We explore in detail the structural, mechanical, and thermodynamic properties of a coarse-grained model of DNA similar to that recently introduced in a study of DNA nanotweezers [T. E. Ouldridge, A. A. Louis, and J. P. K. Doye, Phys. Rev. Lett. 134, 178101 (2010)]. Effective interactions are used to represent chain connectivity, excluded volume, base stacking, and hydrogen bonding, naturally reproducing a range of DNA behavior. The model incorporates the specificity of Watson–Crick base pairing, but otherwise neglects sequence dependence of interaction strengths, resulting in an “average base” description of DNA. We quantify the relation to experiment of the thermodynamics of single-stranded stacking, duplex hybridization, and hairpin formation, as well as structural properties such as the persistence length of single strands and duplexes, and the elastic torsional and stretching moduli of double helices. We also explore the model's representation of more complex motifs involving dangling ends, bulged bases and internal loops, and the effect of stacking and fraying on the thermodynamics of the duplex formation transition.
REFERENCES
1.
W.
Saenger
, Principles of Nucleic Acid Structure
(Springer-Verlag
, New York
, 1984
).2.
J. D.
Watson
and F. H.C.
Crick
, Nature (London)
171
, 737
(1953
).3.
P. J.
Hagerman
, Annu. Rev. Biophys. Biophys. Chem.
17
, 265
(1988
).4.
N. R.
Kallenbach
, R.-I.
Ma
, and N. C.
Seeman
, Nature (London)
305
, 829
(1983
).5.
T. J.
Fu
and N. C.
Seeman
, Biochemistry
32
, 3211
(1993
).6.
H.
Yan
, S. H.
Park
, G.
Finkelstein
, J. H.
Reif
, and T. H.
LaBean
, Science
301
, 1882
(2003
).7.
E.
Winfree
, F. R.
Liu
, L. A.
Wenzler
, and N. C.
Seeman
, Nature (London)
394
, 539
(1998
).8.
J.
Malo
, J. C.
Mitchell
, C.
Venien-Bryan
, J. R.
Harris
, H.
Wille
, D. J.
Sherrat
, and A. J.
Turberfield
, Angew. Chem., Int. Ed.
44
, 3057
(2005
).9.
J.
Chen
and N. C.
Seeman
, Nature (London)
350
, 631
(1991
).10.
Y.
Zhang
and N. C.
Seeman
, J. Am. Chem. Soc.
116
, 1661
(1994
).11.
R. P.
Goodman
, I. A.T.
Sharp
, C. F.
Tardin
, C. M.
Erben
, R. M.
Berry
, C. F.
Schmidt
, and A. J.
Turberfield
, Science
310
, 1661
(2005
).12.
C. M.
Erben
, R. P.
Goodman
, and A. J.
Turberfield
, J. Am. Chem. Soc.
129
, 6992
(2007
).13.
W. M.
Shih
, J. D.
Quispe
, and G. F.
Joyce
, Nature (London)
427
, 618
(2004
).14.
F. F.
Andersen
, B.
Knudsen
, C. L.P.
Oliveira
, R. F.
Frohlich
, D.
Kruger
, J.
Bungert
, M.
Agbandje-McKenna
, R.
McKenna
, S.
Juul
, C.
Veigaard
, J.
Koch
, J. L.
Rubinstein
, B.
Guldbrandtsen
, M. S.
Hede
, G.
Karlsson
, A. H.
Andersen
, J. S.
Pedersen
, and B. R.
Knudsen
, Nucleic Acids Res.
36
, 1113
(2008
).15.
Y.
He
, T.
Ye
, M.
Su
, C.
Zhang
, A.
Ribbe
, W.
Jiang
, and C.
Mao
, Nature (London)
452
, 198
(2008
).16.
P. W.K.
Rothemund
, Nature (London)
440
, 297
(2006
).17.
E. S.
Andersen
, M.
Dong
, M. M.
Nielsen
, K.
Jahn
, R.
Subramani
, W.
Mamdouh
, M. M.
Golas
, B.
Sander
, H.
Stark
, C. L.P.
Oliveira
, J. S.
Pedersen
, V.
Birkedal
, F.
Besenbacher
, K. V.
Gothelf
, and J.
Kjems
, Nature (London)
459
, 73
(2009
).18.
S. M.
Douglas
, H.
Dietz
, T.
Liedl
, B.
Högberg
, F.
Graf
, and W. M.
Shih
, Nature (London)
459
, 414
(2009
).19.
Z.
Li
, B.
Wei
, J.
Nangreave
, C.
Lin
, Y.
Liu
, Y.
Mi
, and H.
Yan
, J. Am. Chem. Soc.
131
, 13093
(2009
).20.
F. A.
Aldaye
and H. F.
Sleiman
, J. Am. Chem. Soc.
129
, 13376
(2007
).21.
J.
Zimmermann
, M. P.
Cebulla
, S.
Monninghoff
, and G.
von Kiedrowski
, Angew. Chem., Int. Ed.
47
, 3626
(2008
).22.
J.
Bath
and A. J.
Turberfield
, Nat. Nanotechnol.
2
, 275
(2007
).23.
B.
Yurke
, A. J.
Turberfield
, A. P.
Mills
, F. C.
Simmel
, and J.
Neumann
, Nature (London)
406
, 605
(2000
).24.
W. B.
Sherman
and N. C.
Seeman
, Nano Lett.
4
, 1203
(2004
).25.
J.-S.
Shin
and N. A.
Pierce
, J. Am. Chem. Soc.
126
, 10834
(2004
).26.
J.
Bath
, S. J.
Green
, K. E.
Allan
, and A. J.
Turberfield
, Small
5
, 1513
(2009
).27.
S. J.
Green
, J.
Bath
, and A. J.
Turberfield
, Phys. Rev. Lett.
101
, 238101
(2008
).28.
C.
Zhang
, J.
Yang
, and J.
Xu
, Langmuir
26
, 1416
(2010
).29.
T.
Liedl
and F. C.
Simmel
, Nano Lett.
5
, 1894
(2005
).30.
31.
M.
Orozco
, A.
Pérez
, A.
Noy
, and F. J.
Luque
, Chem. Soc. Rev.
32
, 350
(2003
).32.
R.
Lavery
, K.
Zakrzewska
, D.
Beveridge
, T. C.
Bishop
, D. A.
Case
, T.
Cheetham
III, S.
Dixit
, B.
Jayaram
, F.
Lankas
, C.
Laughton
, J. H.
Maddocks
, A.
Michon
, R.
Osman
, M.
Orozco
, A.
Perez
, T.
Singh
, N.
Spackova
, and J.
Sponer
, Nucleic Acids Res.
38
, 299
(2010
).33.
A.
Pérez
, F. J.
Luque
, and M.
Orozco
, J. Am. Chem. Soc.
129
, 14739
(2007
).34.
C.
Mura
and A. J.
McCammon
, Nucleic Acids Res.
36
, 4941
(2008
).35.
S.
Kannan
and M.
Zacharias
, Phys. Chem. Chem. Phys.
11
, 10589
(2009
).36.
E. J.
Sorin
, Y. M.
Rhee
, B. J.
Nakatani
, and V. S.
Pande
, Biophys. J.
85
, 790
(2003
).37.
S.
Kannan
and M.
Zacharias
, Biophys. J.
93
, 3218
(2007
).38.
D.
Swigon
, Mathematics of DNA Structure, Function and Interactions
(Springer
, New York
, 2009
), Chap. XIII, pp. 293
–320
39.
S.
Khalid
, P. J.
Bond
, J.
Holyoake
, R. W.
Hawtin
, and M. S.
Sansom
, J. R. Soc., Interface
5
, 241
(2008
).40.
J.
Corsi
, R. W.
Hawtin
, O.
Ces
, G. S.
Attard
, and S.
Khalid
, Langmuir
26
, 12119
(2010
).41.
D.
Poland
and H. A.
Scheraga
, J. Chem. Phys.
45
, 1464
(1966
).42.
J.
SantaLucia
Jr., Proc. Natl. Acad. Sci. U.S.A.
17
, 1460
(1998
).43.
J.
SantaLucia
Jr. and D.
Hicks
, Annu. Rev. Biophys. Biomol. Struct.
33
, 415
(2004
).44.
R.
Everaers
, S.
Kumar
, and C.
Simm
, Phys. Rev. E
75
, 041918
(2007
).45.
T.
Dauxois
, M.
Peyrard
, and A. R.
Bishop
, Phys. Rev. E
47
, 684
(1993
).46.
N. B.
Becker
and R.
Everaers
, J. Chem. Phys.
130
, 135102
(2009
).47.
F.
Lankaš
, O.
Gonzalez
, L. M.
Heffler
, G.
Stoll
, M.
Moakher
, and J. H.
Maddocks
, Phys. Chem. Chem. Phys.
11
, 10565
(2009
).48.
M.
Paliy
, R.
Melnik
, and B. A.
Shapiro
, Phys. Biol.
7
, 036001
(2010
).49.
F.
Trovato
and V.
Tozzini
, J. Phys. Chem. B
112
, 13197
(2008
).50.
M.
Sayar
, B.
Avşaroğlu
, and A.
Kabakçıoğlu
, Phys. Rev. E
81
, 041916
(2010
).51.
P. D.
Dans
, A.
Zeida
, M. R.
Machado
, and S.
Pantano
, J. Chem. Theory Comput.
6
, 1711
(2010
).52.
K.
Voltz
, J.
Trylska
, V.
Tozzini
, V.
Kurkal-Siebert
, J.
Langowski
, and J.
Smith
, J. Comput. Chem.
29
, 1429
(2008
).53.
A.
Morriss-Andrews
, J.
Rottler
, and S. S.
Plotkin
, J. Chem. Phys.
132
, 035105
(2010
).54.
A. A.
Louis
, J. Phys.: Condens. Matter
14
, 9187
(2002
).55.
M. E.
Johnson
, T.
Head-Gordon
, and A. A.
Louis
, J. Chem. Phys.
126
, 144509
(2007
).56.
K.
Drukker
, G.
Wu
, and G. C.
Schatz
, J. Chem. Phys.
114
, 579
(2001
).57.
M.
Sales-Pardo
, R.
Guimera
, A. A.
Moreira
, J.
Widom
, and L.
Amaral
, Phys. Rev. E
71
, 051902
(2005
).58.
M.
Kenward
and K. D.
Dorfman
, J. Chem. Phys.
130
, 095101
(2009
).59.
F.
Ding
, S.
Sharma
, P.
Chalasani
, V. V.
Demidov
, N. E.
Broude
, and N. V.
Dokholyan
, RNA
14
, 1164
(2008
).60.
S.
Pasquali
and P.
Derreumaux
, J. Phys. Chem. B
114
, 11957
(2010
).61.
C.
Hyeon
and D.
Thirumalai
, Proc. Natl. Acad. Sci. U.S.A.
102
, 6789
(2005
).62.
C.
Hyeon
and D.
Thirumulai
, Biophys. J.
92
, 731
(2007
).63.
T. E.
Ouldridge
, I. G.
Johnston
, A. A.
Louis
, and J. P. K.
Doye
, J. Chem. Phys.
130
, 065101
(2009
).64.
E. J.
Sambriski
, V.
Ortiz
, and J. J.
de Pablo
, J. Phys.: Condens. Matter
21
(2009
).65.
E. J.
Sambriski
, D. C.
Schwartz
, and J. J.
de Pablo
, Biophys. J.
96
, 1675
(2009
).66.
S.
Niewieczerzał
and M.
Cieplak
, J. Phys.: Condens. Matter
21
, 474221
(2009
).67.
T. E.
Ouldridge
, A. A.
Louis
, and J. P. K.
Doye
, Phys. Rev. Lett.
104
, 178101
(2010
).68.
S.
Pitchiaya
and Y.
Krishnan
, Chem. Soc. Rev.
35
, 1111
(2006
).69.
M. C.
Murphy
, I.
Rasnik
, W.
Chang
, T. M.
Lohman
, and T.
Ha
, Biophys. J.
86
, 2530
(2004
).70.
J.
Bois
, S.
Venkataraman
, H. M.T.
Choi
, A. J.
Spakowitz
, Z.
Wang
, and N. A.
Pierce
, Nucleic Acids Res.
33
, 4090
(2005
).71.
J. B.
Mills
, E.
Vacano
, and P. J.
Hagerman
, J. Mol. Biol.
285
, 245
(1999
).72.
S. A.
Harris
, C. A.
Laughton
, and T. B.
Liverpool
, Nucleic Acids Res.
36
, 21
(2008
).73.
T.
Schlick
, Molecular Modeling and Simulation
(Springer-Verlag
, New York
, 2002
).74.
S.
Whitelam
, E. H.
Feng
, M. F.
Hagan
, and P. L.
Geissler
, Soft Matter
5
, 1521
(2009
).75.
M.
Swart
, T.
van der Wijst
, C. F.
Guerra
, and F. M.
Bickelhaupt
, J. Mol. Model.
13
, 1245
(2007
).76.
J.
Sponer
, P.
Jurečka
, I.
Marchan
, F. J.
Luque
, M.
Orozco
, and P.
Hobza
, Chem.-Eur. J.
12
, 2854
(2006
).77.
J.
Holbrook
, M.
Capp
, R.
Saecker
, and M.
Record
, Biochemistry
38
, 8409
(1999
).78.
K. M.
Guckan
, B. A.
Schweitzer
, R. X.-F.
Ren
, C. J.
Sheils
, D. C.
Tahmassebi
, and E. T.
Kool
, J. Am. Chem. Soc.
122
, 2213
(2000
).79.
G.
Torrie
and J. P.
Valleau
, J. Comput. Phys.
23
, 187
(1977
).80.
S.
Kumar
, J. M.
Rosenberg
, D.
Bouzida
, R. H.
Swendsen
, and P. A.
Kollman
, J. Comput. Chem.
13
, 1011
(1992
).81.
T. E.
Ouldridge
, A. A.
Louis
, and J. P.K.
Doye
, J. Phys.: Condens. Matter
22
, 104102
(2010
).82.
P.
Chen
and C. M.
Li
, Small
3
, 1204
(2007
).83.
C. R.
Calladine
, H. R.
Drew
, B. F.
Luisi
, and A. A.
Travers
, Understanding DNA
(Elsevier Academic
, London
, 2004
).84.
G.
Vesnaver
and K. J.
Breslauer
, Proc. Natl. Acad. Sci. U.S.A.
88
, 3569
(1991
).85.
M.
Leng
and G.
Felsenfeld
, J. Mol. Biol.
15
, 455
(1966
).86.
R. M.
Epand
and H. A.
Scheraga
, J. Am. Chem. Soc.
89
, 3888
(1967
).87.
D.
Pörschke
, Biochemistry
15
, 1495
(1976
).88.
S. M.
Freier
, K. O.
Hill
, T. G.
Dewey
, L. A.
Marky
, and K. J.
Breslauer
, Biochemistry
20
, 1419
(1981
).89.
J.
Zhou
, S.
Gregurick
, S.
Krueger
, and F.
Schwarz
, Biophys. J.
90
, 544
(2006
).90.
P. J.
Mikulecky
and A. L.
Feig
, Biopolymers
82
, 38
(2006
).91.
J.
Applequist
and V.
Damle
, J. Am. Chem. Soc.
88
, 3895
(1966
).92.
I.
Jelesarov
, C.
Crane-Robinson
, and P. L.
Privalov
, J. Mol. Biol.
294
, 981
(1999
).93.
Bases were counted as stacked if their interaction was stronger than −0.60 kcal mol−1 (relative to a typical stacked interaction of −6 kcal mol−1). Adjusting the cut-off to −1.2 kcal mol−1 had a negligible effect.
94.
D.
Poland
and H. A.
Scheraga
, Theory of Helix-Coil Transitions in Biopolymers: Statistical Mechanical Theory of Order-disorder Transitions in Biological Macromolecules
(Academic, New York
, 1970
).95.
Our simulations are performed in the canonical ensemble, and hence should be described in terms of energy and entropy changes. We assume that, as dilute DNA strands contribute a very small partial pressure, discrepancies between constant volume and constant pressure results are small: we therefore use the term “enthalpy” to describe what are in fact energies in our model, for consistency with experimental literature.
96.
Throughout this paper, lower case symbols represent enthalpy and entropy changes per pair of interacting bases, whereas capitals correspond to enthalpy and entropy changes per pair of interacting strands.
97.
Unless otherwise stated, all melting temperature calculations in this paper used four simulations of 4 × 1010 MC steps, and were performed at a reference concentration of 3.36 × 10−4 M. Simulations of duplexes with more than 12 bp necessitated using a larger periodic cell, and hence a lower concentration. The fraction of bound duplexes was scaled to the higher concentration assuming the separate species are approximately ideal, as justified in Ref. 81.
98.
R. D.
Blake
and S. G.
Delcourt
, Nucleic Acids Res.
26
, 3323
(1998
).99.
M. D.
Frank-Kamenetskii
, Biopolymers
10
, 2623
(1971
).100.
D.
Andreatta
, S.
Sen
, J. L.P.
Lustres
, S. A.
Kovalenko
, N. P.
Ernsting
, C. J.
Murphy
, R. S.
Coleman
, and M. A.
Berg
, J. Am. Chem. Soc.
128
, 6885
(2006
).101.
S.
Nonin
, J.-L.
Leroy
, and M.
Gueron
, Biochemistry
34
, 10652
(1995
).102.
D. J.
Patel
and C. W.
Hilbers
, Biochemistry
14
, 2651
(1975
).103.
A.
Tikhomirova
, N.
Taulier
, and T. V.
Chalikian
, J. Am. Chem. Soc.
126
, 16387
(2004
).104.
C. R.
Cantor
and P. R.
Schimmel
, Biophysical Chemistry Part III: The Behaviour of Biological Macromolecules
(Freeman
, San Francisco
, 1980
).105.
C. G.
Baumann
, S. B.
Smith
, V. A.
Bloomfield
, and C.
Bustamante
, Proc. Natl. Acad. Sci. U.S.A.
94
, 6185
(1997
).106.
C.
Rivetti
, C.
Walker
, and C.
Bustamante
, J. Mol. Biol.
280
, 41
(1998
).107.
M.
Rubinstein
and R. H.
Colby
, Polymer Physics
(Oxford University Press
, New York
, 2003
).108.
D. M.
Crothers
, J.
Drak
, J. D.
Kahn
, and S. D.
Levene
, Methods Enzymol.
212
, 3
(1992
).109.
M.
Vologodskaia
and A.
Vologodskii
, J. Mol. Biol.
317
, 205
(2002
).110.
B. S.
Fujimoto
, G. P.
Brewood
, and J. M.
Schurr
, Biophys. J.
91
, 4166
(2006
).111.
Z.
Bryant
, M. D.
Stone
, J.
Gore
, S. B.
Smith
, N. R.
Cozzarelli
, and C.
Bustamante
, Nature (London)
424
, 338
(2003
).112.
M. D.
Wang
, H.
Yin
, R.
Landick
, J.
Gelles
, and S. M.
Block
, Biophys. J.
72
, 1335
(1997
).113.
J. R.
Wenner
, M. C.
Williams
, I.
Rouzina
, and V. A.
Bloomfield
, Biophys. J.
82
, 3160
(2002
).114.
S. B.
Smith
, Y.
Cui
, and C.
Bustamante
, Science
271
, 795
(1996
).115.
T.
Odijk
, Macromolecules
28
, 7016
(1995
).116.
J.
Gore
, Z.
Bryant
, M.
Nöllman
, M. U.
Le
, N. R.
Cozzarelli
, and C.
Bustamante
, Nature (London)
442
, 836
(2006
).117.
T.
Lionnet
, S.
Joubaud
, R.
Lavery
, D.
Bensimon
, and V.
Croquette
, Phys. Rev. Lett.
96
, 178102
(2006
).118.
D. K.
Hendrix
, S. E.
Brenner
, and S. R.
Holbrook
, Q. Rev. Biophys.
38
, 221
(2005
).119.
S.
Kuznetsov
, Y.
Shen
, A. S.
Benight
, and A.
Ansari
, Biophys. J.
81
, 2864
(2001
).120.
J.
van Mameren
, P.
Gross
, G.
Farge
, P.
Hooijman
, M.
Modesti
, M.
Falkenberg
, G. J. L.
Wuite
, and E. J.G.
Peterman
, Proc. Natl. Acad. Sci. U.S.A.
106
, 18231
(2009
).© 2011 American Institute of Physics.
2011
American Institute of Physics
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