We study the parameter sensitivity of hetero-polymeric DNA within the purview of DNA breathing dynamics. The degree of correlation between the mean bubble size and the model parameters is estimated for this purpose for three different DNA sequences. The analysis leads us to a better understanding of the sequence dependent nature of the breathing dynamics of hetero-polymeric DNA. Out of the 14 model parameters for DNA stability in the statistical Poland-Scheraga approach, the hydrogen bond interaction

$\epsilon _{hb}(\mathtt {AT})$
εhb(AT) for an
$\mathtt {AT}$
AT base pair and the ring factor ξ turn out to be the most sensitive parameters. In addition, the stacking interaction
$\epsilon _{st}(\mathtt {TA}\text{-}\mathtt {TA})$
εst(TA-TA) for an
$\mathtt {TA}\text{-}\mathtt {TA}$
TA-TA nearest neighbor pair of base-pairs is found to be the most sensitive one among all stacking interactions. Moreover, we also establish that the nature of stacking interaction has a deciding effect on the DNA breathing dynamics, not the number of times a particular stacking interaction appears in a sequence. We show that the sensitivity analysis can be used as an effective measure to guide a stochastic optimization technique to find the kinetic rate constants related to the dynamics as opposed to the case where the rate constants are measured using the conventional unbiased way of optimization.

Topics
Entropy, Free energy, Optimization problems, Chemical elements, Reaction rate constants, Chemical bonding, Fluid bubbles, Biological systems and models, Covariance and correlation, Stochastic processes
1.
J. D.
Watson
 and
F. H. C.
Crick
 ,
Nature (London)
 
171
,
737
(
1953
);
https://doi.org/10.1038/171737a0
Crossref
Search ADS
Google Scholar
 
R. E.
Franklin
 and
R. G.
Gosling
 ,
Nature (London)
 
171
,
740
(
1953
);
https://doi.org/10.1038/171740a0
Crossref
Search ADS
Google Scholar
 
F.
 
Crick
,
Nature (London)
 
227
,
561
(
1970
).
https://doi.org/10.1038/227561a0
Crossref
Search ADS
Google Scholar
 
2.
M. D.
 
Frank-Kamenetskii
,
Phys. Rep.
 
288
,
13
(
1997
) .
https://doi.org/10.1016/S0370-1573(97)00020-3
Google Scholar
Crossref
Search ADS
 
3.
R. M.
 
Wartell
 and
A. S.
 
Benight
,
Phys. Rep.
 
126
,
67
(
1985
).
https://doi.org/10.1016/0370-1573(85)90060-2
Google Scholar
Crossref
Search ADS
 
4.
A. Y.
 
Grosberg
 and
A. R.
 
Khokhlov
,
Statistical Physics of Macromolecules
(
AIP
,
New York
,
1994
).
Google Scholar
 
5.
D.
 
Poland
 and
H. A.
 
Scheraga
,
J. Chem. Phys.
 
45
,
1464
(
1966
).
https://doi.org/10.1063/1.1727786
Google Scholar
Crossref
Search ADS
PubMed
 
6.
D.
 
Poland
 and
H. A.
 
Scheraga
,
Theory of Helix-Coil Transitions in Biopolymers
(
Academic
,
New York
,
1970
).
Google Scholar
 
7.
W. R.
 
Bauer
 and
C. J.
 
Benham
,
J. Mol. Biol.
 
234
,
1184
(
1993
).
https://doi.org/10.1006/jmbi.1993.1669
Google Scholar
Crossref
Search ADS
PubMed
 
8.
J.-H.
Jeon
 ,
J.
Adamcik
 ,
G.
Dietler
 , and
R.
Metzler
 ,
Phys. Rev. Lett.
 
105
,
208101
(
2010
);
https://doi.org/10.1103/PhysRevLett.105.208101
Crossref
Search ADS
[PubMed]
Google Scholar
 
J.
 
Adamcik
,
J.-H.
 
Jeon
,
K. J.
 
Karczewski
,
R.
 
Metzler
, and
G.
 
Dietler
,
Soft Matter
 
8
,
8651
(
2012
).
https://doi.org/10.1039/c2sm26089a
Crossref
Search ADS
Google Scholar
 
9.
T. J.
Pollock
 and
H. A.
Nash
 ,
J. Mol. Biol.
 
170
,
1
(
1983
);
https://doi.org/10.1016/S0022-2836(83)80224-1
Crossref
Search ADS
[PubMed]
Google Scholar
 
P.
 
Staczek
 and
N. P.
 
Higgins
,
Mol. Microbiol.
 
29
,
1435
(
1998
).
https://doi.org/10.1046/j.1365-2958.1998.01025.x
Crossref
Search ADS
[PubMed]
Google Scholar
 
10.
K.
 
Pant
,
R. L.
 
Karpel
, and
M. C.
 
Williams
,
J. Mol. Biol.
 
327
,
571
(
2003
).
https://doi.org/10.1016/S0022-2836(03)00153-0
Google Scholar
Crossref
Search ADS
PubMed
 
11.
T.
Ambjörnsson
 and
R.
Metzler
 ,
Phys. Rev. E
 
72
,
030901
–
R
(
2005
);
https://doi.org/10.1103/PhysRevE.72.030901
Crossref
Search ADS
Google Scholar
 
T.
 
Ambjörnsson
, and
R.
 
Metzler
,
J. Phys. Condens. Matter
 
17
,
S1841
(
2005
).
https://doi.org/10.1088/0953-8984/17/20/013
Crossref
Search ADS
Google Scholar
 
12.
I. M.
Sokolov
 ,
R.
Metzler
 ,
K.
Pant
 , and
M. C.
Williams
 ,
Biophys. J.
 
89
,
895
(
2005
);
https://doi.org/10.1529/biophysj.104.057612
Crossref
Search ADS
[PubMed]
Google Scholar
 
I. M.
 
Sokolov
,
R.
 
Metzler
,
K.
 
Pant
, and
M. C.
 
Williams
,
Phys. Rev. E
 
72
,
041102
(
2005
).
https://doi.org/10.1103/PhysRevE.72.041102
Crossref
Search ADS
Google Scholar
 
14.
C. H.
 
Choi
,
G.
 
Kalosakas
,
K. O.
 
Rasmussen
,
M.
 
Hiromura
,
A. R.
 
Bishop
, and
A.
 
Usheva
,
Nucleic Acids Res.
 
32
,
1584
(
2004
).
https://doi.org/10.1093/nar/gkh335
Google Scholar
Crossref
Search ADS
PubMed
 
15.
K.
 
Nowak-Lovato
,
L. B.
 
Alexandrov
,
A.
 
Banisadr
,
A. L.
 
Bauer
,
A. R.
 
Bishop
,
A.
 
Usheva
,
F.
 
Mu
,
E.
 
Hong-Geller
,
K. Ø.
 
Rasmussen
,
W. S.
 
Hlavacek
, and
B. S.
 
Alexandrov
,
PLoS Comput. Biol.
 
9
,
e1002881
(
2013
).
https://doi.org/10.1371/journal.pcbi.1002881
Google Scholar
Crossref
Search ADS
PubMed
 
16.
M.
 
Zoli
,
J. Chem. Phys.
 
138
,
205103
(
2013
).
https://doi.org/10.1063/1.4807381
Google Scholar
Crossref
Search ADS
PubMed
 
17.
C.
 
Phelps
,
W.
 
Lee
,
D.
 
Jose
,
P. H.
 
von Hippel
, and
A. H.
 
Marcus
,
Proc. Natl. Acad. Sci. U.S.A.
 
110
,
17320
(
2013
).
https://doi.org/10.1073/pnas.1314862110
Google Scholar
Crossref
Search ADS
PubMed
 
18.
C. R.
 
Cantor
 and
P. R.
 
Schimmel
,
Biophysical Chemistry
(
W H Freeman
,
New York
,
1980
).
Google Scholar
 
19.
M. M.
 
Senior
,
R. A.
 
Jones
, and
K. J.
 
Breslauer
,
Proc. Natl. Acad. Sci. U.S.A.
 
85
,
6242
(
1988
).
https://doi.org/10.1073/pnas.85.17.6242
Google Scholar
Crossref
Search ADS
PubMed
 
20.
C. A.
 
Gelfand
,
G. E.
 
Plum
,
S.
 
Mielewczyk
,
D. P.
 
Remeta
, and
K. J.
 
Breslauer
,
Proc. Natl. Acad. Sci. U.S.A.
 
96
,
6113
(
1999
).
https://doi.org/10.1073/pnas.96.11.6113
Google Scholar
Crossref
Search ADS
PubMed
 
21.
G.
 
Altan-Bonnet
,
A.
 
Libchaber
, and
O.
 
Krichevsky
,
Phys. Rev. Lett.
 
90
,
138101
(
2003
).
https://doi.org/10.1103/PhysRevLett.90.138101
Google Scholar
Crossref
Search ADS
PubMed
 
22.
K. R.
 
Chaurasiyaa
,
T.
 
Paramanathana
,
M. J.
 
McCauleya
, and
M. C.
 
Williams
,
Phys. Life Rev.
 
7
,
299
(
2010
).
https://doi.org/10.1016/j.plrev.2010.06.001
Google Scholar
Crossref
Search ADS
PubMed
 
23.
A.
 
Hanke
 and
R.
 
Metzler
,
J. Phys. A
 
36
,
L473
(
2003
).
https://doi.org/10.1088/0305-4470/36/36/101
Google Scholar
Crossref
Search ADS
 
24.
D.
 
Bicout
 and
E.
 
Kats
,
Phys. Rev. E
 
70
,
010902
–
R
(
2004
).
https://doi.org/10.1103/PhysRevE.70.010902
Google Scholar
Crossref
Search ADS
 
25.
A.
 
Bar
,
Y.
 
Kafri
, and
D.
 
Mukamel
,
Phys. Rev. Lett.
 
98
,
038103
(
2007
).
https://doi.org/10.1103/PhysRevLett.98.038103
Google Scholar
Crossref
Search ADS
PubMed
 
26.
T.
Novotný
 ,
J. N.
Pedersen
 ,
T.
Ambjörnsson
 ,
M. S.
Hansen
 , and
R.
Metzler
 ,
Europhys. Lett.
 
77
,
48001
(
2007
);
https://doi.org/10.1209/0295-5075/77/48001
Crossref
Search ADS
Google Scholar
 
J. N.
 
Pedersen
,
M. S.
 
Hansen
,
T.
 
Novotný
,
T.
 
Ambjörnsson
, and
R.
 
Metzler
,
J. Chem. Phys.
 
130
,
164117
(
2009
).
https://doi.org/10.1063/1.3117922
Crossref
Search ADS
[PubMed]
Google Scholar
 
27.
H. C.
Fogedby
 and
R.
Metzler
 ,
Phys. Rev. Lett.
 
98
,
070601
(
2007
);
https://doi.org/10.1103/PhysRevLett.98.070601
Crossref
Search ADS
[PubMed]
Google Scholar
 
H. C.
 
Fogedby
, and
R.
 
Metzler
,
Phys. Rev. E
 
76
,
061915
(
2007
).
https://doi.org/10.1103/PhysRevE.76.061915
Crossref
Search ADS
Google Scholar
 
28.
T.
 
Ambjörnsson
,
S. K.
 
Banik
,
O.
 
Krichevsky
, and
R.
 
Metzler
,
Phys. Rev. Lett.
 
97
,
128105
(
2006
).
https://doi.org/10.1103/PhysRevLett.97.128105
Google Scholar
Crossref
Search ADS
PubMed
 
29.
T.
Ambjörnsson
 ,
S. K.
Banik
 ,
O.
Krichevsky
 , and
R.
Metzler
 ,
Biophys. J.
 
92
,
2674
(
2007
);
https://doi.org/10.1529/biophysj.106.095935
Crossref
Search ADS
[PubMed]
Google Scholar
 
T.
 
Ambjörnsson
,
S. K.
 
Banik
,
M. A.
 
Lomholt
, and
R.
 
Metzler
,
Phys. Rev. E
 
75
,
021908
(
2007
).
https://doi.org/10.1103/PhysRevE.75.021908
Crossref
Search ADS
Google Scholar
 
30.
D. T.
 
Gillespie
,
J. Comput. Phys.
 
22
,
403
(
1976
).
https://doi.org/10.1016/0021-9991(76)90041-3
Google Scholar
Crossref
Search ADS
 
31.
D. T.
 
Gillespie
,
J. Phys. Chem.
 
81
,
2340
(
1977
).
https://doi.org/10.1021/j100540a008
Google Scholar
Crossref
Search ADS
 
32.
J. M.
 
Huguet
,
C. V.
 
Bizarro
,
N.
 
Forns
,
S. B.
 
Smith
,
C.
 
Bustamante
, and
F.
 
Ritort
,
Proc. Natl. Acad. Sci. U.S.A.
 
107
,
15431
(
2010
).
https://doi.org/10.1073/pnas.1001454107
Google Scholar
Crossref
Search ADS
PubMed
 
33.
S.
 
Talukder
,
P.
 
Chaudhury
,
R.
 
Metzler
, and
S. K.
 
Banik
,
J. Chem. Phys.
 
135
,
165103
(
2011
).
https://doi.org/10.1063/1.3654958
Google Scholar
Crossref
Search ADS
PubMed
 
34.
A.
 
Saltelli
,
M.
 
Ratto
,
S.
 
Tarantola
, and
F.
 
Campolongo
,
Chem. Rev.
 
105
,
2811
(
2005
).
https://doi.org/10.1021/cr040659d
Google Scholar
Crossref
Search ADS
PubMed
 
35.
S.
 
Marino
,
I. B.
 
Christian
,
J.
 
Ray
, and
D. E.
 
Krishner
,
J. Theor. Biol.
 
254
,
178
(
2008
).
https://doi.org/10.1016/j.jtbi.2008.04.011
Google Scholar
Crossref
Search ADS
PubMed
 
36.
A.
 
Saltelli
,
Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models
(
Wiley
,
Hoboken, NJ
,
2004
).
Google Scholar
 
37.
R. I.
 
Cukier
,
C. M.
 
Fortuin
,
K. E.
 
Schuler
,
A. G.
 
Petschek
, and
J. H.
 
Schailby
,
J. Chem. Phys.
 
59
,
3873
(
1973
).
https://doi.org/10.1063/1.1680571
Google Scholar
Crossref
Search ADS
 
38.
R. I.
 
Cukier
,
J. H.
 
Schaibly
, and
K. E.
 
Schuler
,
J. Chem. Phys.
 
63
,
1140
(
1975
).
https://doi.org/10.1063/1.431440
Google Scholar
Crossref
Search ADS
 
39.
J. H.
 
Schaibly
 and
K. E.
 
Schuler
,
J. Chem. Phys.
 
59
,
3879
(
1973
).
https://doi.org/10.1063/1.1680572
Google Scholar
Crossref
Search ADS
 
40.
D. J.
 
Pannell
,
Agric. Econ.
 
16
,
139
(
1997
).
https://doi.org/10.1016/S0169-5150(96)01217-0
Google Scholar
Crossref
Search ADS
 
41.
G. M.
 
Hornberger
 and
R. C.
 
Spear
,
J. Environ. Manage.
 
12
,
7
(
1981
).
Google Scholar
 
43.
Y.
 
Tohsato
,
K.
 
Ikuta
,
A.
 
Shionoya
,
Y.
 
Mazaki
, and
M.
 
Ito
,
Gene
 
518
,
84
(
2013
).
https://doi.org/10.1016/j.gene.2012.11.080
Google Scholar
Crossref
Search ADS
PubMed
 
44.
S.
 
Talukder
,
S.
 
Sen
,
R.
 
Metzler
,
S. K.
 
Banik
, and
P.
 
Chaudhury
,
J. Chem. Sci.
 
125
,
1619
(
2013
).
https://doi.org/10.1007/s12039-013-0502-y
Google Scholar
Crossref
Search ADS
 
45.
M. C.
 
Whitlock
 and
D.
 
Schluter
,
The Analysis of Biological Data
(
Roberts and Company Publishers
,
2009
)
Google Scholar
 
46.
S. C.
 
Hora
 and
J. C.
 
Helton
,
Reliab. Eng. Syst. Saf.
 
79
,
333
(
2003
).
https://doi.org/10.1016/S0951-8320(02)00240-5
Google Scholar
Crossref
Search ADS
 
47.
A.
 
Krueger
,
E.
 
Protozanova
, and
M. D.
 
Frank-Kamenetskii
,
Biophys. J.
 
90
,
3091
(
2006
).
https://doi.org/10.1529/biophysj.105.078774
Google Scholar
Crossref
Search ADS
PubMed
 
48.
C.
 
Richard
 and
A. J.
 
Guttermann
,
J. Stat. Phys.
 
115
,
925
(
2004
).
https://doi.org/10.1023/B:JOSS.0000022370.48118.8b
Google Scholar
Crossref
Search ADS
 
49.
V.
 
Kaiser
 and
T.
 
Novotný
, “
Loop exponent in DNA bubble dynamics
,” e-print arXiv:cond-mat/1402.1622.
50.
Y.
 
Zeng
,
A.
 
Montrichok
, and
G.
 
Zocchi
,
J. Mol. Biol.
 
339
,
67
(
2004
).
https://doi.org/10.1016/j.jmb.2004.02.072
Google Scholar
Crossref
Search ADS
PubMed
 
51.
D. E.
 
Goldberg
,
Genetic Algorithm in Search, Optimization and Machine Learning
(
Addison Wesley
,
Reading, MA
,
1989
).
Google Scholar
 
52.
H.
 
Cramér
,
Mathematical Methods of Statistics
(
Princeton University Press
,
1946
).
Google Scholar
 
© 2014 AIP Publishing LLC.
2014
AIP Publishing LLC
You do not currently have access to this content.