Secondary Structures

Secondary and tertiary structure are the short-scale and long-scale order in the monomers’ positions, respectively.

The main secondary structures of proteins were discovered in the 1940–

1950s by a chemist Linus Pauling (1901–1994) at California Institute of Technology in Pasadena near Los Angeles (these studies were an important part of the work for which Pauling was awarded the Nobel prize in Chem-istry in 1954; by the way, he also won the Nobel Peace prize). They are called ↵ and structures. They are made stable by the hydrogen bonds.

In fact, the reason why the loops of the helix and the -folds are formed is simply that this is the arrangement that achieves the maximum saturation of the hydrogen bonds.

Both ↵- and -structures of polypeptides are quite universal, their struc-ture is only marginally dependent on the sequence of aminoacids (this

dependence, however small, might still be important, for instance, some aminoacids make ↵-helix more likely, others promote -strands, and yet others prefer to be in the loops between secondary structure elements).

The cartoon of ↵-helix is shown in the Figure C5.8, while similar cartoon of the -sheet is presented in Figure C5.9.

The most common secondary structure of DNA was discovered in 1953 by Francis Crick and James Watson at the University of Cambridge in England using the experimental data of Rosalind Franklin at King’s College in London — it is the famous Watson and Crick double helix. The discovery of the double helix has won a firm and very fair reputation as one of the major achievements in the history of science. The striking beauty of the double-helix model of DNA is the way it explains, with brilliant ease, one of the real marvels of nature — the ability of all living things to reproduce themselves. Indeed, as soon as the two complementary strands move apart, they form something like a pair of “printing plates” or templates which are ready to make two identical copies. This is exactly how biological inheritance occurs at the molecular level. The canonical Watson–Crick double helical DNA is shown in Figure C5.10.

We should also mention in passing that some DNA sections, with par-ticular types of primary structure, may form very unusual — called also non-canonical — secondary structures under certain conditions. These structures are di↵erent from the familiar Watson-and-Crick right-handed double helix (which in this context is called the B-form). In particular, if the DNA is torsionally stressed (e.g., by improperly forming a ring or by magnetic tweezers in the lab), its parts can form a left-handed double helix (the Z-form). There is a possibility to make a triple helix (the H-form), and so on. As another example, you can encounter palindromes in the pri-mary structure of segments of DNA. These are sentences which read the same in both directions; a few funny examples in English are “A man, a plan, a canal — Panama”, “Draw pupil’s lip upward!”, “And DNA”, etc.

Palindromic bits of DNA often take the shape of a cross (Figure 5.11).

There can be some unfavorable conditions when secondary structures do not develop in biopolymer chains. This can be seen upon a close look at the Figure 2.12: it shows electron micrograph of some DNAs prepared under the conditions of very low salt concentration in solution. Under such conditions, negatively charged phosphate groups of the opposite DNA strands repel strongly and this leads to the unwinding of the double helix at least in some places, shown by arrows in the Figure 2.12. More generally, if the temperature is increased, or some low molecular weight substances

72 Giant Molecules: Here, There, and Everywhere

Fig. 5.11 The cross-like structure of a palindromic strand of DNA. To make this struc-ture possible, the sequence must be symmetric, or be a palindrome. The second string’s palindrome is not identical, but complementary to the first string’s one.

a b

Fig. 5.12 DNA strands: (a) in a double helix, and (b) in the molten state.

(such as salt) are added to the solution (or removed from it), it can cause untwisting of the helices, called a helix-coil transition. This transition has this name because a spiral-shaped polymer chain is rather rigid, whereas a non-spiral one is a relatively flexible coil (Figure 5.12). Therefore the helix-coil transition is also called the melting of the helix. The physics of helix-coil transition is of great interest.

Helix-coil transition is beautifully used in PCR. Indeed, once new copies of DNA strands are produced tightly wound with their templates of the previous generation. To unwind them and to make them serve as templates once again, experimenter raises temperature, causing helices to undergo helix-coil transition and complementary strands to di↵use away from each

other, after which temperature can be lowered again to repeat the whole process. In fact, historically, the decisive step in implementing PCR as a routine reliable procedure was to employ the DNA polymerase enzyme (so-called Taq polymerase) isolated from a thermo-stable organism (typically the bacterium Thermus aquaticus) which can withstand multiple heating-cooling cycles.

The analogy of helix-coil transition with the ordinary melting of solids is particularly appropriate since both transitions occur very sharply with increasing temperature, over a narrow temperature range. As in melt-ing, helix-coil transition is accompanied by considerable absorption of heat which is used to break the hydrogen bonds forming the helix. Furthermore, just as a crystal melts in big pieces, not atom by atom, in a similar way in helix-coil transition, not only are individual turns of the helix destroyed (this would be similar to the melting of individual cells of a crystalline lattice), but whole chunks of the helix break down. This is a cooperative e↵ect, i.e. the loss of one turn helps the neighboring one to fall apart.

Thus, the analogy between ordinary melting and the helix-coil “melting”

is rather pervasive, but. . . However good is the analogy, in some ways the helix-coil transition is di↵erent from ordinary melting. The main di↵erence is that spiral and non-spiral strands do not separate out (as, say, regions of ice and water do in a winter river or in your glass of a drink with chunks of ice), but they are mixed along the chain. In the language of theoretical physics, we can say that phase segregation does not occur in the helix-coil transition, and, therefore, strictly speaking, this is not a phase transition.

The theoretical interpretation of all this is rather interesting. Appar-ently, the helix-coil transition is indeed a real melting process, although not of a three-dimensional crystal, but of a dimensional one. In the one-dimensional world, melting is a rather rapid process, but it does not lead to phase separation. This fact is known to physicists as Landau’s theorem

— because it is briefly mentioned in one of the volumes of the 10-volume

“Course of Theoretical Physics” by Lev D. Landau and Evgenii M. Lifshitz.

It is also interesting that a real heteropolymer with a non-uniform pri-mary structure does not melt as sharply as a specially prepared homopoly-mer. Figure C5.13 explains why. It compares polymers with di↵erent pri-mary structures showing their melting curves. These are dependencies of the helical fraction # (sometimes also called helicity; it is the fraction of helical units in the chain) on inverse temperature T ¹. Two uniform ho-mopolymers, sayA A . . . A and B B . . . B, both melt rather sharply, but at di↵erent temperatures. (For example, the di↵erence in

74 Giant Molecules: Here, There, and Everywhere

melting point for DNA molecules which consist only of A T pairs or only of G C pairs is as big as 40 C) — see Figure C5.13 a. Obviously, a copolymerA A . . . A B B . . . B would melt in two stages (see Figure C5.13 b). Hence it is not surprising that the melting of a real het-eropolymer with a complex sequence of monomersA and B is a somewhat gradual process (Figure C5.13 c).

These di↵erences in behavior become even more obvious if we look at the so-called di↵erential melting curves – dependencies of the derivative

@#/@T on the inverted temperature, T ¹ (lower graphs in Figure C5.13).

Di↵erential melting curves characterize the slope of the #(T ¹) dependen-cies (upper graphs in Figure C5.13). Typical di↵erential melting curve looks like a set of peaks, and Figure C5.13 explains why: if a peak is observed at some particular temperature T0, then it suggests melting of a particu-lar piece of the helix at or around T0 — namely the piece whose primary structure happens to mix “stronger” and “weaker” base pairs in such a proportion as to melt at T0.