€½ο„ ο€­

. (7)
The values of

5
s
sL
X
n

and

3
s
sL
X
n

evaluated
in this manner are plotted versus dangling end length in
Figure 1 for X = G (similar plots for X = H and S are
shown in Supplementary Figure 2). This plot was gen-
erated using the thermodynamic data measured for sets I,
II and III in 85 mM, 300 mM and 1.0 M [Na+] shown in
Table 3. Solid symbols represent computed values for

5
s
sL
X
n


3
and open symbols represent values for
s
sL
X
n

.
3.4. 5’ Dangling Ends
When comparing the data of Figure 1, several trends
are clearly seen. The 5’ ends are stabilizing and show a
very weak dependence on [Na+]. The values of

5
s
sL
H
n

and

5
s
sL
Sn

display similar trends as a
function of nL.
The behavior of


5
s
sL
Gn

as a function of nL (Fig-
ure 1) indicates that, despite variations in


5
s
sL
H
n

and


5
s
s
Sn

L
for different molecules, the parameters
are apparently compensatory in such a way as to render


5
s
sL
Gn

essentially linear. That is, values of


5
s
sL
vary only slightly with increasing length of
the dangling end, and the dependence on [Na+] appears
to be minimal. Thermodynamic contributions from the 5’
dangling ends were determined by taking the average of
Gn



5
s
sL
over various values of nL (in each Na+ en-
vironment). These values are summarized in Table 4.
Gn

3.5. 3’ Dangling Ends
In contrast to 5’ ends in Figure 1, the 3’ ends
(


3
s
sL
X
n

-open symbols), appear to be primarily desta-
bilizing, and more strongly affected by [Na+]. Interest-
ingly, they become less destabilizing with higher [Na+].
The free energy imparted by the 3’ end increases to
greater positive values with increasing end length up to
nL = 4 and remains essentially constant thereafter. The
salt dependent stability is also more pronounced and
therefore presumably much stronger than for the set I
molecules. Apparently, lower sodium ion concentrations
(e.g. 85 mM) have an immediate destabilizing influence
on duplex stability that manifests in the corresponding
effect is observed until nL = 4 at which point


3
s
sL
Gn

becomes significantly destabilizing. In the 1.0 M salt
Figure 1. Dangling end parameters calculated for Ξ΄G5 (solid markers) and Ξ΄G3 (open faced
markers) as a function of overhang length (nL). Comparison of the evaluated Ξ΄G thermodynamic
parameters are shown for the 5’ and 3’ dangling ends in sets II and III in all three Na+ environ-
ments. This plot shows the relative free-energy contribution (Ξ΄G) for dangling ends plotted ver-
sus overhang length (nL). Solid curves are drawn through the data to guide the eye. Set II mole-
cules are averaged over all salts. Set III data are shown along with fits of logistical curve Eq.8.
Equation parameters used to fit the data are: (85 mM) A = 4, r = 2, c = –0.2, k = 1, (300 mM) A =
3, r = 2.5, c = –0.3, k = 2, (1.0 M) A = 3.6, r = 5, c = –1, k = 3.5. The value of Ξ΄G3’(nL = 1) for 1.0
M was adjusted within error parameters to improve the fit.
Copyright © 2012 SciRes. OPEN A CCESS
R. Dickman et al. / Journal of Biophysical Chemistry 3 (2012) 1-15 7
Table 4. Thermodynamic contributions of 3’ and 5’ ends.
Length dependent contributions calculated for dangling ends.
Negative values are stabilizing and positive values are destabi-
lizing for the duplex.

L
Gn

nL 85 mM 300 mM 1.0 M
1 –3 –1.7 –0.3
2 - 4 –2.6 –2.6 –2.6
5 –2.6 –1.5 –1.5
5’ ends
>5 –1.5 –1.5 –1.5
1 1.8 –0.1 –1.0
2 3.3 1.2 –1.0
3 3.7 2.5 –0.7
4 3.8 2.7 2.3
6 3.8 2.7 2.6
3’ ends
8 3.8 2.7 2.6
environment,

3
s
sL
Gn

is initially stabilizing before it
becomes increasingly destabilizing at nL = 4. Clearly the
values display a more complicated dependence on nL and
[Na+] than their 5’ analogues.
Behavior of the 3’ data was modeled with a general-
ized sigmoidal growth function given by the parameter-
ized logistic equation


1exp
A
yC
rx k




. (8)
Best fits to the 3’ data are shown in Figure 1. Parame-
ter values determined for c, k, r and A in each Na+ envi-
ronment are listed in the Figure 1 caption. These expres-
sions were used to predict thermodynamic contributions
of 3’ dangling ends to the stability of duplex DNA. Spe-
cific values computed are summarized in Table 4.
3.6. Case Study: ,
D
n=21L
n=4
The values given in Table 4 for


5
sL
X
n

and

3
sL
X
n

offer potential for improving thermodynamic
predictions for short duplex DNAs containing single
strand dangling ends. However, the utility of these values
ultimately relies on the validity of assumptions under
which the parameters were evaluated. As stated, evalua-
tions of

5
sL
X
n

and


3
sL
X
n


3
Xn

are founded on the
n-n model in which individual contributions of the ends
are considered separately from those of the duplex region.
To test validity of this assumption further, an additional
set of DNA molecules were prepared and examined. Set
IV molecules provide a secondary method for evaluating
thermodynamic contributions of dangling ends where nL
= 4, i.e. and ssL. Molecules
of set IV are in a sense β€œhalf-molecules” of those in sets
II and III containing a duplex region of 21 base pairs and
a single dangling end. Sequences IVa and IVb have a
single 5’ dangling end of nL = 4, while IVc and IVd
contain one 3’ dangling end of nL = 4. Duplex and single
strand end sequences are the same as those of sets II and
III where n
D = 21 and nL = 4. Altering Eq.4 and Eq.5
specifically for set IV molecules with one 5’ dangling-
end and one blunt end leads to the following equation for
sequences IVa and IVb,

5
ss L
Xnο€½4


4ο€½



IV I
5
21, 421
4,
ab
calDLcal D
ss L
Xn nXn
Xn




(9a)
and the equation



IV I
3
21, 421
4.
cd
calDLcal D
ss L
Xn nXn
Xn





(9b)
for sequences IVc and IVd in which molecules have one
3’ dangling end and one blunt end. is
the measured thermodynamic parameter for the blunt-
ended duplex with 21 base pairs.

I21
cal D
Xn
Due to the similarities and differences between the sets,
a number of relationships can be found to obtain ther-
modynamic parameters of the dangling ends. Using Eq.9a
and Eq.9b and pertinent results for sets I, II and III
molecules along with those from set IV summarized in
Table 5, estimates on and

54
ss L
Xn

ο€½


34
ss L
Xn

ο€½
were calculated. Consider the following
for


4
5
ss L
Xn

ο€½
:




421,4
a5II IV
s
sLcalDLcal
X
nXnn

 X (10a)
or




5II
421,4
bIV
s
sLcalDLcal
X
nXnn

 X (10b)
or




5 IIIIV
421,4
c
s
sLcalDLcal
X
nXnn

 X. (10c)
Table 5. Thermodynamic data for set IV molecules.
[Na+]Seq. Ξ”H Οƒ Ξ”S Οƒ Ξ”G Οƒ
IVa –153.411.9–436.1 18.7 –23.40.5
IVb–136.3 3.2 –389.0 13.0 –20.30.9
IVc–154.5 4.7 –440.2 19.4 –23.30.7
85 mM
IVd–137.7 15.2–392.1 13.6 –20.83.1
IVa –160.59.2 –456.3 6.0 –24.50.2
IVb–140.2 7.9 –396.4 10.0 –22.00.7
IVc–161.5 5.3 –460.4 8.9 –24.20.2
300 mM
IVd–143.1 13.0–407.9 18.3 –21.51.2
IVa –164.83.9 –468.5 10.1 –25.10.4
IVb–151.4 11.3 –430.2 13.9 –23.11.8
IVc–165.4 1.2 –471.1 7.3 –24.91.2
1.0 M
IVd–154.5 7.2 –440.1 14.2 –23.32.9
Copyright © 2012 SciRes. OPEN A CCESS
R. Dickman et al. / Journal of Biophysical Chemistry 3 (2012) 1-15
8
In a similar manner, consider the following for
,

34
ss L
Xn

ο€½
 
5III
421,4
cIV
s
sLcalDLcal
X
nXnn

 X


. (11)
A total of five equations were generated to determine
and three equations to determine
. Specific values in each salt environment
are displayed in Figure 2. The asterisk on each plot de-
notes values taken from Figure 1 where nL = 4.

54
ss L
Xn

ο€½

34
ss L
Xn

ο€½
5
s
s
X

3
(lighter bars) is shown on the left of each plot and
s
s
X

(darker bars) is shown on the right. Examination of the
histograms in Figure 2 reveals several interesting obser-
vations.
To a first approximation, trends in Figure 2 are con-
sistent with those in Figure 1. Averages of the results
from the different calculation schemes provide values in
agreement with

3
sL
X
n

and

5
sL
X
n

. The 5’ dan-
gling ends appear to be stabilizing across all plots, which
is in agreement with previous observations. Conversely,
the 3’ dangling ends appear to be near zero or destabiliz-
ing in all but a few cases. These exceptions are free en-
ergy values (3
s
s
5
G

) at 85 mM [Na+] and 300 mM [Na+],
where somewhat contradictory results are observed.
Further, the plot for
s
s
G


5
Xn

in 85 mM [Na+] shows sig-
nificant variability. Apparently, at least in some cases,
specific values obtained depend on the particular calcu-
lation method employed. The thermodynamic parameters
and ssL

34
ss L
Xn

ο€½

4
ο€½
depicted in Figure 2,
were determined by utilizing variations of the dangling
ended molecules and subtracting to determine individual
end contributions. Calculations can be grouped together
into five different schemes by the generic type of mole-
cules used, i.e. blunt ended, single dangling end, sym-
metric double dangling end or non-symmetric double
dangling end, and the specific method in which they
were used. The five different schemes are depicted in
Table 6. Under the specific assumptions of the n-n model,
the resulting values should reasonably agree regardless
of the particular calculation scheme used. For compari-
son, histograms of values calculated using the same gen-
eral scheme are paired in Figure 2. This comparison re-
veals the different schemes provide semi-quantitative
results in the higher Na+ environments. In 85 mM, the
calculation scheme involving the set III molecules ap-
pears to provide a different result than the other schemes
using set II or set IV molecules. Although the origins of
this observation are not known, results suggest a signifi-
cant electrostatic effect associated with the 3’ dangling
end in the set III molecules.
3.7. Counterion Binding
The melting data and corresponding thermodynamic
parameters evaluated as a function of [Na+] provide a
means of quantitatively estimating the net Na+ released
upon melting of the short duplex DNAs (as function of
both duplex and dangling end length). The release of Na+
upon melting or the number of ions lost, represented as
βˆ†n, can be estimated assuming a simple binding equilib-
rium and evaluated according to [6],
1
ddlnNa
o
m
RnH T



οƒΉ

 

 (12)
where o
H

is the standard state enthalpy of dissocia-
tion of the duplex, R is the ideal gas constant and

is
a correction term for the sodium ion activity coefficient.
A standard value of

= 0.92 was assumed throughout
a) 85 mM [Na
+
] b) 300 mM [Na
+
]c) 1.0 M [Na
+
]
Figure 2. Comparative histograms of Ξ΄G5 and Ξ΄G3 for nL = 4. Histograms show values of Ξ΄G5 and Ξ΄G3 de-
termined using thermodynamic data from set IV molecules and relevant molecules from sets II and III. Re-
sults from the different calculation schemes are shown in Table 5. They are designated as follows: Ξ΄G5
(lighter bars) (a) II-IVa, (b) II-IVc, (c) IVa-I, (d) IVc-I, (e) III-IVb, (*) (II-I)/2, Ξ΄G3 (darker bars), (f) IVb-I,
(g) IVd-I, (h) III-IVa and (*) III-I-Ξ΄G5’. Stars (or asterisks) depict values determined from data shown in
Figure 1.
Copyright © 2012 SciRes. OPEN A CCESS
R. Dickman et al. / Journal of Biophysical Chemistry 3 (2012) 1-15 9
Table 6. Calculated thermodynamic data for dangling ends by method of subtraction. The dashed duplex region is given by the du-
plex sequence shown in Table 1 for nD = 21 and nL = 4.
Scheme Sequences Compared Parameter
5’ TAGA----------
----------AGAT βˆ’ 5’ TAGA----------
---------- Ξ΄G5
1
5’ TAGA----------
----------AGAT – 5’ ----------
----------AGAT Ξ΄G5
5’ TAGA----------
---------- – 5’ ----------
---------- Ξ΄G5
5’ ----------
----------AGAT – 5’ ----------
---------- Ξ΄G5
5’ ---------- TAGA
---------- – 5’ ----------
---------- Ξ΄G3
2
5’ ----------
TAGA---------- – 5’ ----------
---------- Ξ΄G3
5’ TAGA----------AGAT
---------- – 5’ ----------TAGA
---------- Ξ΄G5
3
5’ TAGA----------AGAT
---------- – 5’ TAGA----------
---------- Ξ΄G3
4 [ 5’ TAGA----------
----------AGAT – 5’ ----------
---------- ] × (1/2) Ξ΄G5
5 5’ TAGA----------AGAT
---------- – 5’ ----------
---------- – Ξ΄G5 Ξ΄G3
[6]. From linear fits of versus

1
m
TK
ο€­ln Na




plots,
the slopes in Eq.12, 1
ddTο€­
lnNa
m


οƒΉ
, and Ξ”n were
evaluated for sets I, II and III duplexes. For comparison,
the counterion release per phosphate
nN  (13)
was plotted versus dangling end length for sets I, II and
III duplexes and is shown in Figure 3. For these calcula-
tions N is the total number of phosphates in the duplex,
including those in the single strand ends.
A close inspection of the plots in Figure 3 reveals in-
Figure 3. Counterions released: ΔΨ (the net counterion re-
leased per phosphate) versus nL for the three main molecule
sets.
teresting behaviors for

 as a function of decreasing
duplex length (and subsequent increase of the dangling
end length) for all three sets. For the set I and set II
molecules,

 decreases stepwise with decreasing
duplex length and is essentially identical for both types
of duplexes. For the set III molecules, decreases
following a similar trend, but is approximately 15%
smaller at each point on the plot. These data indicate a
net lower amount of Na+ released per phosphate (on av-
erage) during the melting process for set III molecules
compared to sets I and II.

Since relatively higher charge density of the duplex
compared to single strands is the underlying origin of
counterions released upon duplex melting, the fact that
set I and set II molecules display similar counterion re-
lease curves suggests the duplexes have similar charge
densities. More importantly, the ends must behave simi-
larly (in a counterion binding sense) and have similar
charge densities and counterion binding properties re-
gardless of end type. Conversely, the observed behavior
for set III molecules suggests several plausible scenarios.
Either the 3’ single strand dangling ends bind less Na+
compared to the 5’ single strand dangling ends, while the
duplex binds counterions to the same extent, or the du-
plex adjoined by a 3’ end is perturbed to an extent that
decreases the local duplex charge density and results in
overall less counterion binding to the duplex state, and
consequently a net lowering of the counterions released
upon melting. Both scenarios will be further considered
below.
Copyright © 2012 SciRes. OPEN A CCESS
R. Dickman et al. / Journal of Biophysical Chemistry 3 (2012) 1-15
10
3.8. Heat Capacities of Dangling Ends
In DSC experiments, the thermodynamic parameters
of the melting transition, cal
H
 and cal are evalu-
ated from the area under the melting curve,
S


p
CT
versus Temperature. The experimental transition en-
thalpy is given by,


ΔΔ
oo
cal p

H
THHCTT

 (14)
where is an arbitrary reference temperature and
o
T
H

is a correction term for small variations in different
salt environments. Generally for short duplex DNA the
assumption is made that differences between and
are small in the transition region where the thermo-
dynamic parameters are evaluated, thus
o
T
0
T
p
C
ο€½
[1].
As a matter of practice, calculated values of ca l
H
 and
cal are routinely used to predict thermodynamic sta-
bilities of duplexes at temperatures far below (37˚C) the
actual transition region (55˚C - 75˚C), where there is
more biological relevance and where practical applica-
tions occur. The accuracy of such predictions relies on
the validity of the assumption that evaluated parameters
are temperature independent and the overall change in
excess heat capacity (
S
p
C). If then the ther-
modynamic parameters evaluated from analysis of the
melting transition region may not be accurate for predic-
tions at lower temperatures.
0
p
C
As the technology to measure these transitions has
grown in sophistication and precision over the past 15
years, some studies have reported the existence of a rela-
tive standard transition heat capacity for all DNA du-
plexes. Estimates for this value are as high as 100
cal·deg–1·(mol·base·pair)–1 and vary slightly with se-
quence and salt [2,3,7]. Recently, the average value of
cal·deg–1·(mol·base·p air)–1 has been
reported as a good approximation [8]. Inclusion of the
64.6 21.4
p
C ο‚±
p
C parameter allows for more accurate predictions of
the transition enthalpy and entropy at temperatures below
the transition region [6,7].
For dangling ended molecules, a question arises re-
garding their effect on, and contributions to
p
C

. To
address this question, plots of cal
H
 versus m
T in all
Na+ environments for sets I, II and III were constructed
and are shown in Figure 4. Using all of the data, each set
of molecules displays a different linear slope. Values of
p
C determined from slopes are 31.2 cal·deg–1·base
pair–1 for set I, 25.1 cal·deg–1·base·pair–1 for set II, and
68.9 cal·deg–1·base·pair–1 for set III. These values for
sets I and II differ somewhat from the average reported
p
C value of 64.6 ± 21.4 cal·deg–1·(mol·base·pair)–1.
However, if values from the lowest [Na+] are omitted,
p
C val- ues of 54.1, 54.6, 85.2 cal·deg–1·b ase·pa ir–1
are found for sets I, II and III respectively, which is in
reasonable agreement with the reported best value.
Figure 4.


m vs Tm for each type of molecule in all salts.
Set II molecules display a Ξ”Cp value of 25.1 cal·deg–1·base·pair–1,
set III molecules have 68.9 cal·deg–1·base·pair–1 and Ξ”Cp for
set I molecules is 31.2 cal·deg–1·base·pair–1.
HT
Differences in
p
C

values for each type of duplex
were estimated using Eq.14. For each dangling-ended
duplex, the difference between transition enthalpies of
the dangling ended molecule of set II and corresponding
blunt-ended molecule of set I, evaluated at the transition
temperature of the corresponding dangling-ended duplex,
, is
II
m
T


IIII IIIIo
mp

mm
H
TTHHCT T

ο€­
 (15)
where II IIII
p
p
CC
ο€­
p
C

 is the difference in the
heat capacities of the dangling-ended duplexes of set II
and the corresponding blunt-ended duplexes of set I.
Clearly a plot of


II
m
H
TT ο€½
II I
p
C
versus should
have a slope of
II
m
T
ο€­
 , viz.


IIIIII I
dd
mm p
H
TT TC
ο€­
 . (16)
An analogous expression for can also be
found with . If there were no difference in
III I
p
Cο€­

III
m
TTο€½
p
C

for set II and set I molecules, a plot of II I
p
C
ο€­

III I
p
Cο€­

versus
would produce a line having zero slope. Such a line
is seen in Figure 5 for the dangling ended molecules of
set II. Conversely, if a plot of versus
produces a line having some non-zero slope, as observed
in Figure 5 for the set III dangling ended molecules,
additional factors related to the dangling ends must con-
tribute to their
II
m
T
III
m
T
p
C

. The slope for set III molecules
from the plot in Figure 5 provides an estimated value of
cal·deg–1·base·pair–1, which is in excess
to
IIII
p
Cο€­ο€½52.5
p
C

of the blunt ended molecule. Thus, if the re-
ported average value of p cal·deg–1·base
pair–1 for the blunt-ended molecules is used, an estimated
64.6C

117 cal·deg–1·base·pair–1 is found for the set III
molecules. Inclusion of this difference with the noted
Copyright © 2012 SciRes. OPEN A CCESS
R. Dickman et al. / Journal of Biophysical Chemistry 3 (2012) 1-15 11
Figure 5.


m vs Tm for each type of molecule in all
salts. As compared to the set I molecules, set II molecules dis-
play a ΔΔCp = –5.8 cal·deg–1·base·pair–1 and set III molecules
have ΔΔCp = 52.5 cal·deg–1·base·pair–1.
HT
difference in sodium release per phosphate further sug-
gests changes in the set III duplexes. These will be dis-
cussed in more detail below.
4. DISCUSSION
4.1. 5’ Dangling Ends
A number of factors are involved in determining the
relative influence a dangling single strand end will have
on the adjoining duplex. These include: the type of
molecule (i.e. whether it is DNA or RNA), identities of
the terminal duplex base pair and initial dangling-end
base, and relative orientation of the first dangling base
with respect to the terminal duplex base pair. Here, the
duplex terminal base pair and adjoining single strand
base were held constant in order to focus on relative ef-
fects of the end position (5’ versus 3’) as a function of
increasing length. Previous studies have examined ther-
modynamic contributions of various permutations and
combinations of dangling end length, end sequence and
sequence of terminating duplex base pair of DNA dan-
gling ends to duplex stability [9,10,13-16]. None, how-
ever, have examined effects of end length in an incre-
mental fashion for ends ranging in length from nL = 1 to
10 bases, nor have they compared 5’ and 3’ ends in dif-
ferent Na+ environments. However, there remain several
places where these results can be compared with pub-
lished work.
Thermodynamic effects of all possible single base
dangling ends were studied by Santa Lucia and cowork-
ers through UV melting analysis [13,17]. In their sys-
tematic study, molecules were designed to have a duplex
fixed at eight base pairs and single dangling bases at-
tached to the 5’ or 3’ ends. Relevant sequence dependent
interactions (e.g. those of the terminal 5’AC/3’G stack)
determined in their study should be comparable with our
results in 1.0 M [Na+]. After conversion to 25˚C, they re-
port an observed stabilization of kcal/
mol. It appears that our value of at 25˚C
for the 5’AC/3’G stack of βˆ’0.3 kcal/mol is not nearly as
stabilizing as reported. However, for longer ends where
nL is greater than 1, an average value of 25
25 1.21G

25 1
L
Gnο€½
G

2.6

ο€½
ο€­
kcal/mol was obtained, which is in better agreement with
published results.
Over 20 years ago, Doktycz et al. published results
from melting studies of four-base dangling-ended DNA
hairpin molecules [14]. The general sequence, 5’(XY)2-
(GGATAC)2(T)4, naturally folds to form a hairpin with a
six base duplex stem, a T4 single strand loop connecting
one end of the duplex and a four base 5’ dangling end on
the other. Considering only the molecules with the same
specific end sequences (i.e. those with a terminal stack of
5’AC/3’G), the reported 25
G

had an average value of
βˆ’1.17 kcal/mol in 115 mM [Na+]. In this salt environ-
ment, for nL = 4 our data has coalesced to an average
value of βˆ’1.5 kcal/mol, in reasonable agreement with
published results.
Ohmichi published results of melting studies using an
eight base pair duplex molecule with 5’ dangling ends
varying from one to four bases [9]. The terminating se-
quence in their molecules was slightly different, 5’AG/3’C
instead of 5’AC/3’G, which prohibits a direct comparison.
Nonetheless, trends reported as a function of increasing
length can be considered. For a single base 5’ dangling
end in 1.0 M [Na+], a stabilization of 25 0.3G

ο€½ο€­ kcal/
mol was reported. Addition of a second dangling end
base increased stabilization to βˆ’0.4 kcal/mol. This trend
seemed to reach a constant value at three bases with
25 0.6G

ο€½
ο€­ kcal/mol. This increase in stability coupled
to the lengthening of the single strand dangling end is
qualitatively consistent with our observations.
4.2. 3’ Dangling Ends
Compared to 5’ dangling ends, fewer studies of 3’ dan-
gling ends have been performed. Overall, reports have
found that 3’ dangling ends make favorable contributions
to duplex stability, and are thus stabilizing, but less so
than their 5’ counterparts [4,9]. In contrast we found 3’
ends to be generally destabilizing. Although unexpected,
observations of destabilizing dangling ends are not un-
precedented. The terminal stacks, 5’GT/3’A, 5’T/3’AC and
5’T/3’TA were found by SantaLucia to be mildly destabi-
lizing [13]. Additionally comparison of the published
temperature corrected value for the 5’C/3’AG stack,
25 1.0G

ο€½
ο€­ kcal/mol [13], is in good agreement with
our results in 1.0 M [Na+], where 25 0.8G

ο€½ο€­ kcal/mol.
Perhaps by focusing only on single dangling bases in
Copyright © 2012 SciRes. OPEN A CCESS
R. Dickman et al. / Journal of Biophysical Chemistry 3 (2012) 1-15
12
high salt, the case found here to have the greatest stabi-
lizing effect, the appearance of 3’ dangling end destabi-
lization was overlooked.
4.3. Origins of Stabilization
Our results indicate that 5’ dangling ends are equally
or more stabilizing than their 3’ counterparts. This be-
havior has been previously documented and can possibly
be explained by examining DNA single strand structure.
In the duplex state, DNA adopts the preferable B-form,
which persists to some degree in the single strand state.
NMR studies of single strand DNA hexamers with mul-
tiple A-A base stacks showed that in DNA, the imidazole
stacks above the pyrimidine in the 5’ to 3’ direction [18].
A systematic review of crystal structures from the pro-
tein database demonstrated for DNA that addition of a
single strand base on the 5’ end is positioned in such a
way that it can freely interact with the hydrogen bonds of
the terminal base pair. In contrast, a 3’ base end is posi-
tioned away from the same hydrogen bonds, and there-
fore is less likely to experience such stabilization [19].
Thus, placement of the dangling base is optimal for ter-
minal base pair interactions in DNA on the 5’ end but
when an additional base is added to the 3’ end of DNA
minimal overlap occurs which apparently translates to
fewer stabilizing interactions.
4.4. Structural Perturbations
Our results indicate a 3’ dangling end is generally de-
stabilizing to a DNA duplex. Previous studies of counte-
rion binding to duplex DNA suggests fewer Na+ ions
bind near the ends compared to in the middle [6,20]. This
suggests differences between the dangling ended and
blunt molecules should result in negligible changes in
counterion binding if the duplex region of the dangling-
ended duplex is not affected by the ends. Comparison of
the blunt ended duplexes and set II molecules support
this assumption. The net counterion release per phos-
phate is the same for the two sets (I and II) of molecules
and the plots of vs. nL (in Figure 3) are the same.
Conversely, for the set III molecules having 3’/5’ dan-
gling ends, the plot of vs. nL is approximately 15%
lower than for the set I and set II molecules and indicates
a net lower Na+ release during melting suggesting the
duplex region for set III is perturbed in some way that
results in slight differences of the associated counterion
binding properties.


When DNA molecules anneal from their single strand
state to form a duplex state, a net change in solvent ex-
posed surface occurs. This change is accompanied by the
burying of hydrophobic residues, which contributes to
p
C. Differences in the estimated
p
C values for set
II, when compared to set III (Figures 4 and 5), further
support the idea of subtle differences between the duplex
regions. Comparison of
p
C

values for the blunt-ended
set I molecules and the set II molecules revealed an es-
sentially constant
p
C

 with a cal
H
 difference of
about 1 cal·deg–1·base·pair–1. There was also no marked
length dependence, indicating that most of the stability
came from interactions of the first base with the terminal
base pair, presumably due to the favorable stacking in-
teractions. Conversely, comparison of
p
C values for
set III and set I molecules revealed a significant differ-
ence, p52C.5

 cal·deg–1·base·pair–1. Here cal
H


is initially around 0.5 and decreases to βˆ’0.5 as the length
of the dangling end increases to nL = 10. This suggests an
initial smaller buried surface area as compared to the 5’
dangling end, which is lost as the dangling end increases
in length. The continued loss of enthalpy suggest that
with longer dangling ends, the duplex region itself may
be perturbed in this particular molecular environment.
4.5. Predictive Ability and Applications to
Probe Design
Ascertaining specific thermodynamics involved in
probe/target alignment and being able to further predict
energies of all possible alignments is key to optimal
probe design. The ability to design probes with exquisite
accuracy is imperative to successfully locate target se-
quences differing by as little as a single nucleotide. In
fact, molecules used in this study were designed to
mimic those that might occur in a multiplex hybridiza-
tion reaction (such as on a DNA microarray) where dan-
gling ends presumably occur with a moderate to high
frequency. The more specific the predictive ability of
thermodynamic binding properties, the more effective
probe design can be achieved.
In the n-n model the free energy of melting a duplex
molecule is given by
initiation
oo
s onal

tack a
o
G
dditi
o
GGG 
οƒ₯
. (17)
For calculations involving the duplex region, this
model uses combinations of the 10 possible n-n values
(stack ) experimentally determined by a number of in-
dependent labs that are generally in good agreement with
one another [17]. The first term, initiation, is the cost
required to begin the annealing process and therefore has
a positive free energy contribution. This value has re-
cently been determined by our group, as well as other
investigators [21,22]. The last term, additional , encom-
passes any extra terms such as those arising from sym-
metry considerations, a terminating A·T base pair or sin-
gle strand dangling ends. The sum of terms estimates the
total free energy.
o
G
o
G
o
G
Current prediction programs relying on the n-n model
o calculate thermodynamic properties are limited by the t
Copyright © 2012 SciRes. OPEN A CCESS
R. Dickman et al. / Journal of Biophysical Chemistry 3 (2012) 1-15
Copyright © 2012 SciRes.
13
Table 7. Ξ”G values predicted using length dependent overhang parameters. Sequences used to predict βˆ†G25 kcal/mol are shown in
column one. The dashed duplex region is given by the duplex sequence shown in Table 1 for nD = 21 and nL = 4. Unified N-N values
were used in calculations [13]. All predicted values were corrected with an averaged difference for set I (i.e. βˆ†Gexp – βˆ†Gmfold, 85 mM
= +6.2, 300 mM = +6.7), and (1000 mM = +7.8).
85 mM [Na+] 300 mM [Na+] 1.0 M [Na+]
Sequence Exp Mfold NN Exp Mfold NN Exp Mfold NN
5’ ----------
3’ ---------- –19.8 –18.6 –19.2 –21.3 –20.9 –21.5 –23.9 –22.4 –23.0
5’ TAGA----------
3’ ----------AGAT –24.6 –20.7 –24.4 –26.7 –23.1 –26.7 –29.5 –25.8 –28.2
5' TAGGA----------
3’ ----------AAGTCGAT
* –20.7 –23.5 * –23.1 –24.9 * –25.8 –26.4
5’ TAGA----------AGAT
3’ ---------- –16.5 –20.5 –18.1 –23.2 –22.9 –21.4 –23.5 –24.6 –23.3
5' ATCGA----------AGAATCT
3’ ----------
* –20.5 –18.0 * –22.9 –20.5 * –24.6 –22.1
quality of parameters used in the calculation. Mfold is
one such program readily available via the Internet [23].
In this program, a computational algorithm searches for
the most stable structure formed from the sequence of
two DNA strands, through a calculation of the thermo-
dynamic stabilities using tabulated n-n parameter values.
To include effects of dangling ends, the specific value of
–1.18 kcal/mol for the 5’ dangling end (5’AC/3’G) and
–1.05 kcal/mol for the 3’ dangling end (5’C/3’AG) are
added to n-n calculations [13]. Potential stability differ-
ences due to dangling ends longer than one base are not
considered.
OPEN A CCESS
To test the applicability and utility of dangling end
parameters evaluated here, five sequences having a 21
base pair duplex region were designed with variable end
lengths. Calculated thermodynamic parameters were
generated using two methods, Mfold and the n-n model.
Sequences differed in the placement and length of dan-
gling ends. The sequences were: 1) a 21 base blunt ended
control, 2) a 21 base duplex with two four-base 5’ dan-
gling ends, 3) a 21 base duplex with two 5’ dangling ends
having five and eight bases respectively, 4) a 21 base
duplex with one four-base 3’ and one four-base 5’ dan-
gling end, and 5) a 21 base duplex with one five-base 3’
dangling end and one seven-base 5’ dangling end. Where
available, experimental data has been included as a com-
parison. Results of computations are shown in Table 7.
Upon closer examination, the n-n model and Mfold
stability predictions are quite comparable for 5’ ended
molecules. However, Mfold predicts a greater stability
for the 3’ ended molecules than that predicted using the
end parameters described here. Since no reported meas-
urements have been made of these specific 3’ ends desta-
bilizing the duplex, it is not surprising the standard pro-
gram (Mfold) overestimates the stability of those mole-
cules. These comparisons suggest the dangling ended
parameters in Ta b l e 4 may provide more accurate quan-
titative predictions of the stability of dangling ended
molecules. Confirmation of the ultimate practical utility
of the evaluated dangling end parameters must be dem-
onstrated through more accurate probe design and im-
proved quantitative performance of multiplex hybridiza-
tion reactions.
5. ACKNOWLEDGEMENTS
Portions of this work appeared in a thesis by Rebekah Dickman sub-
mitted in partial fulfillment for requirements of the Master of Science
in Chemistry at Portland State University, December 2010. This work
was supported by grants GM080904 and GM084603 from the National
Institutes of Health.
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R. Dickman et al. / Journal of Biophysical Chemistry 3 (2012) 1-15 15
Supplementary Figures
85 mM [Na
+
]
300 mM [Na
+
]
1000 mM [Na
+
]
Supplementary Figure 1. cal versus cal
TS (T = 298.15 K) for
the 27 duplex DNAs in 85 mM, 300 mM and 1.0 M [Na+].
H
Supplementary Figure 2. Comparison of the evaluated thermodynamic parameters for
the 5’ and 3’ dangling ends in sets II and III ((a) Ξ΄H and (b) Ξ΄S), in the three Na+ envi-
ronments plotted versus overhang length, nL.
Copyright © 2012 SciRes. OPEN A CCESS