Using rare event simulation techniques, we calculated DNA denaturation rate constants for a range of sequences and temperatures for the Peyrard-Bishop-Dauxois (PBD) model with two different parameter sets. We studied a larger variety of sequences compared to previous studies that only consider DNA homopolymers and DNA sequences containing an equal amount of weak AT- and strong GC-base pairs. Our results show that, contrary to previous findings, an even distribution of the strong GC-base pairs does not always result in the fastest possible denaturation. In addition, we applied an adaptation of the PBD model to study hairpin denaturation for which experimental data are available. This is the first quantitative study in which dynamical results from the mesoscopic PBD model have been compared with experiments. Our results show that present parameterized models, although giving good results regarding thermodynamic properties, overestimate denaturation rates by orders of magnitude. We believe that our dynamical approach is, therefore, an important tool for verifying DNA models and for developing next generation models that have higher predictive power than present ones.
REFERENCES
1.
International Human Genome Sequencing Consortium
, “Finishing the euchromatic sequence of the human genome
,” Nature
431
(7011
), 931
–945
(2004
).2.
B.
Alexandrov
, N. K.
Voulgarakis
, K. Ø.
Rasmussen
, A.
Usheva
, and A. R.
Bishop
, “Pre-melting dynamics of DNA and its relation to specific functions
,” J. Phys. Condens. Matter
21
(3
), 034107
(2009
).3.
Y.
Lubelsky
, J. A.
Prinz
, L.
DeNapoli
, Y.
Li
, J. A.
Belsky
, and D. M.
MacAlpine
, “DNA replication and transcription programs respond to the same chromatin cues
,” Genome Res.
24
(7
), 1102
–1114
(2014
).4.
T. S.
van Erp
, “Reaction rate calculation by parallel path swapping
,” Phys. Rev. Lett.
98
(26
), 268301
(2007
).5.
M.
Peyrard
and A. R.
Bishop
, “Statistical mechanics of a nonlinear model for DNA denaturation
,” Phys. Rev. Lett.
62
, 2755
–2758
(1989
).6.
T.
Dauxois
, M.
Peyrard
, and A. R.
Bishop
, “Entropy-driven DNA denaturation
,” Phys. Rev. E
47
, R44
–R47
(1993
).7.
A.
Campa
and A.
Giansanti
, “Experimental tests of the peyrard-bishop model applied to the melting of very short DNA chains
,” Phys. Rev. E
58
, 3585
–3588
(1998
).8.
A.
Campa
and A.
Giansanti
, “Melting of DNA oligomers: Dynamical models and comparison with experimental results
,” J. Biol. Phys.
24
(2-4
), 141
–155
(1999
).9.
N.
Theodorakopoulos
, “Melting of genomic DNA: Predictive modeling by nonlinear lattice dynamics
,” Phys. Rev. E
82
, 021905
(2010
).10.
R. B.
Inman
and R. L.
Baldwin
, “Helix-random coil transitions in DNA homopolymer pairs
,” J. Mol. Biol.
8
(4
), 452
–469
(1964
).11.
T.
Dauxois
, M.
Peyrard
, and A. R.
Bishop
, “Dynamics and thermodynamics of a nonlinear model for DNA denaturation
,” Phys. Rev. E
47
, 684
–695
(1993
).12.
T. S.
van Erp
, S.
Cuesta-López
, and M.
Peyrard
, “Bubbles and denaturation in DNA
,” Eur. Phys. J. E
20
(4
), 421
–434
(2006
).13.
D.
Poland
and H. A.
Scheraga
, “Phase transitions in 1 dimension and helix-coil transition in polyamino acids
,” J. Chem. Phys.
45
, 1456
(1966
).14.
D. J.
Proctor
, H.
Ma
, E.
Kierzek
, R.
Kierzek
, M.
Gruebele
, and P. C.
Bevilacqua
, “Folding thermodynamics and kinetics of ynmg RNA hairpins: Specific incorporation of 8-bromoguanosine leads to stabilization by enhancement of the folding rate
,” Biochemistry
43
(44
), 14004
–14014
(2004
).15.
E.
Zazopoulos
, E.
Lalli
, D. M.
Stocco
, and P.
Sassone-Corsi
, Nature (London)
390
, 311
–315
(1997
).16.
M.
Menger
, F.
Eckstein
, and D.
Porschke
, “Dynamics of the RNA hairpin GNRA tetraloop
,” Biochemistry
39
(15
), 4500
–4507
(2000
).17.
J.
Jung
and A.
Van Orden
, “Folding and unfolding kinetics of DNA hairpins in flowing solution by multiparameter fluorescence correlation spectroscopy
,” J. Phys. Chem. B
109
(8
), 3648
–3657
(2005
).18.
S. J.
Froelich-Ammon
, K. C.
Gale
, and N.
Osheroff
, J. Biol. Chem.
269
, 7719
–7725
(1994
).19.
M.
Takinoue
and A.
Suyama
, “Hairpin-DNA memory using molecular addressing
,” Small
2
(11
), 1244
–1247
(2006
).20.
D.
Liu
and S.
Balasubramanian
, “A proton-fuelled DNA nanomachine
,” Angew. Chem., Int. Ed.
42
(46
), 5734
–5736
(2003
).21.
Y.
Chen
, S.-H.
Lee
, and C.
Mao
, “A DNA nanomachine based on a duplex-triplex transition
,” Angew. Chem., Int. Ed.
43
(40
), 5335
–5338
(2004
).22.
J.
Errami
, M.
Peyrard
, and N.
Theodorakopoulos
, “Modeling DNA beacons at the mesoscopic scale
,” Eur. Phys. J. E
23
(4
), 397
–411
(2007
).23.
J.
Hanne
, G.
Zocchi
, N. K.
Voulgarakis
, A. R.
Bishop
, and K. Ø.
Rasmussen
, “Opening rates of DNA hairpins: Experiment and model
,” Phys. Rev. E
76
, 011909
(2007
).24.
H.
Eyring
, “The activated complex in chemical reactions
,” J. Chem. Phys.
3
(2
), 107
–115
(1935
).25.
E.
Wigner
, “The transition state method
,” Trans. Faraday Soc.
34
, 29
–41
(1938
).26.
J.
Keck
, “Statistical investigation of dissociation cross-sections for diatoms
,” Discuss. Faraday Soc.
33
, 173
–182
(1962
).27.
D.
Frenkel
and B.
Smit
, Understanding Molecular Simulation; From Algorithms to Applications
, 2nd ed. (Academic Press
, San Diego
, 2002
).28.
T. S.
van Erp
and P. G.
Bolhuis
, “Elaborating transition interface sampling methods
,” J. Comput. Phys.
205
, 157
–181
(2005
).29.
C.
Dellago
, P. G.
Bolhuis
, F. S.
Csajka
, and D.
Chandler
, “Transition path sampling and the calculation of rate constants
,” J. Chem. Phys.
108
(5
), 1964
(1998
).30.
T. S.
van Erp
, D.
Moroni
, and P. G.
Bolhuis
, “A novel path sampling method for the sampling of rate constants
,” J. Chem. Phys.
118
, 7762
–7774
(2003
).31.
R. J.
Allen
, P. B.
Warren
, and P. R.
ten Wolde
, “Sampling rare switching events in biochemical networks
,” Phys. Rev. Lett.
94
, 018104
(2005
).32.
T. S.
Van Erp
, Dynamical Rare Event Simulation Techniques for Equilibrium and Nonequilibrium Systems
(John Wiley and Sons, Inc
, Hoboken, NJ, USA
, 2012
), Chap. 2, pp. 27
–60
.33.
T. S.
van Erp
and M.
Peyrard
, “The dynamics of the DNA denaturation transition
,” Europhys. Lett.
98
(4
), 48004
(2012
).34.
J. B.
Anderson
, Predicting Rare Events in Molecular Dynamics
(John Wiley and Sons, Inc
, Hoboken, NJ, USA
, 2007
), pp. 381
–431
.35.
T. S.
van Erp
, “Efficiency analysis of reaction rate calculation methods using analytical models I: The two-dimensional sharp barrier
,” J. Chem. Phys.
125
(17
), 174106
(2006
).36.
T. S.
van Erp
, S.
Cuesta-López
, J.-G.
Hagmann
, and M.
Peyrard
, “Can one predict DNA transcription start sites by studying bubbles?
,” Phys. Rev. Lett.
95
, 218104
(2005
).37.
R. W.
Pastor
, B. R.
Brooks
, and A.
Szabo
, “An analysis of the accuracy of langevin and molecular-dynamics algorithms
,” Mol. Phys.
65
(6
), 1409
–1419
(1988
).38.
M. T.
Woodside
, W. M.
Behnke-Parks
, K.
Larizadeh
, K.
Travers
, D.
Herschlag
, and S. M.
Block
, “Nanomechanical measurements of the sequence-dependent folding landscapes of single nucleic acid hairpins
,” Proc. Natl. Acad. Sci. U.S.A.
103
(16
), 6190
–6195
(2006
).39.
G.
Bonnet
, O.
Krichevsky
, and A.
Libchaber
, “Kinetics of conformational fluctuations in DNA hairpin-loops
,” Proc. Natl. Acad. Sci. U.S.A.
95
(15
), 8602
–8606
(1998
).40.
A. K.
Jissy
and A.
Datta
, “Designing molecular switches based on DNA-base mispairing
,” J. Phys. Chem. B
114
(46
), 15311
–15318
(2010
).41.
M.
Barbi
, S.
Cocco
, and M.
Peyrard
, “Helicoidal model for DNA opening
,” Phys. Lett. A
253
, 358
(1999
).42.
B. S.
Alexandrov
, V.
Gelev
, Y.
Monisova
, L. B.
Alexandrov
, A. R.
Bishop
, K. Ø.
Rasmussen
, and A.
Usheva
, Nucleic Acids Res.
37
(7
), 2405
–2410
(2009
).43.
G.
Weber
, “Sharp DNA denaturation due to solvent interaction
,” Europhys. Lett.
73
(5
), 806
(2006
).44.
M.
Peyrard
, S.
Cuesta-López
, and D.
Angelov
, “Experimental and theoretical studies of sequence effects on the fluctuation and melting of short DNA molecules
,” J. Phys. Condens. Matter
21
(3
), 034103
(2009
).45.
A. E.
Bergues-Pupo
, J. M.
Bergues
, and F.
Falo
, “Modeling the interaction of DNA with alternating fields
,” Phys. Rev. E
87
, 022703
(2013
).46.
M.
Peyrard
and G.
James
, “Intrinsic localized modes in nonlinear models inspired by DNA
,” NOLTA
3
(1
), 27
–51
(2012
).47.
E.
Giudice
, P.
Várnai
, and R.
Lavery
, “Base pair opening within b-DNA: Free energy pathways for GC and AT pairs from umbrella sampling simulations
,” Nucleic Acids Res.
31
(5
), 1434
–1443
(2003
).48.
M.
Guéron
, M.
Kochoyan
, and J.-L.
Leroy
, “A single mode of DNA base-pair opening drives imino proton exchange
,” Nature
328
, 89
–92
(1987
).© 2015 AIP Publishing LLC.
2015
AIP Publishing LLC
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