Genomics- The Science and Technology Behind the Human Genome Project. Charles R. Cantor, Cassandra L / genomics1-10 / 3

THERMODYNAMICS OF IMPERFECTLY PAIRED DUPLEXES

75

TABLE

3.2 Predicted and Observed Stabilities

(free energy of formation) of Various

Oligonucleotide Duplexes

Comparison of Calculated and Observed

G

(kcal/mol)

Oligomeric Duplex

G

pred

G obs

1

GCGCGC

11.1

11.1

CGCGCG

2

CGTCGACG

11.2

11.9

GCAGCTGC

3

GAAGCTTC

7.9

8.7

CTTCGAAG

4

GGAATTCC

9.3

9.4

CCTTAAGG

5

GGTATACC

6.7

7.4

CCATATGG

6

GCGAATTCGC

16.5

15.5

CGCTTAAGCG

7

CAAAAAG

6.1

6.1

GTTTTTC

8

CAAACAAAG

9.3

10.1

GTTTGTTTC

9

CAAAAAAAG

9.9

9.6

GTTTTTTTC

10

CAAATAAAG

8.5

8.5

GTTTATTTC

11

CAAAGAAAC

9.3

9.5

GTTTCTTTC

12

CGCGTACGCGTACGCG

32.9

34.1

GCGCATGCGCATGCGC

Note: Calculations use the equations given in the text and the mea-

sured thermodynamic values given in Table 3.1.

Source:

Adapted from Breslauer et al. (1986).

because the first base of the dangling end can still stack on the

last base pair of the

du-

plex. Note that there are two distinct types of dangling ends: a 3

-overhang and a 5

-over-

hang. At the current level of available information, we treat these as equivalent. Simple

dangling ends will arise whenever a target and a probe are different in size.

The next imperfection, which leads to considerable destabilization, is an internal mis-

match. As

shown

in Figure

3.7

b, this leads to the

loss

of two internal

and two inH- s0 's

ternal

G

s0 'sApparently. this is empirically compensated by some

residual

stacking

ei-

ther between the bases that are mispaired and the duplex borders or between the bases

themselves. Whatever the detailed mechanism, the result is to

gain

back

about

8

kcal/mol

in

H.

There is no effect on the

G.

A larger internal mismatch is called an

internal

loop.

Considerable data on the thermodynamics of

such loops exist for RNA,

and much

less

for DNA. In general, such structures will be

far less stable than the

perfect duplex

because of

the loss

of additional free energies and

enthalpies of

stacking.

Figure 3.7

Stacking interactions

in various types of imperfectly matched duplexes.

(a)Dangling

ends.

(b)Internal mismatch.

(c)Terminal mismatch.

A related imperfection is a bulge loop in which two strands of unequal size come together

so that one is perfectly paired while the other has an internal loop of unpaired residues.

There

can

also

be internal loops in which the single-stranded

regions are of different

length on the two strands. Again the data describing the thermodynamics of such struc-

tures are available mostly just for RNAs (Cantor and Schimmel, 1981). There are many

complications. See, for example, Schroeder et al. (1996).

A key imperfection that needs to be

considered

to understand the specificity of

hybridization is

a terminal

mismatch. As shown

in Figure

3.7

c, this

results in

the

loss of

one

H

0

one

0

an external mismatch

should be

less destabilizing than an

and

. SuchG

s

s

internal mismatch because one less stacking interaction is disrupted. It is not clear, at the

present time, how much any stacking of the mismatch to the end of the duplex partially

compensates for the lost duplex stacking. It may be adequate to model an end-mismatch

like

a dangling

end. Alternatively, one might consider it like an internal mismatch with

only one lost set of duplex stacking interactions. Both of these cases require no correction

to the predicted

G of duplex formation, once the lost stacking interactions have been ac-

counted for. Therefore at present it is simplest to concentrate on

G

estimates

and

ignore

H

estimates. More studies are needed in this area to clear up these uncertainties. In

Chapter 12 we will discuss attempts to use hybridization of short oligonucleotides to infer

KINETICS OF THE MELTING OF SHORT DUPLEXES

77

sequence information about a larger

DNA target. As interest in this approach becomes

more developed, the necessary model

compound data will doubtlessly be accumulated.

Note that there are 12 distinct terminal mismatches, and their energetics could depend not

only on the sequence of the neighboring duplex stack but also on whether one or both

strands of

the

duplex are further elongated. A large number of model compounds will

need to be investigated.

Despite the limitations and complications just described, our current ability to predict

the effect of a mismatch on hybridization is quite good. A typical example is shown in

Figure 3.8. Note

that the

melting

transitions of oligonucleotide

duplexes with 8 or more

base pairs

are quite

sharp. This reflects the large

and

0

of the

the all-or-Hnone 'snature

s

reaction. The key practical concern is finding a temperature where there is good discrimi-

nation between the amount of perfect duplex formed and the amount of mismatched du-

plex. The results shown in Figure 3.8 indicate that a single internal mismatch in a 14-mer

leads to a 7°C decrease in

T m . Because of

the sharpness of the melting

transitions, this

can easily be translated into a discrimination of about a factor of ten in amount of duplex

present.

KINETICS OF THE MELTING OF SHORT DUPLEXES

The major issue we want to address here is whether, by kinetic studies of duplex dissocia-

tion, one can achieve a comparable or greater discrimination between the stability of dif-

ferent duplexes than by equilibrium melting experiments. In practice, equilibrium melting

experiments

are

technically

difficult

because one must discriminate between free and

bound probe or target. If the analysis is done spectroscopically, it can be done in homoge-

neous solution, but this usually requires large amounts of sample. If it is done with a ra-

dioisotopic tag (or a fluorescent label that shows no marked change on duplex formation),

it is usually done by physical isolation of the duplex. This assumes that the rate of duplex

dissociation is slow compared with the rate of physical separation, a constraint that usu-

ally can be met.

In typical hybridization formats a complex is formed between probe and target, and

then the immobilized complex is washed to remove excess

unbound

probe (Fig. 3.9).

The complex is stored under conditions where little further dissociation occurs, and af-

terward

the amount of

probe

bound to the target is measured. A variation on this theme

is to allow the complex to

dissociate for a fixed time period and then to measure the

amount of probe remaining bound. It turns out that this procedure gives results very sim-

ilar to equilibrium duplex formation. The reason is that the temperature dependence for

the reaction between two long single strands to form a duplex is very slight. The activa-

tion energy for this reaction has been estimated to be only about 4 kcal/mol. Figure 3.10

shows

a

hypothetical

reaction profile for interconversion between duplex and single

strands. If we assume that the forward and reverse reaction pathways are the same, then

the

activation energy

for

the

dissociation of the double strand will be just

H 4

kcal/mol. Since

H

is much larger than 4 kcal/mol for most duplexes, the temperature

dependence of the reaction kinetics will mirror the equilibrium melting of the duplex.

It is simple to estimate the effect of temperature on the dissociation rate. At

T m we ex-

pect an equation of the form

km

A exp

[ H

4]

RT

m

KINETICS OF DOUBLE-STRAND FORMATION

81

In practice, renaturations are carried out most successfully when the renaturation tem-

perature is (

T m 25)°C. In free solution the simple model, shown in Figure 3.5, is suffi-

cient to account for renaturation kinetics under such conditions. It is identical to the pic-

ture used for short duplexes. The rate-limiting step is

nucleation, when

two

strands

collide in an orientation that allows the first base pair to be formed. After this, rapid du-

plex growth occurs in both directions by a

rapid

zippering

of the two strands together.

This model predicts that the kinetics of renaturation should be a pure second-order reac-

tion. Indeed,

they are. If

we call the two strands

A

and

B we can

describe

the

reaction

as

A

B

:AB

The kinetics will be governed by a second-order rate constant

k2:

d [AB ] k2[A ][B ]

dt

d [A ]

d [B ] k2[A ][B ]

dt

dt

In a typical renaturation experiment, the two strands have the same initial concentra-

tion: [A ] [B ] C

s

, where

C

s

is 1 the initial total concentration of DNA strands,

o

o

2

[A ] [B

]

C s

o

o

2

At any subsequent time in the reaction, simple mass conservation indicates that the con-

centrations of single strands remaining will be [

A ] [B

] C,

where

C

is the total instan-

taneous concentration of each strand at time

t. This allows us to write the rate equation

for the renaturation reaction as in terms of the disappearance of single strands as

dC

k2C 2

dt

We can integrate this directly from the initial concentrations to those at any time

t,

t

dC

k2dt

C 2

0

which becomes

1

1

k2t

C

C

s

and can be rearranged to

C s

1

k2tC

s

C

C

fs

1

C

(k2tC

s 1)

s

where

fs is the fraction of original single strands remaining.

When

fs 0.5, we call the time of the reaction the half time,

t1/2 . Thus

k2t1/2 C

s 1

or

t1/2

1

k2C s

measurements on bound dyes. To convert

C

0

to

C s , we have to know something about the

sequence of the DNA. Suppose that our DNA was the intact genome of an organism, with

N base pairs, as shown schematically in Figure 3.13. The concentration of each of the two

strands at a fixed nucleotide concentration,

C

0 , is just

C

s

C

0

2N .

write the product of

k2, the concentration and half-time, as

k2t1/2 C s

k2t1/2 C

0

1

2N