(Received for publication, August 19, 1994; and in revised form, November 7, 1994)
From the
We investigate enthalpy-entropy compensation for melting of
nearest-neighbor doublets in DNA. Based on data for 10 normal doublets
and for doublets containing a mispaired or analog base, the correlation
of S° with
H° follows a rectangular
hyperbola. Doublet melting temperature relates linearly to
H° by T
= T
+
H°/a , where T
273 K and a
80 cal/mol-K. Thus T
is
proportional to
H° + aT
rather than to
H° alone as previously thought by assuming
S° to be constant. The term aT
21.8 kcal/mol may
reflect a constant enthalpy change in solvent accompanying the DNA
enthalpy change for doublet melting and is roughly equivalent to
breaking four H-bonds between water molecules for each melted doublet.
The solvent entropy change (aT
/T
)
declines with increasing T
, while the DNA
entropy change (
H°/T
)
rises, so the combined DNA + solvent entropy change stays constant
at 80 cal/K/mol of doublet. If such constancy in DNA + solvent
entropy changes also holds for enzyme clefts as ``solvent,''
then free energy differences for competing correct and incorrect base
pairs in polymerase clefts may be as large as enthalpy differences and
possibly sufficient to account for DNA polymerase accuracy. The
hyperbolic relationship between
S° and
H° observed in 1 M salt can be used to
evaluate
H° and
S° from T
at lower, physiologically relevant,
salt concentrations.
Thermal denaturation studies of DNA have revealed that the
melting temperature, T, (
)of a
DNA double helix depends on strand
length(1, 2, 3) , strand concentration (4, 5, 6, 7) , base
sequence(8, 9, 10) , and ionic strength of
added salt (8, 9, 10, 11) . Such
studies indicate that double helix stability can be predicted in terms
of the standard free energy change,
G° =
H° - T
S°, if one
knows the standard enthalpy and entropy changes (
H°
and
S°) for the melting of each nearest-neighbor
doublet of base pairs in DNA(9) . Normal B-form helical DNA,
with Watson-Crick base pairs stabilized by nearest-neighbor base
stacking, has 10 possible kinds of nearest-neighbor doublets. For the
melting of each doublet,
H° and
S°
have been evaluated experimentally in 1 M NaCl but only T
(
H°/
S°) has been measured at
lower salt concentrations. In this paper we provide a formula to
describe the relationship between
H° and
S° measured in 1 M salt and show how
standard enthalpy and entropy changes may be evaluated from T
at lower salt concentrations to predict
B-DNA stability under more physiologically relevant conditions.
The
focal point of this work pertains to ``enthalpy-entropy
compensation,'' the strong correlation between enthalpy and
entropy changes observed for molecular association/dissociation
reactions in aqueous solution and attributed to water's influence
as solvent (12, 13, 14) . For the melting of
DNA doublets, we find that S° correlates with
H° in the manner of a rectangular hyperbola. The
hyperbolic curve that we obtain by fitting normal doublet data (4, 9) also applies to the melting of doublets
containing base mispairs (4, 7) and the base analog O
-methylguanine(7) .
A DNA duplex with n base pairs (bp), having the
first bp stacked on the second, the second on the third, etc., has n-1 doublets of stacked bp contributing to duplex stability.
For each doublet (MN) there is a characteristic enthalpy change upon
melting (H
) that depends on the stacking
interaction between nearest neighbors M and N. The average enthalpy
change per mole of doublet in the duplex is given by
where f is the mole fraction of doublet MN
and
is the sum for all MN types in the duplex. In terms of the
two strands in the duplex, MN means MN/M`N`, i.e. base
sequence 5`-MN-3` on one strand paired with complementary base sequence
3`-M`N`-5` on the opposite strand. Since the two strands are
antiparallel, MN/M`N` is equivalent to N`M`/NM, so there are 10
distinct MN types arising from the 16 possible nearest-neighbor base
sequences in normal DNA.
Corresponding to H given by , the average entropy change per mole of doublet is
S =
H/T
, where T
is the duplex melting temperature in degrees
Kelvin. If all doublets have the same entropy change, i.e.
S
=
H
/T
= c, then the duplex T
value is an average
of doublet T
values,
where T =
H
/c is the T
value for doublet MN. This formula applies to DNA duplexes that
are long enough so that end effects are negligible, and T
is practically independent of strand
concentration. In the case of short duplexes, the sum in is multiplied by a factor less than 1, about (n-1)/n, to account for the decrease in T
with decreasing n because of end
effects(1, 2) , and another term is required to
describe T
dependence on strand
concentration(4) .
Measurements of DNA Melting
Temperatures at Various Salt Concentrations-has
been used to describe DNA melting temperatures in terms of doublet T values, for duplexes of length 100 bp or
greater, in salt solutions of low ionic strength, µ = 0.020 M(8) and 0.075 M(10) . In such low
concentrations of salt, long duplexes have melting temperatures
sufficiently below the boiling point of water to be measured
accurately. By a least-squares fit to duplex T
values obtained for a wide range of known base sequences,
self-consistent T
values have have been
determined for all normal MN doublets in 0.020 and 0.075 M NaCl. The corresponding ``constant'' doublet entropy
change (
S
= c) at these NaCl
concentrations were estimated to be c = 24 cal/mol-K
and 25 cal/mol-K, respectively, for the purpose of evaluating
H
= cT
for each
doublet(8, 10) .
In salt solutions of 1 M or above, T for long DNA duplexes may exceed
the boiling point of water and so cannot be measured directly, but
short duplexes of 10 bp or less have T
values low
enough to be measured accurately over a wide range of total strand
concentration (C
). Tinoco and co-workers (4) have shown that the equilibrium constant (K
) for duplex dissociation at T
has the value C
/4 ideally, so the
corresponding standard free energy change is
For each short (7-10 bp) duplex examined, a van't
Hoff plot of Rln(4/C) versus 1/T
was found to give a straight line with
slope and intercept yielding
H° and
S° values for the
duplex(4, 7, 14) . This experimental
(van't Hoff) method of measuring
H° and
S° has been confirmed by Breslauer and co-workers (9) using calorimetry. A systematic replacement of one bp by
another in short duplexes enabled Breslauer and co-workers to evaluate
H°
and
S°
for each normal doublet in 1 M NaCl (Table 1).
Figure 1:
Enthalpy-entropy compensation found for
DNA melting in salt solutions of 1 and 0.1 M ionic strength.
In a, the standard entropy change, S°,
evaluated for melting in 1 M NaCl, is shown plotted against
the corresponding enthalpy change,
H°, for each
nearest-neighbor doublet of base pairs in normal DNA (9) and
for doublet combinations containing normal pairs and
mispairs(4) . Eight of the 10 normal doublets are represented
by solid circles (
) and two by open circles (
). The latter are doublets TG/AC and GA/CT, whose values (9) appear anomalous by comparison with results for doublet
combinations(4) , (TG/AC + GT/CA)/2 and (GA/CT +
AG/TC)/2, represented by solid squares (
). Doublet
combinations containing a mispair (TX/AY + XT/YA)/2 are represented by open squares (
). The solid curve is the rectangular hyperbola,
described by , fitted by nonlinear regression to the eight solid circles and two solid squares. The dashed
line is a linear least-squares fit to the same normal doublet
data. In b is shown a similar plot for melting in 0.1 M NaCl, using
S° and
H° obtained
for internal doublet combinations, (TX/AY + XT/YA)/2, where X/Y is a normal base pair
(
), a mismatched base pair (
), or a pair containing the
base analogue, O
-methyl G (
). Each doublet
combination is evaluated from triplet (TXT/AYA) in
the center of the 9-bp duplex(7) ,
(GTTTXTTTG/CAAAYAAAC), as described in text. The solid curve and dashed line are the same as shown in a.
These results raise
an interesting question: how can enthalpy-entropy compensation be
formulated, consistent with the observation that T relates to doublets in the simple manner(8, 10) described by ? A straight-line approximation
of
S° versus
H°, shown by
the dashed line in Fig. 1a, is unsatisfactory
because the line intersects the
S° axis at a positive
value. The value of
S° cannot remain positive when
H° becomes negative because T
=
H°/
S° would then
become negative on the Kelvin scale, which is physically impossible.
A satisfactory fit to the data is obtained with a rectangular
hyperbola (Fig. 1, solid line). An analytic expression
for the hyperbolic curve is generated simply by introducing a
constant(T) in the linear relationship between T
and
H°,
Substitution of H°/
S° for T
in and solving for
S° results in the enthalpy-entropy compensation
formula,
This expression for S° versus
H° has the form of a rectangular hyperbola
passing through the origin (
H° = 0,
S° = 0). Near the origin, where
H° is much less than aT
,
S° is close to
H°/T
, since the initial slope is
1/T
. However, as
H° increases,
the slope decreases continuously as
S° approaches a. With
H° related to doublets by and
S° described by , T
=
H°/
S° remains related to doublets
as in ,
where T = T
+ (
H°
/a) is the T
value for doublet MN, with
H°
being its standard enthalpy change
upon melting.
The constant T may reflect the
influence of solvent on DNA melting. If T
were
simply proportional to
H°, then at
H° = 0, the melting temperature would be 0 K,
as expected for melting in vacuum. The presence of solvent may provide
a resistance to DNA melting, so that as
H° approaches
0, the melting temperature approaches T
> 0 K.
Thus, T
in degrees Kelvin is proportional to
H° + aT
rather
than to
H° alone, and instead of the DNA entropy
change,
S° =
H°/T
, being constant for all
doublets, we now have the DNA + solvent entropy change,
(
H° + aT
)/T
, equal to the
constant a. The higher T
is above 0 K,
the higher a is above
S° =
H°/T
. The constants a and T
can be evaluated by fitting to the experimental data (Fig. 1) and, as shown
below, T
is within experimental error the same as
the melting temperature of ice.
The solid curve in Fig. 1a is the hyperbola described by fitted by nonlinear regression to the 10 points represented by the (eight) solid circles and (two) solid squares. For comparison, a dashed straight line showing the result of a linear least-squares fit to the same 10 points is also presented. By comparing the hyperbolic curve and straight line (Fig. 1a) with additional points (open squares) obtained for various X/Y mispairs (4) in the doublet combination, (TX/AY + XT/YA)/2, we see that the curve successfully predicts the trend of mispair data whereas the straight line does not.
The hyperbolic curve fitted by nonlinear
regression yields T = 275 K and a = 81 cal/mol-K. Similar results, T
= 273 ± 13 K and a = 79 ± 9
cal/mol-K, are obtained by rearranging to give linear
expressions,
H°/
S°versus
H° and
H° versus
H°/
S°, to which linear
regression is applied as in the Hanes-Woolf method of fitting the
rectangular hyperbola in Michaelis-Menten enzyme kinetics(15) .
Thus for normal DNA doublets in 1 M NaCl, we find T is close to 273 K (ice melting point) and a is about 80 cal/mol-K, with an uncertainty of ±15 degrees
and ±10 cal/mol-K, respectively. Within this margin of error,
the same constant values may be expected to hold at lower salt
concentrations also, since the melting point of ice differs by less
than 5 degrees between 0 and 1 M NaCl. As shown in Fig. 1b, this expectation is supported by measurements
in 0.1 M NaCl (7) for doublet combinations of type,
(TX/AY + XT/YA)/2, where X/Y includes normal pairs, mispairs, and also pairs and
mispairs with the base analog, O
-methyl G.
Fig. 1b shows a plot of
S° versus
H° for the
melting of these doublet combinations in comparison with the same (solid) hyperbolic curve and (dashed) straight line
drawn in Fig. 1a. The data are consistent with a
hyperbola describing enthalpy-entropy compensation and not a straight
line. Since the data fall on or near the same curve as in Fig. 1a, they indicate that the same compensation constants evaluated for normal DNA doublets in 1 M NaCl also hold at 0.1 M NaCl. Furthermore, since
the doublet combinations include O
-methyl G (open triangles) along with normal base pairs (solid
squares) and mispairs (open squares), it appears that T
273 K and a
80 cal/mol-K
apply even when DNA bases are chemically modified.
For the majority of
doublets, the predicted T values (Table 1)
are above 100 °C, as one might expect by extrapolation from lower
salt concentrations(10) . Additionally, the uncertainty
(± deviation from average) is acceptable for all the original
assignments, except for the two doublets TG/AC and GA/CT, shown as open circles falling below the curve in Fig. 1a. The alternative assignments (Table 1, in
brackets) reduce the uncertainty from ± 21° and ±
15° to much lower values (± 6° and ± 5°,
respectively), close to those found for the other doublets.
Table 2shows a comparison of our calculated T values at µ = 1 M with experimental results
obtained at two lower ionic strengths, µ = 0.02 M(8) and 0.075 M(10) . The calculated and
experimental results are consistent in showing that seven of the 10
normal doublets have a large T
dependence on
µ, while three have only a small dependence. Since duplex T
values tend to show a linear dependence on
logµ, the following linear formula has been suggested(16) ,
where T is the T
value at µ = 1.0 and S is a characteristic
slope for each doublet, in degrees/unit change in logµ.
According to , if one evaluates
T
/
logµ, using the T
difference (
T
) between any two µ
values (µ
and µ
, with
logµ
= logµ
- logµ
), one should
find an approximately constant S value for each doublet. The
last column in Table 2shows the average value of S =
T
/
logµ (±
deviation from average) calculated from corresponding T
and logµ differences between each pair of preceding columns.
As seen in Table 2(last column), seven of the 10 normal DNA
doublets have similarly large S values, ranging from 42 to 25
degrees/unit change in logµ, while the other three have much
smaller values (7 or less).
The three doublets with small S all have base G in position 1 of the doublet, namely GT/CA, GA/CT,
and GC/CG. In contrast, all the doublets with G in position 2, namely
CG/GC, GG/CC, TG/AC, and AG/TC, have some of the largest S values. CG/GC has the highest value of T (
149 °C) and largest value of S (
42) of
all normal doublets. Its reverse counterpart GC/CG has the second
highest T
(
139 °C) but smallest S (
0). These results suggest that CG/GC is the most stable of
all doublets at 1 M ionic strength or above, while GC/CG is
the most stable at lower ionic strengths.
The hyperbolic variation of S° with
H° observed experimentally (Fig. 1, a and b) indicates a significant enthalpy-entropy
compensation in DNA melting thermodynamics. This behavior shows that T
=
H°/
S° is not proportional to
H°, as previously suggested(8, 10) ,
but may be linearly related to
H°, as described by . This equation includes a melting temperature constant, T
, which is introduced as a parameter to represent
the complex and poorly understood influence of solvent on DNA
stability.
The inclusion of T leads to an
expression for enthalpy-entropy compensation in the form of a
rectangular hyperbola, . The hyperbolic curve obtained by
fitting experimental data for normal doublets in 1 M NaCl (Fig. 1a) indicates that T
is
close to the melting temperature of ice. The same hyperbolic
curve, with no further adjustment of the two parameters (T
and a) appears to hold reasonably well
for mispaired doublets in 1 M NaCl (Fig. 1a)
and for both normal and mispaired doublets, including the base analog O
-methyl G in 0.1 M NaCl (Fig. 1b). Thus, the constants evaluated by fitting
data at 1 M ionic strength, T
=
273 ± 15 K and a = 80 ± 10 cal/mol-K,
appear to hold at lower ionic strengths as well.
In the case of protein denaturation, enthalpy-entropy compensation is attributed to interactions with surrounding water molecules(12) . However, the detailed interactions between water and proteins are not well understood. In the absence of an adequate theory to account for enthalpy-entropy compensation, we can only speculate on the nature of the interactions between water and DNA that might provide new insight into the phenomenon.
The finding that T
273 K implies that
H° for
the melting of DNA doublets is approximately proportional to T
evaluated in degrees Celsius, as seen from , instead of being proportional to T
evaluated in degrees Kelvin,
The corresponding entropy change for doublet melting,
S° =
H°/T
, is not constant, but is
proportional to the ratio of T
(°C) to T
(K), as seen from ,
Since T(K) = 273 + T
(°C), a plot of
S° against T
(°C) should also yield a rectangular
hyperbola, like the plot of
S° versus
H° described by (solid curves in Fig. 1, a and b).
According to , H° is the difference between aT
and aT
.
What do these empirical terms represent? We suggest that aT
represents an enthalpy change in solvent
(water) accompanying the DNA enthalpy change
H° for
doublet melting. According to this interpretation, aT
=
H°+ aT
is the combined DNA + solvent
enthalpy change for each doublet, with a =
(
H° + aT
)/T
being the combined DNA + solvent
entropy change for doublet melting. The constancy of the parameter a implies that T
approaches T
when
H° approaches 0, and that
as
H° increases, the DNA entropy change
(
S° =
H°/T
) increases by the same
amount as solvent entropy change (aT
/T
) decreases, so
that their sum stays constant at the value a for each doublet.
The large value of a (80 cal/mol-K) indicates that the
solvent enthalpy change, aT = 21.8
kcalmol, is considerably larger than any
H° value
found for normal doublets (Table 1). The implication is that the
change in solvent enthalpy is always greater than the change in DNA
enthalpy when DNA melting occurs, and also that the solvent entropy
change (aT
/T
)
exceeds the DNA entropy change
(
H°/T
).
The magnitude of aT is large enough to require that at
least four H-bonds between water molecules be broken, per DNA doublet,
when melting occurs. This estimate is made by considering the melting
of ``Watson-Crick'' DNA, W
C
W + C, as being
accompanied by the breakage of H-bonds between H
O
molecules,
where m is the number of water H-bonds broken for each
DNA (WC) unit melted. Since about 5 kcal/mol is required to break
an H-bond between water molecules(17) , m must be at
least 21.8/5 = 4.3/melted doublet. The number could be larger,
depending on the strength of H-bonding between H
0 and
dissociated W and C (right-hand side of ).
Doublet GC/CG is known to have the highest intrinsic base stacking energy in B-DNA because it has a large, attractive electrostatic base-stacking component(8) . The intrinsic base stacking energy of CG/GC is considerably lower because it has a repulsive electrostatic component. Calculations of electrostatic interactions versus twist angle (20) indicate that the electrostatic attraction in GC/CG promotes a large twist angle, around 40°, while the repulsion in CG/GC promotes a small twist angle, around 25°, compared to the average 36° angle between stacked base pairs in B-DNA.
The favorable alignment of oppositely charged atoms in the stacked base pairs of GC/CG may be sufficiently stable in B-form duplex as not to attract salt ions, whereas the unfavorable alignment in CG/GC may attract salt ions to counteract repulsions between atoms of like charge. Such differences in ion attraction might be the reason why GC/CG stability shows almost no dependence on salt concentration, while CG/GC stability rises dramatically, as indicated by S = 1° and 42°, respectively (Table 2).
Having described enthalpy-entropy compensation and evaluated the
influence of solvent, by , we now see that free energy
differences for DNA + solvent may be as large as differences in
H°. The DNA + solvent change in enthalpy for
doublet melting is
H =
H°+ aT
, while the corresponding change in
entropy is
S = a. Thus, for DNA +
solvent at temperature T, the free energy change for doublet
melting is
G =
H° + a(T
- T). Since a and T
are constant, then differences in
G may equal differences in
H° at
constant T. In other words, the magnitude of
G for DNA + solvent may equal
H° for DNA
and be sufficient to account for DNA polymerase accuracy.
The above
finding provides an unexpected source of free energy that a polymerase
might exploit. The result, G equals
H, while not applicable to DNA alone, is found to
apply to DNA in combination with solvent, with water as solvent.
Perhaps, it also applies to enzyme as ``solvent.'' Possibly,
as we have suggested previously, the geometric constraints placed on
substrate and template bases in the polymerase active cleft can
suppress
S sufficiently to make
G equal
H(21) . To the extent that dNTP
and template bases confront one another in a lower dielectric medium
that tends to exclude water,
H values between
correct and incorrect base pairs may be even larger than in
water(24) . Thus it seems likely that the enzyme active site
can exploit the large differences in enthalpy between matched and
mismatched base pairs to achieve high nucleotide insertion
fidelity(14) . Replication and repair polymerases and reverse
transcriptases exhibit different levels of insertional accuracy perhaps
by placing different constraints on bound dNTP and DNA, and by
achieving different levels of water exclusion.