,”
Nat. Chem.
9
,
1005
1011
(
2017
).
12.
S.
Vangaveti
,
S. V.
Ranganathan
, and
A. A.
Chen
, “
Advances in RNA molecular dynamics: A simulator’s guide to RNA force fields
,”
Wiley Interdiscip. Rev.: RNA
8
,
e1396
(
2017
).
13.
L. G.
Smith
,
J.
Zhao
,
D. H.
Mathews
, and
D. H.
Turner
, “
Physics-based all-atom modeling of RNA energetics and structure
,”
Wiley Interdiscip. Rev.: RNA
8
,
e1422
(
2017
).
14.
J.
Šponer
,
G.
Bussi
,
M.
Krepl
,
P.
Banáš
,
S.
Bottaro
,
R. A.
Cunha
,
A.
Gil-Ley
,
G.
Pinamonti
,
S.
Poblete
,
P.
Jurečka
,
N. G.
Walter
, and
M.
Otyepka
, “
RNA structural dynamics as captured by molecular simulations: A comprehensive overview
,”
Chem. Rev.
118
,
4177
4338
(
2018
).
15.
P. D.
Dans
,
D.
Gallego
,
A.
Balaceanu
,
L.
Darré
,
H.
Gómez
, and
M.
Orozco
, “
Modeling, simulations, and bioinformatics at the service of rna structure
,”
Chem
5
,
51
73
(
2019
).
16.
C.
Schütte
,
A.
Fischer
,
W.
Huisinga
, and
P.
Deuflhard
, “
A direct approach to conformational dynamics based on hybrid Monte Carlo
,”
J. Comput. Phys.
151
,
146
168
(
1999
).
17.
W. C.
Swope
,
J. W.
Pitera
, and
F.
Suits
, “
Describing protein folding kinetics by molecular dynamics simulations. 1. Theory
,”
J. Phys. Chem. B
108
,
6571
6581
(
2004
).
18.
F.
Noé
,
I.
Horenko
,
C.
Schütte
, and
J. C.
Smith
, “
Hierarchical analysis of conformational dynamics in biomolecules: Transition networks of metastable states
,”
J. Chem. Phys.
126
,
155102
(
2007
).
19.
J. D.
Chodera
,
N.
Singhal
,
V. S.
Pande
,
K. A.
Dill
, and
W. C.
Swope
, “
Automatic discovery of metastable states for the construction of Markov models of macromolecular conformational dynamics
,”
J. Chem. Phys.
126
,
155101
(
2007
).
20.
J.-H.
Prinz
,
H.
Wu
,
M.
Sarich
,
B.
Keller
,
M.
Senne
,
M.
Held
,
J. D.
Chodera
,
C.
Schütte
, and
F.
Noé
, “
Markov models of molecular kinetics: Generation and validation
,”
J. Chem. Phys.
134
,
174105
(
2011
).
21.
E. H.
Lee
,
J.
Hsin
,
M.
Sotomayor
,
G.
Comellas
, and
K.
Schulten
, “
Discovery through the computational microscope
,”
Structure
17
,
1295
1306
(
2009
).
22.
C.
Bergonzo
,
N. M.
Henriksen
,
D. R.
Roe
, and
T. E.
Cheatham
, “
Highly sampled tetranucleotide and tetraloop motifs enable evaluation of common RNA force fields
,”
RNA
21
,
1578
1590
(
2015
).
23.
P.
Kuhrova
,
R. B.
Best
,
S.
Bottaro
,
G.
Bussi
,
J.
Sponer
,
M.
Otyepka
, and
P.
Banáš
, “
Computer folding of RNA tetraloops: Identification of key force field deficiencies
,”
J. Chem. Theory Comput.
12
,
4534
4548
(
2016
).
24.
S.
Bottaro
,
P.
Banáš
,
J.
Sponer
, and
G.
Bussi
, “
Free energy landscape of gaga and uucg RNA tetraloops
,”
J. Phys. Chem. Lett.
7
,
4032
4038
(
2016
).
25.
M.
Betterton
and
F.
Jülicher
, “
Opening of nucleic-acid double strands by helicases: Active versus passive opening
,”
Phys. Rev. E
71
,
011904
(
2005
).
26.
J. F.
Sydow
,
F.
Brueckner
,
A. C.
Cheung
,
G. E.
Damsma
,
S.
Dengl
,
E.
Lehmann
,
D.
Vassylyev
, and
P.
Cramer
, “
Structural basis of transcription: Mismatch-specific fidelity mechanisms and paused RNA polymerase II with frayed RNA
,”
Mol. Cell
34
,
710
721
(
2009
).
27.
F.
Colizzi
and
G.
Bussi
, “
RNA unwinding from reweighted pulling simulations
,”
J. Am. Chem. Soc.
134
,
5173
5179
(
2012
).
28.
L.-T.
Da
,
F.
Pardo-Avila
,
L.
Xu
,
D.-A.
Silva
,
L.
Zhang
,
X.
Gao
,
D.
Wang
, and
X.
Huang
, “
Bridge helix bending promotes RNA polymerase II backtracking through a critical and conserved threonine residue
,”
Nat. Commun.
7
,
11244
(
2016
).
29.
W.
Huang
,
J.
Kim
,
S.
Jha
, and
F.
Aboul-Ela
, “
The impact of a ligand binding on strand migration in the sam-I riboswitch
,”
PLoS Comput. Biol.
9
,
e1003069
(
2013
).
30.
A.
Serganov
and
E.
Nudler
, “
A decade of riboswitches
,”
Cell
152
,
17
24
(
2013
).
31.
K.
Snoussi
and
J.-L.
Leroy
, “
Imino proton exchange and base-pair kinetics in RNA duplexes
,”
Biochemistry
40
,
8898
8904
(
2001
).
32.
J. D.
Liu
,
L.
Zhao
, and
T.
Xia
, “
The dynamic structural basis of differential enhancement of conformational stability by 5′-and 3′-dangling ends in RNA
,”
Biochemistry
47
,
5962
5975
(
2008
).
33.
M.
Zgarbová
,
M.
Otyepka
,
J.
Šponer
,
F.
Lankas
, and
P.
Jurečka
, “
Base pair fraying in molecular dynamics simulations of DNA and RNA
,”
J. Chem. Theory Comput.
10
,
3177
3189
(
2014
).
34.
X.
Xu
,
T.
Yu
, and
S.-J.
Chen
, “
Understanding the kinetic mechanism of RNA single base pair formation
,”
Proc. Natl. Acad. Sci. U. S. A.
113
,
116
121
(
2016
).
35.
T.
Xia
,
J.
SantaLucia
, Jr
,
M. E.
Burkard
,
R.
Kierzek
,
S. J.
Schroeder
,
X.
Jiao
,
C.
Cox
, and
D. H.
Turner
, “
Thermodynamic parameters for an expanded nearest-neighbor model for formation of RNA duplexes with Watson-Crick base pairs
,”
Biochemistry
37
,
14719
14735
(
1998
).
36.
K.-Y.
Wong
and
B. M.
Pettitt
, “
The pathway of oligomeric DNA melting investigated by molecular dynamics simulations
,”
Biophys. J.
95
,
5618
5626
(
2008
).
37.
A.
Perez
and
M.
Orozco
, “
Real-time atomistic description of DNA unfolding
,”
Angew. Chem., Int. Ed.
49
,
4805
4808
(
2010
).
38.
M. F.
Hagan
,
A. R.
Dinner
,
D.
Chandler
, and
A. K.
Chakraborty
, “
Atomistic understanding of kinetic pathways for single base-pair binding and unbinding in DNA
,”
Proc. Natl. Acad. Sci. U. S. A.
100
,
13922
13927
(
2003
).
39.
N.-V.
Buchete
and
G.
Hummer
, “
Coarse master equations for peptide folding dynamics
,”
J. Phys. Chem. B
112
,
6057
6069
(
2008
).
40.
C.
Schütte
,
F.
Noé
,
J.
Lu
,
M.
Sarich
, and
E.
Vanden-Eijnden
, “
Markov state models based on milestoning
,”
J. Chem. Phys.
134
,
204105
(
2011
).
41.
A.
Rodriguez
and
A.
Laio
, “
Clustering by fast search and find of density peaks
,”
Science
344
,
1492
1496
(
2014
).
42.
M.
d’Errico
,
E.
Facco
,
A.
Laio
, and
A.
Rodriguez
, “
Automatic topography of high-dimensional data sets by non-parametric Density Peak clustering
,” e-print arXiv:1802.10549 (
2018
).
43.
D.
Tan
,
S.
Piana
,
R. M.
Dirks
, and
D. E.
Shaw
, “
RNA force field with accuracy comparable to state-of-the-art protein force fields
,”
Proc. Natl. Acad. Sci. U. S. A.
115
,
E1346
E1355
(
2018
).
44.
P.
Banáš
,
D.
Hollas
,
M.
Zgarbová
,
P.
Jurečka
,
M.
Orozco
,
T. E.
Cheatham
 III
,
J.
Šponer
, and
M.
Otyepka
, “
Performance of molecular mechanics force fields for RNA simulations: Stability of UUCG and GNRA hairpins
,”
J. Chem. Theory Comput.
6
,
3836
3849
(
2010
).
45.
W. D.
Cornell
,
P.
Cieplak
,
C. I.
Bayly
,
I. R.
Gould
,
K. M.
Merz
,
D. M.
Ferguson
,
D. C.
Spellmeyer
,
T.
Fox
,
J. W.
Caldwell
, and
P. A.
Kollman
, “
A second generation force field for the simulation of proteins, nucleic acids, and organic molecules
,”
J. Am. Chem. Soc.
117
,
5179
5197
(
1995
).
46.
A.
Pérez
,
I.
Marchán
,
D.
Svozil
,
J.
Šponer
,
T. E.
Cheatham
 III
,
C. A.
Laughton
, and
M.
Orozco
, “
Refinement of the AMBER force field for nucleic acids: Improving the description of α γ conformers
,”
Biophys. J.
92
,
3817
3829
(
2007
).
47.
S.
Piana
,
A. G.
Donchev
,
P.
Robustelli
, and
D. E.
Shaw
, “
Water dispersion interactions strongly influence simulated structural properties of disordered protein states
,”
J. Phys. Chem. B
119
,
5113
5123
(
2015
).
48.
W. L.
Jorgensen
,
J.
Chandrasekhar
,
J. D.
Madura
,
R. W.
Impey
, and
M. L.
Klein
, “
Comparison of simple potential functions for simulating liquid water
,”
J. Chem. Phys.
79
,
926
935
(
1983
).
49.
A. D.
MacKerell
, Jr
,
D.
Bashford
,
M.
Bellott
,
R. L.
Dunbrack
, Jr
,
J. D.
Evanseck
,
M. J.
Field
,
S.
Fischer
,
J.
Gao
,
H.
Guo
,
S.
Ha
 et al., “
All-atom empirical potential for molecular modeling and dynamics studies of proteins
,”
J. Phys. Chem. B
102
,
3586
3616
(
1998
).
50.
J.
Aaqvist
, “
Ion-water interaction potentials derived from free energy perturbation simulations
,”
J. Phys. Chem.
94
,
8021
8024
(
1990
).
51.
L. X.
Dang
, “
Mechanism and thermodynamics of ion selectivity in aqueous solutions of 18-crown-6 ether: A molecular dynamics study
,”
J. Am. Chem. Soc.
117
,
6954
6960
(
1995
).
52.
I.
Beššeová
,
P.
Banáš
,
P.
Kührová
,
P.
Kosinova
,
M.
Otyepka
, and
J.
Sponer
, “
Simulations of A-RNA duplexes. the effect of sequence, solute force field, water model, and salt concentration
,”
J. Phys. Chem. B
116
,
9899
9916
(
2012
).
53.
G.
Pinamonti
,
S.
Bottaro
,
C.
Micheletti
, and
G.
Bussi
, “
Elastic network models for RNA: A comparative assessment with molecular dynamics and SHAPE experiments
,”
Nucleic Acids Res.
43
,
7260
7269
(
2015
).
54.
B.
Hess
,
H.
Bekker
,
H. J.
Berendsen
, and
J. G.
Fraaije
, “
LINCS: A linear constraint solver for molecular simulations
,”
J. Comput. Chem.
18
,
1463
1472
(
1997
).
55.
T.
Darden
,
D.
York
, and
L.
Pedersen
, “
Particle mesh Ewald: An N log(N) method for Ewald sums in large systems
,”
J. Chem. Phys.
98
,
10089
10092
(
1993
).
56.
G.
Bussi
,
D.
Donadio
, and
M.
Parrinello
, “
Canonical sampling through velocity rescaling
,”
J. Chem. Phys.
126
,
014101
(
2007
).
57.
M.
Parrinello
and
A.
Rahman
, “
Polymorphic transitions in single crystals: A new molecular dynamics method
,”
J. Appl. Phys.
52
,
7182
7190
(
1981
).
58.
D. E.
Condon
,
S. D.
Kennedy
,
B. C.
Mort
,
R.
Kierzek
,
I.
Yildirim
, and
D. H.
Turner
, “
Stacking in RNA: NMR of four tetramers benchmark molecular dynamics
,”
J. Chem. Theory Comput.
11
,
2729
2742
(
2015
).
59.
S.
Bottaro
,
F.
Di Palma
, and
G.
Bussi
, “
The role of nucleobase interactions in RNA structure and dynamics
,”
Nucleic Acids Res.
42
,
13306
(
2014
).
60.
S.
Bottaro
,
G.
Bussi
,
G.
Pinamonti
,
S.
Reisser
,
W.
Boomsma
, and
K.
Lindorff-Larsen
, “
Barnaba: Software for analysis of nucleic acid structures and trajectories
,”
RNA
25
,
219
231
(
2019
).
61.
R. T.
McGibbon
,
K. A.
Beauchamp
,
M. P.
Harrigan
,
C.
Klein
,
J. M.
Swails
,
C. X.
Hernández
,
C. R.
Schwantes
,
L.-P.
Wang
,
T. J.
Lane
, and
V. S.
Pande
, “
MDTraj: A modern open library for the analysis of molecular dynamics trajectories
,”
Biophys. J.
109
,
1528
1532
(
2015
).
62.
G.
Pinamonti
,
J.
Zhao
,
D. E.
Condon
,
F.
Paul
,
F.
Noé
,
D. H.
Turner
, and
G.
Bussi
, “
Predicting the kinetics of RNA oligonucleotides using Markov state models
,”
J. Chem. Theory Comput.
13
,
926
934
(
2017
).
63.
X.
Huang
,
G. R.
Bowman
,
S.
Bacallado
, and
V. S.
Pande
, “
Rapid equilibrium sampling initiated from nonequilibrium data
,”
Proc. Natl. Acad. Sci. U. S. A.
106
,
19765
19769
(
2009
).
64.
D.
Shukla
,
Y.
Meng
,
B.
Roux
, and
V. S.
Pande
, “
Activation pathway of src kinase reveals intermediate states as targets for drug design
,”
Nat. Commun.
5
,
3397
(
2014
).
65.
K. J.
Kohlhoff
,
D.
Shukla
,
M.
Lawrenz
,
G. R.
Bowman
,
D. E.
Konerding
,
D.
Belov
,
R. B.
Altman
, and
V. S.
Pande
, “
Cloud-based simulations on google exacycle reveal ligand modulation of GPCR activation pathways
,”
Nat. Chem.
6
,
15
(
2014
).
66.
S. K.
Sadiq
,
F.
Noé
, and
G.
De Fabritiis
, “
Kinetic characterization of the critical step in HIV-1 protease maturation
,”
Proc. Natl. Acad. Sci. U. S. A.
109
,
20449
20454
(
2012
).
67.
O.
Lemke
and
B. G.
Keller
, “
Density-based cluster algorithms for the identification of core sets
,”
J. Chem. Phys.
145
,
164104
(
2016
).
68.
G.
Pérez-Hernández
,
F.
Paul
,
T.
Giorgino
,
G.
De Fabritiis
, and
F.
Noé
, “
Identification of slow molecular order parameters for Markov model construction
,”
J. Chem. Phys.
139
,
015102
(
2013
).
69.
F.
Noé
and
C.
Clementi
, “
Kinetic distance and kinetic maps from molecular dynamics simulation
,”
J. Chem. Theory Comput.
11
,
5002
5011
(
2015
).
70.
A.
Rodriguez
,
M.
d’Errico
,
E.
Facco
, and
A.
Laio
, “
Computing the free energy without collective variables
,”
J. Chem. Theory Comput.
14
,
1206
1215
(
2018
).
71.
E.
Facco
,
M.
d’Errico
,
A.
Rodriguez
, and
A.
Laio
, “
Estimating the intrinsic dimension of datasets by a minimal neighborhood information
,”
Sci. Rep.
7
,
12140
(
2017
).
72.
G. R.
Bowman
,
K. A.
Beauchamp
,
G.
Boxer
, and
V. S.
Pande
, “
Progress and challenges in the automated construction of Markov state models for full protein systems
,”
J. Chem. Phys.
131
,
124101
(
2009
).
73.
B.
Trendelkamp-Schroer
,
H.
Wu
,
F.
Paul
, and
F.
Noé
, “
Estimation and uncertainty of reversible Markov models
,”
J. Chem. Phys.
143
,
174101
(
2015
).
74.
M. K.
Scherer
,
B.
Trendelkamp-Schroer
,
F.
Paul
,
G.
Perez-Hernandez
,
M.
Hoffmann
,
N.
Plattner
,
C.
Wehmeyer
,
J.-H.
Prinz
, and
F.
Noé
, “
PyEMMA 2: A software package for estimation, validation, and analysis of Markov models
,”
J. Chem. Theory Comput.
11
,
5525
5542
(
2015
).
75.
W.
Kabsch
, “
A solution for the best rotation to relate two sets of vectors
,”
Acta Crystallogr. Sect. A
32
,
922
923
(
1976
).
76.
S.
Bottaro
,
G.
Bussi
,
S. D.
Kennedy
,
D. H.
Turner
, and
K.
Lindorff-Larsen
, “
Conformational ensembles of RNA oligonucleotides from integrating NMR and molecular simulations
,”
Sci. Adv.
4
,
eaar8521
(
2018
).
77.
R. B.
Best
,
K.
Lindorff-Larsen
,
M. A.
DePristo
, and
M.
Vendruscolo
, “
Relation between native ensembles and experimental structures of proteins
,”
Proc. Natl. Acad. Sci. U. S. A.
103
,
10901
10906
(
2006
).
78.
S.
Bottaro
,
A.
Gil-Ley
, and
G.
Bussi
, “
RNA folding pathways in stop motion
,”
Nucleic Acids Res.
44
,
5883
5891
(
2016
).
79.
E.
Weinan
and
E.
Vanden-Eijnden
, “
Towards a theory of transition paths
,”
J. Stat. Phys.
123
,
503
(
2006
).
80.
F.
Noé
,
C.
Schütte
,
E.
Vanden-Eijnden
,
L.
Reich
, and
T. R.
Weikl
, “
Constructing the equilibrium ensemble of folding pathways from short off-equilibrium simulations
,”
Proc. Natl. Acad. Sci. U. S. A.
106
,
19011
19016
(
2009
).
81.
R. A.
Cunha
and
G.
Bussi
, “
Unravelling Mg2+-RNA binding with atomistic molecular dynamics
,”
RNA
23
,
628
638
(
2017
).
82.
A.
Spasic
,
J.
Serafini
, and
D. H.
Mathews
, “
The amber ff99 force field predicts relative free energy changes for rna helix formation
,”
J. Chem. Theory Comput.
8
,
2497
2505
(
2012
).
83.
S.
Sakuraba
,
K.
Asai
, and
T.
Kameda
, “
Predicting RNA duplex dimerization free-energy changes upon mutations using molecular dynamics simulations
,”
J. Phys. Chem. Lett.
6
,
4348
4351
(
2015
).
84.
P.
Kuhrova
,
V.
Mlynsky
,
M.
Zgarbova
,
M.
Krepl
,
G.
Bussi
,
R. B.
Best
,
M.
Otyepka
,
J.
Sponer
, and
P.
Banas
, “
Improving the performance of the amber RNA force field by tuning the hydrogen-bonding interactions
,”
J. Chem. Theory Comput.
(published online,
2019
).
85.
V.
Bloomfield
,
D.
Crothers
, and
I.
Tinoco
,
Nucleic Acids: Structures, Properties, and Functions
(
University Science Books
,
2000
).
86.
S.
Mohan
,
C.
Hsiao
,
H.
VanDeusen
,
R.
Gallagher
,
E.
Krohn
,
B.
Kalahar
,
R. M.
Wartell
, and
L. D.
Williams
, “
Mechanism of RNA double helix-propagation at atomic resolution
,”
J. Phys. Chem. B
113
,
2614
2623
(
2009
).
87.
F.
Vitalini
,
A. S.
Mey
,
F.
Noé
, and
B. G.
Keller
, “
Dynamic properties of force fields
,”
J. Chem. Phys.
142
,
084101
(
2015
).
88.
S.
Piana
,
K.
Lindorff-Larsen
, and
D. E.
Shaw
, “
How robust are protein folding simulations with respect to force field parameterization?
,”
Biophys. J.
100
,
L47
L49
(
2011
).

Supplementary Material

You do not currently have access to this content.