The competition between toroidal and rod-like conformations as possible ground states for DNA condensation is studied as a function of the stiffness, the length of the DNA, and the form of the long-range interactions between neighboring molecules, using analytical theory supported by Monte Carlo simulations. Both conformations considered are characterized by a local nematic order with hexagonal packing symmetry of neighboring DNA molecules, but differ in global configuration of the chain and the distribution of its curvature as it wraps around to form a condensate. The long-range interactions driving the DNA condensation are assumed to be of the form pertaining to the attractive depletion potential as well as the attractive counterion induced soft potential. In the stiffness-length plane we find a transition between rod-like to toroid condensate for increasing stiffness at a fixed chain length L. Strikingly, the transition line is found to have a L1/3 dependence irrespective of the details of the long-range interactions between neighboring molecules. When realistic DNA parameters are used, our description reproduces rather well some of the experimental features observed in DNA condensates.

1.
H. H.
Strey
,
R.
Podgornik
,
D. C.
Rau
, and
V. A.
Parsegian
,
Curr. Opin. Struct. Biol.
8
,
309
313
(
1998
).
2.
V. A.
Bloomfield
,
Curr. Opin. Struct. Biol.
6
,
334
(
1996
);
[PubMed]
J.
Pelta
,
D.
Durand
,
J.
Doucet
, and
F.
Livolant
,
Biophys. J.
71
,
48
(
1996
);
[PubMed]
J.
Pelta
,
F.
Livolant
, and
J.-L.
Sikorav
,
J. Biol. Chem.
271
,
5656
(
1996
);
[PubMed]
K.
Yoshikawa
,
Adv. Drug Deliv. Rev.
52
,
235
(
2001
);
[PubMed]
M.
Takahashi
,
K.
Yoshikawa
,
V. V.
Vasilevskaya
, and
A. R.
Khokhlov
,
J. Phys. Chem. B
101
,
9396
(
1997
).
3.
T.
Maniatis
,
J. H.
Venable
, and
L. S.
Lerman
,
J. Mol. Biol.
84
,
37
64
(
1974
).
4.
Yu. M.
Evdokimov
,
T. L.
Pyatigorskaya
,
O. F.
Polyvtsev
,
N. M.
Akimenko
,
V. A.
Kadykov
,
D. Ya.
Tsvankin
, and
Ya. M.
Varshavsky
,
Nucl. Acids Res.
3
,
2353
(
1976
).
5.
D. C.
Rau
,
B.
Lee
, and
V. A.
Parsegian
,
Proc. Natl. Acad. Sci. U.S.A.
81
,
2621
(
1984
).
6.
R.
Podgornik
,
D. C.
Rau
, and
V. A.
Parsegian
,
Biophys. J.
66
,
962
(
1994
).
7.
H. H.
Strey
,
V. A.
Parsegian
, and
R.
Podgornik
,
Phys. Rev. E
59
,
999
(
1999
).
8.
J. X.
Tang
,
T.
Ito
,
T.
Tao
,
P.
Traub
, and
P. A.
Janmey
,
Biochemistry
36
,
12600
12607
(
1997
);
[PubMed]
J. X.
Tang
and
P. A.
Janmey
,
Biol. Bull.
194
,
406
(
1998
).
[PubMed]
9.
N. V.
Hud
and
I. D.
Vilfan
,
Annu. Rev. Biophys. Biomol. Struct.
34
,
295
(
2005
).
10.
I. D.
Vilfan
,
C. C.
Conwell
,
T.
Sarkar
, and
N. V.
Hud
,
Biochemistry
45
,
8174
(
2006
).
11.
Z.
Ou
and
M.
Muthukumar
,
J. Chem. Phys.
123
,
074905
(
2005
).
12.
A. Yu.
Grosberg
and
A. R.
Khokhlov
,
Adv. Polym. Sci.
41
,
53
(
1981
).
13.
A. Y.
Grosberg
,
Biofizika
24
,
32
(
1979
);
[PubMed]
A. Y.
Grosberg
and
A. V.
Zhestkov
,
J. Biomol. Struct. Dyn.
3
,
859
(
1986
);
[PubMed]
J.
Ubbink
and
T.
Odijk
,
Biophys. J.
68
,
54
(
1995
);
[PubMed]
T.
Odijk
,
J. Chem. Phys.
105
,
1270
(
1996
);
K.
Yoshikawa
,
M.
Takahashi
,
V. V.
Vasilevskaya
, and
A. R.
Khokhlov
,
Phys. Rev. Lett.
76
,
3029
(
1996
);
[PubMed]
Y. A.
Kuznetsov
,
E. G.
Timoshenko
, and
K. A.
Dawson
,
J. Chem. Phys.
104
,
336
(
1996
);
D. T.
Seaton
,
S.
Schnabel
,
D. P.
Landau
, and
M.
Bachmann
,
Phys. Rev. Lett.
110
,
028103
(
2013
).
[PubMed]
14.
Y.
Ishimoto
, and
N.
Kikuchi
,
J. Chem. Phys.
128
,
134906
(
2008
).
15.
N.
Rawat
and
P.
Biswas
,
J. Chem. Phys.
131
,
165104
(
2009
).
16.
M. R.
Stukan
,
E. A.
An
,
V. A.
Ivanov
, and
O. I.
Vinogradova
,
Phys. Rev. E
73
,
051804
(
2006
).
17.
V. V.
Vasilevskaya
,
A. R.
Khokhlov
,
Y.
Matsuzawa
, and
K.
Yoshikawa
,
J. Chem. Phys.
102
,
6595
(
1995
).
18.
M. R.
Stukan
,
V. A.
Ivanov
,
A. Yu.
Grosberg
,
W.
Paul
, and
K.
Binder
,
J. Chem. Phys.
118
,
3392
(
2003
).
19.
C.
Stanley
and
D. C.
Rau
,
Curr. Opin. Colloid Interfact Sci.
16
,
551
(
2011
).
20.
B.
Schnurr
,
F.
Gittes
, and
F. C.
MacKintosh
,
Phys. Rev. E
65
,
061904
(
2002
).
22.
H. N. W.
Lekkerkerker
and
R.
Tuinier
,
Colloids and the Depletion Interaction
, 1st ed. (
Springer
,
2011
).
23.
H. H.
Strey
,
R.
Podgornik
,
D. C.
Rau
, and
V. A.
Parsegian
,
Curr. Opin. Colloid Interface Sci.
8
,
309
(
1998
).
24.
A. G.
Cherstvy
,
Phys. Chem. Chem. Phys.
13
,
9942
(
2011
).
25.
V. B.
Teif
and
K.
Bohinc
,
Prog. Biophys. Mol. Biol.
105
,
208
(
2011
).
26.
A.
Naji
,
M.
Kanduč
,
R. R.
Netz
, and
R.
Podgornik
, in
Understanding Soft Condensed Matter via Modeling and Computations
, edited by
W.-B.
Hu
and
A.-C.
Shi
, (
World Scientific
,
Singapore
,
2010
), p.
265
.
27.
Electrostatics of Soft and Disordered Matter
, edited by
D. S.
Dean
,
J.
Dobnikar
,
A.
Naji
, and
R.
Podgornik
(
Pan Stanford Publishing
, 31 March 2014).
28.
A.
Naji
,
M.
Kanduč
,
J.
Forsman
, and
R.
Podgornik
,
J. Chem. Phys.
139
,
150901
(
2013
).
29.
J.
DeRouchey
,
V. A.
Parsegian
, and
D. C.
Rau
,
Biophys. J.
99
,
2608
(
2010
).
30.
D. C.
Rau
and
V. A.
Parsegian
,
Biophys. J.
61
,
246
(
1992
);
[PubMed]
D. C.
Rau
and
V. A.
Parsegian
,
Biophys. J.
61
,
260
(
1992
).
[PubMed]
31.
D. C.
Rau
and
C.
Stanley
,
Curr. Opin. Colloid Interface Sci.
16
,
551
(
2011
).
32.
H.
Yamakawa
,
Helical Wormlike Chains in Polymer Solutions
, 1 ed. (
Springer
,
1997
).
33.
P. L.
Hansen
,
R.
Podgornik
,
D.
Svensek
, and
V. A.
Parsegian
,
Phys. Rev. E
60
,
1956
(
1999
).
34.
A. Y.
Grosberg
and
A. R.
Khokhlov
,
Statistical physics of macromolecules
(
AIP
,
New York
,
1994
).
35.
H. S. M.
Coxeter
,
Introduction to Geometry
(
Wiley
,
1969
).
36.
See, e.g.,
M.
Rubinstein
and
R. H.
Colby
,
Polymer Physics
(
Oxford University Press
,
2003
).
37.
N. V.
Hud
,
K. H.
Downing
, and
R.
Balhorn
,
Proc. Natl. Acad. Sci. U.S.A.
92
,
3581
(
1995
).
38.
E. L.
Starostin
,
J. Phys.: Condens. Matter
18
,
S187
(
2006
).
39.
B. A.
Todd
,
V. A.
Parsegian
,
A.
Shirahata
,
T. J.
Thomas
, and
D. C.
Rau
,
Biophys. J.
94
,
4775
(
2008
).
40.
A. G.
Cherstvy
,
J. Phys.: Condensed Matter
17
,
1363
(
2005
).
41.
This is not true in the case of
$\rm Mn^{2+}$
Mn 2+
condensed DNA that does show a large temperature effect, see Ref. 30.
42.
J. A.
Cohen
,
R.
Podgornik
,
P. L.
Hansen
, and
V. A.
Parsegian
,
J. Phys. Chem. B
113
,
3709
(
2009
).
43.
A.
Lappala
and
E.
Terentjev
,
Macromolecules
46
,
7125
(
2013
).
44.
C. C.
Conwell
,
I. D.
Vilfan
, and
N. V.
Hud
,
Proc. Natl. Acad. Sci. U.S.A.
100
,
9296
(
2003
).
45.
C.
Poletto
,
A.
Giacometti
,
A.
Trovato
,
J. R.
Banavar
, and
A.
Maritan
,
Phys. Rev. E
77
,
061804
(
2008
).
46.
A.
Maritan
,
C.
Micheletti
,
A.
Trovato
, and
J. R.
Banavar
,
Nature (London)
406
,
287
(
2000
).
47.
J. R.
Banavar
and
A.
Maritan
,
Rev. Mod. Phys.
75
,
23
(
2003
).
You do not currently have access to this content.