Goldfarb D. Biophysics DeMYSTiFied

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232 Biophysics De mystifieD

that the term coil (in the expression, helix-coil) is short for random coil. The

melting transition, or helix-coil transition, is from a highly ordered helical state,

to a less ordered random-coil state. That is, in the coil state, the polymer has a

no specific secondary structure. Instead the polymer chain is randomly config-

ured like a piece of string or rope tossed aside.

Proteins typically contain both helical and nonhelical (beta-sheet) secondary

structures. So denaturation in proteins includes helix-coil transitions only to the

extent that the protein molecule contains helical structures. By contrast, nucleic

acid secondary structure is almost exclusively helical, with some exceptions

such as kinks and loops. Even cruciform and stem-and-loop formations are

structures made up mostly of helix. Therefore denaturation or melting in

nucleic acids always involves a helix-coil transition. Also, in double-stranded

DNA, the transition from helix to coil involves going from a double-stranded

to a single-stranded conformation. And formation of single-stranded regions in

DNA is a natural part of DNA function. Table 10-2 compares denaturation in

DNA and proteins.

TABLE 10-2 comparison of denaturation in dNA and proteins.

DNA Proteins

Common

terms for

denaturation

Melting, helix-coil

transition.

Denaturation, unfolding.

Helix-coil

transition

Always. Only to the extent that the protein

contains some alpha-helix seg-

ments.

Reversibility Relatively easy. Typically not reversible, but may

be under specific conditions.

Biological

function

Helix-coil transition is

an intrinsic part of nor-

mal function. DNA must

unwind, and later wind

back up again, during

transcription, replica-

tion, and other func-

tions.

Protein folding is the final part of

protein construction, in order for

a protein to become useful. Some

conformational changes take

place during biological function,

but denaturation is typically

destructive rendering the protein

useless.

DNA Melting Studies

One of the ways we can unwind DNA is by raising the temperature. Anything

that denatures a nucleic acid or protein to is called a denaturing agent. Denatur-

ing agents that unwind DNA include temperature, strong acids, strong bases,

chapter 10 Nucleic Acid Biophysics 233

alcohols, and certain organic compounds such as urea and formamide. All of

these are typically used in the laboratory. In cells, there are enzymes that can

catalyze the unwinding of DNA. The most common of these is an enzyme

called helicase. We will see later that other enzymes also affect the unwinding

of DNA, but indirectly, through modifying the DNA’s tertiary structure. In

addition to this, some proteins that bind to DNA specifically stabilize the

unwound state, and so contribute to a favorable free-energy change for unwind-

ing the helix.

DNA melting studies are usually done by slowly raising the temperature of

a sample of DNA. Alternatively one can gradually add a chemical denaturing

agent. The melting transition can be detected in a variety of ways. The two most

common are measuring absorbance at a wavelength of 260 nm or measuring

the average excess heat capacity. Let’s talk about each of these. Nucleotide

bases absorb ultraviolet light with an absorption maximum at 260 nm. When

the bases are stacked in a helical structure (even single stranded), some of the

absorbance is quenched. This is because the electrons that participate in base-

stacking interactions are energetically constrained from absorbing photons. As

the helix melts, base-stacking interactions are lost and absorbance increases,

reaching a maximum when all of the molecules in the sample are completely

in the coil state. This can be seen in Fig. 10-8.

The halfway point of the melting transition is called the melting temperature

and is designated T

. It is at this temperature where we interpret it to mean

that the molecules are, on average, halfway melted. However, depending on

Temperature (°C)

Fractional increase in

absorbance at 260 nm

50 70 90

FIgure 10-8 • Absorbance melting profile for

poly-A/poly-T, a synthetic DNA double helix

consisting entirely of adenine nucleotides on one

strand, and thymine nucleotides on the other.

234 Biophysics DemystifieD

how energy is distributed among the molecules some may be more than halfway

melted, and others less.

The average excess heat capacity is another convenient way to measure the

melting transition in DNA. Heat capacity is defined as the amount of heat

required to raise the temperature of a sample by one degree. At the point where

the sample undergoes the melting transition, some of the energy goes into

unwinding the helix instead of into raising the temperature. So the heat capac-

ity (the amount of energy required to raise the temperature) appears to increase.

At temperatures above the transition, the heat capacity is again similar to what

it was before the transition. This is because energy is no longer needed for the

melting transition and so all of the energy again goes into simply raising the

temperature. Figure 10-9 shows the average excess heat capacity as a function

of temperature for poly-A/poly-T. We can measure heat capacity as a function

of temperature using an instrument called a differential scanning calorimeter. The

term differential is used because it measures the difference between energy flow-

ing into our sample and energy flowing into a reference sample such as plain

water. Scanning is used simply because we are scanning over a range of tempera-

tures as we gradually raise the temperature. And a calorimeter is of course

(see Chap. 2) an instrument for making thermodynamic measurements.

Temperature (°C)

Excess heat capacity (kcal/mol/degree)

Poly-A/poly-T

50 60 70 80 90

FIgure 10-9 • Heat capacity melting profile for poly-A/poly-T.

chapter 10 Nucleic Acid Biophysics 235

The two typical methods for following the helix-coil transition in DNA have

advantages and disadvantages. Absorbance spectroscopy requires only a small

amount of DNA, but it does not give direct thermodynamic data except for the

melting temperature. Differential scanning calorimetry provides direct thermo-

dynamic measurement of the heat capacity, enthalpy change, and melting tem-

perature. These in turn can be used to calculate the entropy change and Gibbs

energy change, but calorimetry requires relatively large amounts of DNA for

each experiment.

Synthetic versus Natural Nucleic Acid Melting Studies

By chemically synthesizing DNA (as opposed to extracting natural DNA from

a living cell), we can create DNA with a much simpler nucleotide sequence

than is found in nature. Simpler DNA is easier to understand, and studying such

DNA provides insights that can then be applied to understanding more com-

plex natural DNA. When the nucleotide sequence is simple and repetitive

throughout the molecule, we say that the sequence is homogenous. An example

is synthetic poly-A/poly-T where one nucleotide strand is made of entirely

adenine residues and the other strand is entirely thymine residues. Another

common laboratory example is poly-AT, where the sequence of both strands

consists of alternating adenine and thymine resides, as shown here.

5’ ATATATATATATATATATATATATATATATAT 3’

3’ TATATATATATATATATATATATATATATATA 5’

In contrast to these synthetic DNA, the sequence of natural DNA is heterog-

enous. Melting studies of homogenous and heterogenous sequence DNA have

shown clearly that the sequence of DNA has a significant effect on how the

molecule unwinds.

Model for Helix-Coil Transition in Homogenous DNA

We envision the helix-coil transition in synthetic, homogenous sequence DNA

to take place as follows: As the temperature is raised, unwinding begins at mul-

tiple locations along the DNA double helix. These locations, where unwinding

begins, are more or less random, with one exception: the ends of the molecule

tend to melt first. The number of different locations where melting begins can

vary from molecule to molecule. In part this depends on the length of the mol-

ecule. A longer DNA molecule is more likely to have unwinding occur simul-

taneously at more locations along the helix, than a shorter DNA molecule.

236 Biophysics DemystifieD

Once unwinding begins it then proceeds in a zipper-like fashion in both

directions from each location where it began. (Of course, unwinding that begins

at the ends of the molecule obviously can only proceed in one direction: away

from the ends and in toward the center of the molecule.) Figure 10-10 illus-

trates this model of melting in homogenous sequence DNA.

Unwinding at the Ends or in the Middle in Homogenous DNA

Although melting begins at several more-or-less random locations along the

helix, the exception to this rule is that the ends of the molecule are most likely

to begin melting first. The reason for this is simple. The Gibbs energy change

for unwinding a nucleotide base at an end of the molecule is more negative

than it is for unwinding a base in the middle of the molecule. We can under-

stand this better by taking a close look at the Gibbs energy change for unwind-

ing the very first few bases (or base pairs) in an otherwise completely helical

molecule.

FIgure 10-10 • Model for the helix-coil melting transition in homogenous

sequence dNA.

Fully wound double helix.

Unwinding begins at ends.

Unwinding continues.

Additional unwinding

begins at multiple

locations along the

nucleotide sequence.

DNA strands separate

when fully unwound.

Unwinding continues in a

zipper-like fashion.

chapter 10 Nucleic Acid Biophysics 237

When the entire molecule is in the helical state, each base is constrained

within the geometric parameters as noted in Table 10-1. The force holding the

bases in their helical conformation comes primarily from base-stacking interac-

tions. In the case of a double helix, hydrogen bonds between base pairs also play

a role, but the majority of the energy still comes from the aromatic stacking

interaction. Let’s say we have a DNA molecule with its bases entirely in their

helical conformation. The Gibbs energy change for shifting a single base from

its helical conformation to the random-coil conformation has two components.

Recall that G 5 H 2 T S. The first component is the enthalpy change

H

necessary to overcome the stacking interaction. (We can ignore the enthalpy

needed to break the base pair hydrogen bonds because its contribution is small

compared with the enthalpy of stacking interactions and because we have to

break the same number of hydrogen bonds regardless of whether the base is in

the middle or at the end of the DNA strand.) The second component is the

entropy change S for a single base to going from its helical to random-coil

conformation. Remember that entropy is a measure of how many different

ways there are to achieve a given state or energy level.

For a given helical conformation (as specified in Table 10-1), there is pretty

much only one position, one way, for the base to be situated. However, once

the stacking interaction is broken, the base is free to swivel about. The covalent

bond that attaches the base to the deoxyribose allows the base to freely rotate.

Only steric interactions (bumping into other parts of the molecule) limit its

motion. This free rotation allows a lot of different positions for the individual

base, all of which have the same amount of energy, and all of which are the

ways to achieve the random-coil conformation. Therefore the random-coil con-

formation represents a much higher entropy state for the base than when it is

constrained into its position within the helical conformation.

Now let’s compare the case where the first base to unwind is at the end of

the molecule, versus the case where the first base to unwind is in the middle of

the molecule. Both components of the Gibbs energy contribute to making it

more likely that a base at the end of the molecule will unwind before a base in

the middle of the molecule. At the end of the molecule, the last nucleotide base

has an adjacent base on only one side. So there is only a single stacking interac-

tion to overcome. At temperatures just below the melting temperature, H is

only slightly positive, representing the amount of energy that must be added to

the molecule to break the single stacking interaction. However, in the middle

of the molecule, there are adjacent bases on both sides of any given base, so

there are two stacking interactions to overcome. H for overcoming the stacking

238 Biophysics DemystifieD

interaction is more positive for the base in the middle of the molecule. The base

at the end of the molecule, with the smaller positive H, is that much closer to

having a negative G and spontaneously unwinding.

The second component of the Gibbs energy, entropy, also makes it more likely

that, for a homogenous DNA, the end of the molecule will unwind first. We just

saw that the entropy change for a single base going from its helical state to its coil

state is positive, since there are more ways to achieve the coil state. A positive

entropy makes a favorable contribution to the Gibbs energy change (G 5 H 2

T S). But a single, coil state base in the middle of the molecule is not as free to

move as a single, coil state base at the end of the molecule. In the middle of the

molecule, our lone, coil state base is surrounded on both sides by bases that are

still constrained in their helical state. This limits the movements of both the sugar

phosphate backbone and of the coil base itself. A single, coil state base at the end

of the molecule has more ways that it can move and still be in the random-coil

conformation for that base. In both cases S is positive. But for the base at the

end of the molecule S is larger. Both the larger S and the smaller H for the

end base make G more negative for the base at the end of the molecule than it

is for the base in the middle of the molecule. Figure 10-11 compares unwinding

When unwound, the movement

of a base pair in the middle is

still constrained, due to the

DNA backbone.

Unwound bases at the end of

the molecuIe have much

more freedom of movement.

A base in the middle has stacking

interactions on both sides.

A base on the end only has

stacking interactions on

one side.

FIgure 10-11 • Unwinding the very first base.

chapter 10 Nucleic Acid Biophysics 239

the first base pair in the middle of the molecule, with unwinding the first base

pair at an end of the molecule.

Unwinding Continues

Once we have melted a single base, unwinding an additional base next to the

already unwound base is still more likely at the end of the molecule than it is

in the middle of the molecule. Regarding bases in the middle, unwinding a

second base next to the first is easier than it was to unwind the first base,

because we now only have a single stacking interaction to overcome. But it is

still less likely than continuing the unwinding at the end of the molecule. Why?

The answer in this case involves only the entropy component of the Gibbs

energy. It is true that in the middle of the molecule, unwinding the second base

increases both its own entropy and the entropy of the first unwound base, since

the first base is now also less constrained (since it now has a melted base on one

side). However, both bases in the middle of the molecule are still more con-

strained than two melted bases at the end of the molecule. This is illustrated in

Fig. 10-12. The two melted bases in the middle of the molecule are still some-

what limited in their ability to move, because together they are attached on

both sides to bases that are still in their helical state. However, at the end of the

Still constrained, due to the

DNA backbone.

A second unwound base in the middle

adds to the freedom of movement of the

first unwound base, but both are still

somewhat constrained since the DNA

backbone is held in place by base pairs

on both sides.

Unwinding a second base at the end

produces even more freedom of

movement for the first unwound base.

This is because it also increases

freedom of movement for the DNA

backbone.

A second unwound base at the end still has

more freedom of movement than a second

unwound base in the middle.

More freedom of movement.

FIgure 10-12 • Unwinding the second nucleotide base.

240 Biophysics DemystifieD

molecule, only one of the two unwound bases is attached to a base in its helical

state. This gives these two unwound bases a larger degree of freedom than the

two unwound bases in the middle of the molecule. In other words

S is larger

for unwinding the second base at the end of the molecule than for the second

base near the beginning of the molecule.

This same logic can be continued for unwinding the third nucleotide base,

and the fourth, and so on. However, as we unwind more and more adjacent

bases, the loop in the middle of the molecule gets larger and larger. As the loop

gets larger, it gains freedom to move about. The constraining effect of having

both sides of the loop attached to helical regions of the molecule becomes

smaller. It is still not as free to move as an unwound region (of the same size)

at the end of the molecule, but the difference between them becomes smaller.

Eventually, if we unwind a large enough segment of the molecule, the Gibbs

energy change for unwinding the entire segment is approximately equal regard-

less of whether that segment is in the middle of the molecule or at the end.

Unwinding at the end will only be slightly more likely than unwinding at the

middle. See Fig. 10-13.

Unzipping DNA

There is another aspect of DNA melting worth looking into. Why does unwind-

ing of additional bases or base pairs typically continue in a zipper-like fashion,

from where unwinding began? Why not simply unwind single bases here and

there throughout the molecule? The tendency of bases or base pairs to unwind

As an unwound portion in the middle becomes

large, its freedom of movement becomes more

like that of the unwound ends.

FIgure 10-13 • As an unwound portion in the center of the molecule gets

large, the freedom of movement of the unwound loop begins to approximate

that of an unwound end.

chapter 10 Nucleic Acid Biophysics 241

next to already unwound bases is a type of cooperativity (which was briefly

discussed in Chap. 2). In fact the tendency is so strong that it is almost impos-

sible to open or unwind just a few base pairs. Instead, entire segments of the

helix tend to unwind together very quickly, almost simultaneously. The number

of nucleotides that tend, on average, to unwind together is called the cooperative

unit length. The cooperative unit length can vary depending on the size of the

DNA molecule, the sequence and homogeneity of the bases, and various envi-

ronmental conditions (temperature, salt concentration, etc.). We can explain

the cooperative nature of the helix-coil transition in two ways. First, using logic

similar to what we used previously, unwinding a base next to an already

unwound base takes less energy (enthalpy) compared with unwinding a base

that is surrounded on both sides with bases in their helical state. This, as men-

tioned, is because there is only one aromatic stacking interaction to overcome

instead of two. We can also explain this cooperativity in terms of entropy, and

within the context of entropy considerations, there are two competing entropy

effects, one that favors cooperativity and one that works against it.

The two entropy effects that affect cooperativity are (1) the entropy change

due to unwinding an additional base pair as part of an already unwound seg-

ment (as opposed to unwinding a lone base pair surround by helical bases) and

(2) the entropy of the entire molecule in terms of unwinding long segments of

the molecule versus unwinding single bases or smaller segments scattered about

along the length of the helix. The first entropy effect was discussed above.

Unwinding bases next to an already unwound region increases the size of that

region, which in turn increases the mobility of that region. This is so regardless

of whether the region is at the end of the molecule or a loop in the middle. This

increased freedom of movement means increased entropy, more ways in which

the molecule can achieve the same energy state. So unwinding bases next to an

already unwound region has a more favorable entropic contribution to the

Gibbs energy change, as compared with continuing the unwinding by starting

to unwind new regions of the molecule.

Notice that the same logic that told us it’s easier to unwind DNA at the

ends of the molecule as compared to unwinding in the middle of the molecule

also tells us that it’s easier to unwind the DNA in a zipper-like fashion, that

is, continuing to unwind a region that has already begun to unwind as opposed

to starting to unwind an all new segment. One could ask the question why

unwinding would even begin at more than one location in the first place. Why

doesn’t unwinding just begin at the ends and proceed toward the middle until

it’s done?