Obsolete models of DNA structure

File:Watson-Crick double helix.gif

Fig. 1A. Watson-Crick plectonemic structure

Fig. 1B. Example of non-helical (paranemic) structure

That DNA has a variety of possible structures is well-established, most of them being either right-handed or left-handed helices. This article describes the settings in which a non-helical structure for DNA is necessary to explain the published data.

Fig. 1A (above) shows the now-traditional Watson-Crick helical structure, and Fig. 1B shows one example of a non-helical structure.

Terminology

The term "helical", in this article, refers to net helicity. In Fig. 1B, there is no helical twist at all. But in some non-helical structures, to be described presently, there are equal numbers of right-handed and left-handed twists, yet the net number of helical twists remains zero.

The strands of a helical DNA duplex, if covalently closed into a circular structure, are topologically linked, and cannot be separated without breaking one or both strands. This sort of structure is referred to as "plectonemic" (British: "plectonaemic"). The model below, made from rope, illustrates the knot which forms when one attempts to separate the intact strands of a plectonemic circular duplex:

In order to separate these rope circles, at least one must be cut open, and every twist must be painstakingly removed. In actual circular DNA replication, not only does every twist need to be removed, but the twists must then be all re-wound in the next generation.

In contrast, the strands of a non-helical DNA duplex are topologically non-linked, and can be separated without strand breakage. This sort of structure is referred to as "paranemic" (British: "paranaemic"). The paranemic rope model is rather trivial:

The abbreviation "TN", to refer to any DNA structure whose strands are topologically non-linked, has been proposed

Historical background

Most of the details of the "traditional" Watson-Crick structure have been proven beyond all doubt, but, as we shall see, one aspect of the structure, namely the helical twist, has been problematical from the outset.

In commercial applications of molecular biology, where scientists typically deal with short lengths of deproteinized DNA (destined, for example, to be used as cloning vectors), the presence or absence of a helical twist really doesn’t matter very much. But it would be highly-desirable to know much more than we do about the structure of DNA inside the living cell nucleus, a place where our knowledge remains in the realm of cartoon representations and artists’ conceptions, and far-removed from that most-desirable realm of exact virtual modeling which characterizes much of the rest of molecular biology.

Does DNA have a helical twist inside living cells? We do not know. The problem is that, with few exceptions, the structure of DNA in its normal chromosomal environment cannot be studied directly, because the tools ordinarily used to probe DNA structure are destructive to that environment.

The primary tool has always been x-ray crystallography. Concerning this tool, however, Francis Crick himself said, with respect to the adjudication of the question of helicity vs. non-helicity:

..."we consider it unwarranted to rely solely on the details of exact model building...nor is it advisable to put one’s faith completely on the fine details of X-ray diffraction patterns. That of the B form has always been rather poor and may not yield a clear, unambiguous decision between the two alternative types of structure. One must turn to evidence of quite a different type."

In addition to the poverty of the fine details, there are serious conceptual limitations in the fundamental design of the X-ray crystallography studies themselves. In order to use the tool, the DNA must be forcefully separated from the approximately equivalent mass of protein with which it is invariably associated in all known cell types. These proteins (histones, protamines, etc.) always have a powerful positive charge, due to their preponderance of the basic amino acids arginine, lysine and histidine, whereas DNA has a powerful negative charge. The possibility that normal native DNA structure (whatever it proves to be) may require the presence of the positively-charged proteins is rarely discussed. If, however, the close proximity of positively-charged proteins does in fact alter DNA structure, then the native structure may be completely destroyed when the DNA is extracted and the proteins removed.

Another potentially severe limitation of x-ray crystallography is that it requires a relatively dehydrated form of DNA, whereas the intracellular environment has a humidity of 100%.

Thus, the evidence that DNA has a helical twist inside cell nuclei is, of necessity, indirect. When the situation is examined in detail, it emerges that the hard evidence in favor of "traditional" Watson-Crick helicity in intracellular DNA boils down to two key observations:

1. The individual single strands of small circular viral and plasmid DNA are inseparable under the usual types of denaturation conditions, supporting a plectonemic, i.e., twisted structure whose strands are topologically locked together, and

   
   

2. Enzymes theoretically capable of unwinding and rewinding the presumed Watson-Crick twists, namely topoisomerases and gyrases, seem to be necessary for DNA replication in various in vitro synthesis systems.

With respect to observation (2), one needs to keep in mind that there is an important difference between topoisomerases/gyrases, and the enzymes known to participate in DNA synthesis in the replicative fork. The latter enzymes are so well-coordinated that Lehninger refers to their various activities as "elegant enzymatic choreography". Their locations, specific actions and timings are known in great detail. This is not the case, however, for the winding/unwinding enzymes. They are not known to participate in the activities within the replicative fork. Where exactly do they work? At what point in the replication process do they act? These things are not known. It therefore cannot be said that their roles in normal DNA synthesis have been proven.

Circular DNA created conceptual difficulties in DNA replication

Doubts about the helicity of DNA in vivo began in 1963, when John Cairns published his famous autoradiographs of the E. coli chromosome, showing it to be, topologically speaking, a double-stranded continuous circle. Such a structure, if it had the form of a Watson-Crick double helix, would have some 400,000 helical twists, each of which would have to be be removed in as little as 20 minutes, if the strands are to separate during cell replication. This creates a two-part problem, one part topological and the other mechanical. The topological part is the necessity of discovering a scheme for breaking one or both strands open, to make possible the required unwinding. The mechanical part relates to the rapid spinning of the chromosome as it unwinds (the "angular momentum" problem).

Cairns, at that time, recognized the topological problem only. He proposed that the twists were unwound by means of a hypothetical "swivel", a sort of molecular biological "universal joint" about which the DNA, presumably nicked in one or both strands, would be free to rotate as necessary for the un-winding/re-winding operations.

This, however, solved only the topological problem, but obviously failed to address the angular momentum problem, namely the apparent need of the chromosome to be spinning at about 20,000 rpm (20x faster than an electric drill!) throughout the life of the bacterial cell.

In time, there came to be a gradual realization that DNA synthesis is discontinuous, so that only a small part of the chromosome had to be spinning at 20,000 rpm at any one time. Moreover, the topologically-active enzymes topoisomerase and gyrase were discovered, which could nick and re-seal the strands, thus allowing for the presumed winding/unwinding operations.

This solved the various problems, conceptually at least. By that time, however, a number of researchers had already rejected the helical structure for DNA as being a mere laboratory artifact, and had begun exploring non-helical structures for chromosomal DNA in living systems.

The evidence in favor of non-helicity, while still inconclusive, has increased so much through the years that it cannot be properly ignored.

First non-helical structures proposed

Fig. 2. Rodley Side-By-Side structure (2AW8).

In 1976, Gordon Rodley and his co-workers published the first non-helical DNA structure, which they named the "side-by-side" (hereafter "SBS") structure. A rotating model appears in Fig. 2.

(A similar model was published a few months later by Sasisekharan and his associates.)

The SBS structure was purely hypothetical, that is, it was not based upon any physical evidence. It was created to provide a theoretical solution to the angular momentum problem in DNA replication, which Rodley believed to be otherwise unsolvable.

The SBS structure can be readily understood as being a relatively minor modification of the original Watson-Crick structure where, instead of one fully-right-handed helical twist every 10 base pairs, there is, instead, only a half-twist of 5 base pairs’ length, followed immediately by a half-twist in the opposite direction, that is, a left-handed half-twist, also of 5 base pairs’ length. This alternating pattern of right- and left-handed half-twists is repeated throughout the length of the chromosome, resulting in an undulating ribbon-like structure which, topologically speaking, has no net twists.

Such a chromosome does not need to either spin or unwind during replication.

The publication of the Rodley structure produced a small but significant ripple of interest in the molecular biological community. The level of interest was sufficiently high that Crick, by that time one of the world’s most influential scientists, publicly suggested that the SBS structure, whose existence he doubted, should be laid to rest by intentionally creating it. Then, he reasoned, its properties could be ascertained, and shown to be abnormal with respect to the known properties of native DNA.

Two investigations followed closely on the heels of the Crick suggestion, but both were seriously compromised, wherefore the SBS structure was not laid to rest. The value of the first investigation was compromised in that it employed certain experimental methods previously proven to be ineffective. The value of the second investigation was even more compromised in that it was never formally published.

The first investigation was done by Stettler et al, who isolated the intact circular single strands of a circular duplex viral chromosome (a laborious process in those days), then allegedly re-annealed them in 1M salt, at pH 8.5, 60º. This re-annealed product, they declared, was SBS DNA, i.e., a base-paired circular duplex with no net helical twist. They then went on to demonstrate that the electrophoretic mobility of their product was clearly different from that of the native chromosome.

The problem with the study was that these workers ignored several published papers on the subject of the re-annealing of denatured circular DNA, the most important of which were by Robert Warner and his associates. Circular DNA has strikingly different physical properties compared with its linear counterpart. One of these differences is that at any given temperature and ionic strength, there is only a tiny range of pH within which a denatured circular structure can be induced to re-anneal. This behavior stands in stark contrast to that of linear DNA, which is easy to denature and easy to re-anneal.

The following are the renaturation curves for denatured circular DNA in 1M salt, as a function of pH , at the indicated temperatures. Note the fastidiousness of the requirement for a narrow range of pH, at each temperature used:

Renaturation data from the work of Strider, Camien & Warner, showing that denatured Form I DNA (“Form IV”) will not renature except under very narrow conditions of pH, temperature and ionic strength.

Fig. 3
Adapted from: Strider W, Camien MN & Warner RC (1981). Renaturation of Denatured, Covalently Closed Circular DNA. J Biol Chem, 256, 7820-7829. PMID 6455418. © the American Society for Biochemistry and Molecular Biology.

It is easy to see that at 60º, the percent renaturation would have fallen to zero somewhere between pH 10-11. There is thus no chance whatsoever of reconstitution of the normal base-paired native structure in 1M salt at pH 8.5, the re-annealing conditions employed in the Stettler study. The only known DNA renaturation product which can appear under these circumstances is "Form IV" (see below), which is a non-base-paired artifact.

The second investigator, and the source of the above-referenced unpublished study, was Robert W. Chambers, who discovered, quite unexpectedly, that the separated strands of the circularized chromosome (RF, or "replicative form") of the virus ΦX174, when merely incubated together in the refrigerator for several months, regenerated the native structure with its physical properties restored! This obviously contradicts Stettler et al, but Chambers, who was neither seeking nor expecting this result, never published it

Why? Chambers believed that the re-appearance of the native structure came about because of (1) spontaneous strand breakage, followed by (2) spontaneous re-annealing of a circular half-chromosome with its linearized complementary strand, followed by (3) spontaneous repair of the nick in the linearized strand (Fig. 4):

Fig. 4

The thermodynamics of this explanation is highly doubtful, since a DNA solution is a system within which the net tendency is unequivocally in the direction of strand breakage. Whereas the spontaneous repair of a nicked DNA strand may occasionally be seen, the net accumulation of repaired chromosomes, in a system in which nicking is thermodynamically favored, would be a clear violation of the 2nd Law of Thermodynamics.

Furthermore, native DNA is superhelical (see below) to an extent which cannot possibly be attained by spontaneous nicking/sealing operations. (In topoisomerase experiments, the electrophoretic mobility of the topoisomers never exceeds that of the native chromosome). Yet Chambers was certain that his re-annealed DNA had the sedimentation coefficient of native DNA, which means it was superhelically-wound beyond that which is possible through any non-energy-driven spontaneous process. Nevertheless, Chambers believed that the unlikely mechanism illustrated in Fig. 4 was the explanation, and he therefore rejected his own discovery as "trivial".

Definitive re-annealing experiment to prove (or disprove) the non-helicity of circular DNA

Both Stettler et al and Chambers, working with primitive enzyme techniques, had to labor for months to complete their respective studies. Nowadays, thanks to the advent of site-specific, strand-specific nucleases ("nicking" enzymes), it is possible to repeat their experiments in a matter of days, and at little or no cost. Incredibly, for over 30 years since their ill-fated works were done, no one has seen fit to repeat them, even though the future of all nucleic acid structural research may hinge upon the outcome.

A medical doctor, who himself has no laboratory, has published a minutely-detailed protocol, which would allow even a non-specialist with the necessary basic equipment to quickly and inexpensively repeat the Stettler-Chambers re-annealing experiments. As of the posting of this Wikipedia article, however, no one has done so.

Separation of the strands of duplex circular DNA without strand breakage

Human and bacterial chromosomes are far too large to isolate intact, but rather break into innumerable small fragments when extracted from their respective cells. (It should perhaps be specifically mentioned that in the Cairns study, the bacterial chromosome was by no means isolated as a single length of DNA, but rather the unhandled contents of radioactively-labeled E. coli nuclei were permitted to gently fall onto a photographic plate, where they sat for some months, in effect "photographing themselves" by virtue of their radioactivity.)

There exist, however, many species of small viral and plasmid chromosomes which, because of their small sizes, are stable in solution, and remain intact even with vigorous handling. These have been of great value in the study of circular DNA.

The first important work on small circular DNA began shortly after the publication of the Cairns autoradiographs. Early studies quickly revealed that the strands of duplex circular chromosomes do not separate when subjected to conditions which readily denature linear DNA. For example, if calf thymus DNA (a heterogeneous collection of linear fragments) is merely boiled, the strands separate, and when slowly cooled, they re-anneal. In contrast, when the circular chromosomes of such organisms as the replicative form (RF) of the bacteriophage φX174, or the mammalian virus polyoma, are boiled, nothing at all happens to the native structure; they are completely resistant to thermal denaturation. When subjected to high pH (i.e., pH 13), however, these chromosomes do indeed denature (as demonstrated by increased light absorption at 260 nm), but the strands remain physically associated as the previously-mentioned "Form IV", a duplex form whose structure has never been determined. Renaturation of Form IV, as we have seen (Fig. 3 above), requires painstakingly-precise adjustment of pH, temperature and ionic strength.

Without a doubt, the single most skepticism-inspiring aspect of non-helical DNA theory is the failure of the strands of circular chromosomes to separate under conditions where the strands of linear DNA would readily do so. Because this phenomenon was discovered at the very dawn of the era of circular DNA research, c. 1963, it is perhaps not surprising that most scientists have had little sympathy for non-helical DNA structures, which, common sense might seem to suggest, ought to readily undergo strand separation under conditions of denaturation.

But is the failure of the strands to separate really due to topological linkage?

The researcher Tai Te Wu thought not. His studies on DNA structure began in 1969, at which time he made the relatively non-controversial proposal that x-ray crystallographs of purified linear DNA were more suggestive of a tetraplex than a duplex structure. His proposed tetraplex consisted of two Watson-Crick-like duplexes, non-covalently joined together by mutual intercalation of their base pairs (an arrangement already known to exist in structures such as the Gehring tetramer).

This proposal, by itself, was hardly noticed by the molecular biological community. But Wu went on to suggest further that, based upon the increases in pitch which were known to exist in DNA crystals under conditions of increasing relative humidity, extrapolation of these data to 100% humidity, i.e., the humidity inside a living cell, suggested that in the aqueous cellular environment, all secondary Watson-Crick twists would be gone, leaving what he called a "straight ladder" structure, consisting of a pair of totally untwisted duplexes, each with twice the expected base pair spacing, i.e., 6.8 Å. After mutual intercalation of the base pairs of each duplex, the base pair spacing of the tetraplex would be restored to 3.4 Å:

First duplex

+

Second duplex

=

Fully intercalated tetraplex

FIGURE 5

If, as Wu believed, the strands of native circular DNA were not plectonemically intertwined, then they ought to be separable. Since they are not separable under common denaturing conditions, he set out to find new conditions for effecting their separation.

In 1996 he reported having found such conditions, and having employed them to separate the fully-intact single strands of several different circular duplex plasmids. If Wu’s result is to be accepted, then these plasmid chromosomes cannot have had the plectonemic Watson-Crick twisted structure, whose strands are inseparable unless one or both are nicked.

The method Wu used to separate the strands was based upon the fact that RNA transcription occurs on only one strand of the DNA duplex, termed the "sense" strand. The complementary strand, known as the "anti-sense" strand, is not ordinarily a template for RNA synthesis. If DNA is isolated during the process of transcription, D-loops will be seen, consisting on one side of a DNA-RNA hybrid duplex, and on the other side of the temporarily unpaired anti-sense strand of DNA. The principle is illustrated in this highly-exaggerated pictorial representation of the phenomenon, where the RNA is depicted in red:

Fig. 6

It was known, by 1996, that on gel electrophoresis, the bond between DNA and complementary RNA is stronger that the analogous bond between DNA and DNA. Wu proposed to take advantage of this for separating the strands of DNA.

He grew cells to stationary phase, where there is no DNA replication, but plentiful transcription. He chose a system within which there were no dimers or trimers to confuse the outcome. Under these conditions, there is a theoretical difference in the structure of the "sense" and "anti-sense" strands of the DNA, and hence also of their electrophoretic mobility, because one only, namely the "sense" strand, has considerable amounts of bound m-RNA.

In order to facilitate the separation of the strands by electrophoresis, he employed a very low voltage, so that the electrophoresis required 48 hours to go to completion. At 12 hours, the strands had begun to separate into two bands, and at 36 hours the separation was complete:

File:Separation of plasmid strands by electrophoresis.gif

Fig. 7A. Wu DNA at 12, 24 and 36h.

The above animated gif was extracted from the original figure below, in order to facilitate the comprehension of the numerous lanes of gel electrophoresis data:

FIGURE 7B FIGURE 7B FIGURE 7B FIGURE 7B FIGURE 7B FIGURE 7B FIGURE 7B

The yellow arrows indicate the locations of the experimental DNA at 12, 24 and 36 hours. The middle lanes, labeled "L", consisted of control DNA which had intentionally been linearized by treatment with a restriction nuclease. Note that the control DNA did not split into its component strands.

(The left lanes contained a "ladder" of size markers).

The two separated experimental DNA bands were cut out of the gels and identified. Southern blotting, employing DNA sequences known to be in either one or the other strand, demonstrated that the two bands indeed corresponded to the two strands of the chromosome. This was further demonstrated by employing sequences known to be in one or the other strand as primers in DNA sequencing, which only proceeded efficiently in the presence of DNA from the corresponding band of the gel.

The possibility that the strands separated because of inadvertent nicking was excluded by the middle-lane control, which remained a single, sharp band throughout. The question of why the control DNA did not split into two bands also is important, but Wu did not address the question at all.. Nevertheless, in his hands, it was persuasively demonstrated that the separation of duplex plasmid circular DNA into its fully-intact circular single strands not only did take place in the absence of nicking, but absolutely required that absence. Moreover, he demonstrated this in not just one, but two different plasmids, pHTB4 and pUC19

The Wu paper was published in the Journal Of Mathematical Biology, a peer-reviewed journal found in most university libraries. This, however, is a lesser-read journal which ordinarily attracts little attention. As of the date of this Wikipedia article, the Wu study has never been either praised or criticized by any published author. It remains almost totally ignored.

Topology of circular DNA explained by a non-helical model

The topological properties of circular DNA are complex, and only a brief introduction can be presented here. In standard texts, these properties are invariably explained in terms of a helical model for DNA, because the majority of scientists continue to believe that no other structure is possible.

When the sedimentation coefficient, s, of circular DNA is ascertained over a large range of pH, the following curves are seen:

(FIGURE 8)
(FIGURE 8)
(FIGURE 8)
(FIGURE 8)
(FIGURE 8)
(FIGURE 8)
(FIGURE 8)

Three curves are shown here, representing three species of DNA. From top-to-bottom they are: "Form IV" (●-●-●), "Form I" (○-○-○) and "Form II" (Δ-Δ-Δ).

"Form I" (○) is the traditional nomenclature used for the native form of duplex circular DNA, as recovered from viruses and intracellular plasmids. Form I is covalently closed, and any plectonemic winding which may be present is therefore locked in.

If one or more nicks are introduced to Form I, free rotation of one strand with respect to the other becomes possible, and Form II (Δ) is seen.

Form IV (●) is the product of alkali denaturation of Form I. Its structure is unknown, except that it is persistently duplex, and extremely dense.

Between pH 7 and pH 11.5, the sedimentation coefficient s, for Form I, is constant. Then it dips, and at a pH just below 12, reaches a minimum. With further increases in pH, s then returns to its former value. It doesn’t stop there, however, but continues to increase relentlessly. By pH 13, the value of s has risen to nearly 50, two to three times its value at pH 7, indicating an extremely compact structure.

If the pH is then lowered, the s value is not restored. Instead, one sees the upper curve (●). The DNA, now in the state known as Form IV, remains extremely dense, even if the pH is restored to the original physiologic range. As stated previously, the structure of Form IV is almost entirely unknown, and there is no currently-accepted explanation for its extraordinary density. About all that is known about the tertiary structure is that it is duplex, but has no hydrogen bonding between bases.

These behaviors of Forms I and IV are considered to be due to the peculiar properties of duplex DNA which has been covalently closed into a double-stranded circle. If the covalent integrity is disrupted by even a single nick in one of the strands, all such topological behavior ceases, and one sees the lower Form II curve (Δ). Note that for Form II, alterations in pH have very little effect on s. Its physical properties are, in general, identical to those of linear DNA. At pH 13, the strands of Form II simply separate, just as the strands of linear DNA do. The separated single strands have slightly different s values, but display no significant changes in s with further increases in pH.

A complete explanation for these data is beyond the scope of this article. In brief, the alterations in s come about because of changes in the superhelicity of circular DNA. These changes in superhelicity are schematically illustrated by four little drawings which have been strategically superimposed upon the figure above.

In nature, circular DNA is always isolated as a higher-order helix-upon-a-helix, known as a superhelix. In discussions of this subject, the Watson-Crick twist is referred to as a "secondary" winding, and the superhelices as a "tertiary" winding. The following sketch indicates a "relaxed", or "open circular" Watson-Crick double-helix, and, next to it, a right-handed superhelix. The "relaxed" structure on the left is not found unless the chromosome is nicked; the superhelix is the form usually found in nature:

File:Helix-superhelix.jpg

Fig. 9

For purposes of mathematical computations, a right-handed superhelix is defined as having a "negative" number of superhelical turns, and a left-handed superhelix is defined as having a "positive" number of superhelical turns. In the drawing above, both the secondary (i.e., "Watson-Crick") winding and the superhelical winding are right-handed, hence the supertwists are negative (-3 in this example).

Why should native DNA be superhelical at all? In "traditional" Watson-Crick theory, the superhelicity is presumed to be a result of "underwinding". This means that, for some unknown reason, there is a deficiency in the number of secondary Watson-Crick twists. Such a chromosome will be strained, just as a macroscopic metal spring is strained when it is either overwound or unwound. In DNA which is thusly strained, supertwists will appear, according to the following topology equation:

L_k = T + W

L_k, known as the "linking number", is the number of Watson-Crick twists found in a circular chromosome when it is forced (usually in imagination only) to lie in a plane. This number is physically "locked in" at the moment of covalent closure of the chromosome, and cannot be altered without strand breakage. In "traditional" theory, this number is presumed to be abnormally low, because circular DNA, as stated above, is widely believed to be "underwound".

T, called "twist", refers to the number of Watson-Crick twists in the chromosome when it is not constrained to lie in a plane. We have already seen that native DNA is usually found to be superhelical. If one goes around the superhelically-twisted chromosome, counting secondary Watson-Crick twists, that number will be different from the number counted when the chromosome is constrained to lie flat (although it is unlikely that the artist who drew the picture above went to so much trouble as to depict this with mathematical accuracy). In general, the number of secondary twists in the native, supertwisted chromosome is expected to be the "normal" Watson-Crick winding number, meaning a single 10-base-pair helical twist for every 34 Å of DNA length.

W, called "writhe", is the number of superhelical twists. Since "traditional" theory says that circular DNA is "underwound", L_k will generally be less than T, which means that W will typically be negative.

Now we can see that if DNA is "underwound", it will be under strain, exactly as a metal spring is strained when forcefully unwound, and that the appearance of supertwists will allow the chromosome to relieve its strain by taking on negative supertwists, which correct the secondary "underwinding" in accordance with the topology equation above.

The topology equation teaches further that there is a one-to-one relationship between changes in T and W. For example, if a secondary "Watson-Crick" twist is removed, then a right-handed supertwist must have been removed simultaneously (or, if the chromosome is relaxed, with no supertwists, then a left-handed supertwist must be added).

Without going into great detail, let it simply be said that the alterations of s seen in the pH titration curve above are widely believed to be due to changes in the superhelical winding of DNA under conditions of increasing pH. Up to pH 11.5, the purported "underwinding" produces a right-handed ("negative") supertwist. But as the pH increases, and the secondary helical structure begins to denature and unwind, the chromosome (if we may speak anthropomorphically) no longer "wants" to have the full Watson-Crick winding, but rather "wants", increasingly, to be "underwound". Since there is less and less strain to be relieved by superhelical winding, the superhelices therefore progressively disappear as the pH increases. At a pH just below 12, all incentive for superhelicity has expired, and the chromosome will appear as a relaxed, open circle.

At higher pHs still, the chromosome, which is now denaturing in earnest, wishes to unwind entirely, which it cannot do (because L_k is covalently locked in). Under these conditions, what was once treated as "underwinding" has actually now become "overwinding". Once again there is strain, and once again it is (in part at least) relieved by superhelicity, but this time in the opposite direction (i.e., left-handed or "positive"). Each left-handed tertiary supertwist removes a single, now undesirable right-handed Watson-Crick secondary twist.

The titration ends at pH 13, where Form IV appears.

Alkali denaturation data (Fig. 8) according to TN theory

Most molecular biologists automatically assume that the Watson-Crick structure is necessary to explain circular DNA topology. In 2002, however, a paper appeared in which the topology of circular DNA was explained in terms of a topologically non-linked (TN) model.

According to this view, the superhelicity of circular DNA at pH 7 is not due to "underwinding" at all, but simply to the fact that non-helical DNA is, topologically speaking, 50% left-handed. The paper made no attempt to precisely define the distribution of left-handedness throughout the chromosome, with respect to whether the left-handed regions were confined to a discreet area, or rather distributed evenly throughout the structure, or whether perhaps they were simply randomly-distributed and subject to continuous fluctuation.

Regardless, the topology was considered to reflect the energetics which emerge from a consideration of the well-established fact that left-handed, or "Z" DNA is more loosely-wound than Watson-Crick right-handed DNA, as the following picture and table show for a 12-base-pair nucleotide:

[INSERT Z-DNA/B-DNA FIGURE

	Rise per residue	Residues per helical turn	Pitch
B-DNA	3.4 Å	10	34 Å
Z-DNA	3.7 Å	12	45 Å

FIGURE 10

Since Z-DNA does not ordinarily appear at physiological pH, we may safely assume that the 50% of the TN chromosome consisting of Watson-Crick right-handed secondary twists is energetically more favorable. Nevertheless, the TN chromosome is, by its nature, 50% left-handed, "whether it likes it or not". If we may speak anthropomorphically again, the left-handed portions "wish" to be right-handed, which is impossible, but some of the left-handed secondary twists may unwind as right-handed, or negative superhelical turns, in accordance with the topology equation above (L_k = T + W). Since a superhelix is more compact than a relaxed open circle, this therefore accounts for the higher s value for Form I (○-○-○) than for nicked DNA (Δ-Δ-Δ) in the low pH portion of the pH titration curve from Fig. 8, which is reproduced here:

(FIGURE 8 - REPRODUCED)
(FIGURE 8 - REPRODUCED)
(FIGURE 8 - REPRODUCED)
(FIGURE 8 - REPRODUCED)
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(FIGURE 8 - REPRODUCED)

There is very little effect of pH on either the secondary or tertiary structure between pH 7 and 11.5, but as the pH increases beyond 11.5, the hydrogen bonds weaken and the DNA begins to unwind. Since the secondary structure is locked in, unwinding can only be accomplished through changes in tertiary superhelical winding. Initially (i.e., pH 11.5 to about 11.8) this means a decrease in the left-handed ("negative") superhelicity.

Just as the coils of an unwinding spring move farther apart, so do the base pairs of unwinding helical DNA. There comes a point at which the separation between adjacent base pairs is too great for normal Watson-Crick right-handed DNA, with its 3.4 Å spacing, but increasingly favorable for left-handed Z DNA, with its more loosely-wound 3.7 Å spacing. At a pH just below 12, the two forms have become energetically equivalent, wherefore there is no longer any driving force for superhelicity. The superhelical twists therefore disappear, and the chromosome becomes a relaxed, open circle. This is reflected by the dip in the Form I curve, and the open-circular drawing above it (Fig. 8, pH just below 12).

As the pH continues to increase, the unwinding of DNA progresses, until the left-handed, or Z secondary structure suddenly becomes energetically more favorable than the right-handed Watson-Crick structure. Now it’s the right-handed portions of the chromosome which "wish" to be left-handed. That remains impossible, but just as some of the left-handed secondary twists unwound as right-handed ("negative") supertwists at neutral pH, now some of the right-handed Watson-Crick secondary twists unwind as left-handed ("positive") supertwists, wherefore the superhelical structure returns, now in the opposite sense. This causes s to again increase, until it resumes its original value (Fig. 8, pH about 11.8 to 12).

At higher pH (i.e., 12-13), the secondary structure unwinds as much as is physically possible, which can only be accomplished by ever-increasing numbers of left-handed supertwists. The s value therefore increases relentlessly, culminating in the appearance of the extremely compact but mysterious Form IV.

What is Form IV? In TN theory, this high-density and persistently-duplex structure is based upon the self-evident tightness of the superhelical winding at pH 13 (see the last of the little drawings superimposed on the data in Fig. 8). This tightness is clearly reflected in the high s value at that point. Such extremely tight superhelical winding causes the DNA to become, in effect, a 4-stranded helical structure, with progressive removal of water from its core, like the wringing out of a wet towel. It was proposed, by Biegeleisen, that the 4 strands then each rotate along their longitudinal axes, so that the phosphate groups point inward, and that a new structure appears, similar to that proposed by Corey and Pauling for DNA in 1953. All that is required is to replace the hydrogen-bonds of the world-famous Pauling blunder with salt bridges (since both types of bond have the same optimal length of about 3 Å). There is no reason for such a structure to disintegrate at still higher pH, since that will only increase the ionization of the phosphate groups, thereby increasing the stability of the salt bridges.

Since Form IV never spontaneously appears at pH 7, we may safely assume that the native form, Form I, is energetically more favorable under physiological conditions. Yet native Form I, in this experiment, does not reappear when Form IV is neutralized. We may therefore conclude that at pH 7, there is what might be thought of as an activation energy barrier which prevents the process of conversion of Form IV back to Form I from beginning. We have seen, however, that this barrier is overcome by careful adjustment of the pH, temperature and ionic strength, as illustrated in Fig. 3 above.

A virtual model of Form IV has been proposed:

Form IV, x-z projection

Form IV, z-y projection

Form IV, axial projection

Form IV, rotating model

FIGURE 11

Ethidium bromide and pH titration data are similar

Data very similar to the pH titration data above are also seen in titrations of circular DNA employing the intercalating agent ethidium bromide, whether studied by velocity gradient centrifugation or electrophoresis .

In both cases, the titration reveals an initial unwinding of negative supertwists, followed by a re-winding in the opposite direction (i.e., positive supertwists). The only essential difference is that at ethidium bromide concentrations above 1 μg/ml, no further increase in positive superhelicity is seen, because DNA cannot bind any further dye above this concentration. There is therefore no denaturation, and no appearance of Form IV.

Structure of the protamine-DNA complex

One of the strongest arguments in favor of TN structure is that it provides a solution to the puzzle of the protamine-DNA complex, a mystery which remained unsolved for over 50 years.

Protamine and DNA are the two principal components of the head of the sperm cell. As far as anyone knows, the sperm head is mainly a warehouse for DNA and protein, storing these in an inert form, in preparation for the trip from the seminiferous tubules to the unfertilized ovum.

For biochemists, however, the importance of protamine is that it is the most fundamental and simple of all nuclear proteins, being little more than a long string of basic, or positively-charged amino acids. DNA, for these purposes, may be thought of as a long string of negatively-charged phosphate groups. It must surely have seemed likely to early researchers, in the 1950s, that a detailed model revealing the nature of the relationship between the positive charges of protamine and the negative charges of DNA would be forthcoming, but that was not to be the case.

In 2006, a half-century later, Biegeleisen published the first detailed molecular model showing a logical structure for the complex between protamine and DNA. The publication states that the structure is fairly self-evident, and had eluded scientists previously for one reason only, namely that previous investigators had insisted on a helical twist for the DNA component. The dogmatic requirement for DNA helicity had created a puzzle with no solution, since it is impossible to anastomose the many positive charges in protamine with the many negative charges in DNA, if the DNA is presumed helical.

The article further suggested that the protamine-DNA structure might prove to be a prototype for other nucleoprotein structures, since the portions of the histone octamer that are believed to bind DNA have about the same basic amino acid composition as protamine.

Once the possibility of a non-helical DNA component is allowed, the other details of the protamine-DNA structure are all but mandated by consideration of the following logical principles:

1. In the presence of what would be an otherwise extraordinarily fortuitous alignment of cysteine residues in the P1 and P2 strands of protamine, it is preferable to presume the alignment to be suggestive of disulfide bonds, rather than to arbitrarily reject the alignment as mere coincidence.

   
   

2. If two of the three common protein structure types (globular and α-helix) can be decisively ruled out for protamine, then it is preferable to presume that the sole remaining structure type (β-sheet) is correct, rather than to arbitrarily presume the protein to have some hitherto undefined type of structure, or, worse still, that the protein has no structure at all.

   
   

3. If there is no steric hindrance, or other evident hindrance to the formation of multiple 3 Å hydrogen bonds between the polymer chains, it is preferable to presume that the bonds will form, rather than to reject the alignment between the members of the putative hydrogen bonds as mere coincidence.

   
   

4. Likewise, if there is no steric hindrance, or other evident hindrance to the formation of multiple 3 Å salt bridges between the polymer chains, it is preferable to presume that they too will form, rather than to reject the alignment between the members of the putative salt bridges as mere coincidence.

In considering the protein component of the protamine-DNA complex, a globular structure can be decisively excluded, because protamine, being nearly 100% hydrophilic, is virtually devoid of the hydrophobic amino acid residues necessary to stabilize a globular protein core. Likewise, the outside chance that the core could, alternatively, be stabilized by negatively-charged acidic amino acid residues, to neutralize the preponderant number of positively-charged basic residues, can also be decisively excluded, because protamines generally have very few acidic residues. Human protamine has none at all.

The possibility of an α-helix can, almost as emphatically, be excluded. Alpha helices are not ordinarily seen in amino acid sequences containing large numbers of bulky side chains, especially if the side chains have mutually-repulsive electrical charges. It would be difficult to find an amino acid sequence more unfavorable to α-helix formation than protamine, half of whose residues are arginine, the longest and most electrically-charged (R group pKa=12.48) of all side chains.

The only way to make such a "forbidden" α-helix work would be to align the positive charges on the protein with the negative charges on DNA, so that the DNA could somehow provide a "scaffolding" to support the helical protein structure. If the DNA is presumed to have the Watson-Crick structure, however, no such alignment is possible.

We are therefore left with only one standard protein structure remaining, namely the β-sheet. This a fairly flat ribbon-like structure with R-group side chains projecting from either side. If the φ and ψ angles are optimized according to the Ramachandran plot (in this case, ultimately having the values of –130.5º and +130.5º respectively), the distances between amino acid residues, on either side of the sheet, will be about 7 Å (i.e., about twice the 3.4 Å base pair spacing found in purified Watson-Crick helical DNA):

Fig. 12

This also happens to be about the same as the distance between the negatively-charged phosphate groups of all known DNA structures, when measured along the sugar-phosphate backbone:

Fig. 13

It is thus clear that nature has generously provided a charge distribution which is a free gift to the model-builder who seeks a basis for the anastomosis of these positive and negative charges. In order to take advantage of this fortuitous spacing, however, the DNA must be fully unwound, giving essentially the straight-ladder structure proposed 10 years earlier by Wu. This was illustrated above.

The picture on the left below (Fig. 14A) illustrates a sort of "unit cell" of protamine-DNA structure. The center of this schematic drawing shows the P1 and P2 β-sheets, one black, the other gray. A large number of arginine side chains project outward from the peptide backbone, interacting with the DNA sugar-phosphate backbones of two fully-extended Wu duplexes. Note the fortuitous alignment of positively-charged arginine guanidinium groups with negatively-charged DNA phosphate groups. The picture to the right (B) is an actual 2-dimensional projection of the virtual structure file, showing some details of the "unit cell". Two of the four ionic bonds, which link this portion of the nucleic acid and protein chains, are indicated by dotted lines (the other two are omitted for graphic clarity). Also shown is a single disulfide bond linking the P1 and P2 protamine chains:

FIGURE 14 - SCHEMATIC DRAWING AND PDB PROJECTION OF PROTAMINE-DNA STRUCTURE
FIGURE 14 - SCHEMATIC DRAWING AND PDB PROJECTION OF PROTAMINE-DNA STRUCTURE
FIGURE 14 - SCHEMATIC DRAWING AND PDB PROJECTION OF PROTAMINE-DNA STRUCTURE
FIGURE 14 - SCHEMATIC DRAWING AND PDB PROJECTION OF PROTAMINE-DNA STRUCTURE
FIGURE 14 - SCHEMATIC DRAWING AND PDB PROJECTION OF PROTAMINE-DNA STRUCTURE
FIGURE 14 - SCHEMATIC DRAWING AND PDB PROJECTION OF PROTAMINE-DNA STRUCTURE
FIGURE 14 - SCHEMATIC DRAWING AND PDB PROJECTION OF PROTAMINE-DNA STRUCTURE
FIGURE 14 - SCHEMATIC DRAWING AND PDB PROJECTION OF PROTAMINE-DNA STRUCTURE

Note that the base pair spacing is 6.8 Å. The structure is completed when another unit cell approaches, and the base pairs of the two unit cells become mutually intercalated. This is difficult to portray in a 2-dimensional drawing, but in the following actual projection of the structure files, two adjacent "unit cells" (one black, the other gray) have been pulled apart just slightly to show the intercalation:

FIGURE 15 - PDB PROJECTION SHOWING TWO ADJACENT "UNIT CELLS", PULLED APART TO SHOW INTERCALATION.
FIGURE 15 - PDB PROJECTION SHOWING TWO ADJACENT "UNIT CELLS", PULLED APART TO SHOW INTERCALATION.
FIGURE 15 - PDB PROJECTION SHOWING TWO ADJACENT "UNIT CELLS", PULLED APART TO SHOW INTERCALATION.
FIGURE 15 - PDB PROJECTION SHOWING TWO ADJACENT "UNIT CELLS", PULLED APART TO SHOW INTERCALATION.
FIGURE 15 - PDB PROJECTION SHOWING TWO ADJACENT "UNIT CELLS", PULLED APART TO SHOW INTERCALATION.
FIGURE 15 - PDB PROJECTION SHOWING TWO ADJACENT "UNIT CELLS", PULLED APART TO SHOW INTERCALATION.

The astute virtual chemist will notice that not all the amino acid residues are arginine, only about half. But most of the others are hydrophilic amino acids capable of donating a proton for a hydrogen bond with DNA phosphate (i.e., serine, tyrosine, etc.).

A PowerPoint presentation showing the history and complete description of the protamine-DNA complex is available. The complete structure is best comprehended by study of the virtual structure files, but some idea of its nature can be had from the following rotational movie, showing a longitudinal section from an arginine-rich region:

Fig. 16. Protamine-DNA complex.

The pictures above begin to reveal an important feature of the structure, namely that, when viewed in longitudinal orientation, one can see that there are regularly alternating columns of DNA and protein. In the views we have been looking at, these columns proceed from left-to-right on the screen. What will we see if we look at right angles to that direction?

Below (Fig. 17) is an axial view of a number of DNA-protein columns. The "X" figures are the pairs of DNA duplexes, whose base pairs are intercalated in the center of the "X" figures, with the sugar-phosphate backbones projecting outward at all four corners. The adjacent columns are protamine, showing the P1 and P2 β-sheets, each having a sort of semi-circular shape in this view. The cross section is taken at an arginine-rich region, so most of what is seen of the protein are the four arginine side-chains projecting outward; two from the P1 β-sheet, and two from the P2 β-sheet. Disulfide bonds are not present in this particular cross-section:

FIGURE 17. ALTERNATING COLUMNS OF DNA AND PROTEIN
FIGURE 17. ALTERNATING COLUMNS OF DNA AND PROTEIN
FIGURE 17. ALTERNATING COLUMNS OF DNA AND PROTEIN
FIGURE 17. ALTERNATING COLUMNS OF DNA AND PROTEIN
FIGURE 17. ALTERNATING COLUMNS OF DNA AND PROTEIN
FIGURE 17. ALTERNATING COLUMNS OF DNA AND PROTEIN

When the charge relationships between DNA and protein are examined (Fig. 18, below), they are found to be favorable to a degree that exceeds all expectations of a nucleoprotein chemist seeking "elegance" in a structure. The charge symbols in the gray squares show that in every place where DNA and protamine approach one another, there is a perfect square array of 3 Å salt bridges stabilizing the overall structure:

FIGURE 18
FIGURE 18
FIGURE 18
FIGURE 18
FIGURE 18
FIGURE 18
FIGURE 18

More than any other feature, this is the part of the structure puzzle which can truly be said to have "solved itself". This fortuitous array of charge interactions is so favorable, that any skeptic who dismisses it as mere coincidence commits an act which borders on being gratuitous violence against logic itself.

Paranaemic structure

The final structure we shall consider is that of Clive Delmonte. He refers to his model as the "Paranaemic" model, although that term could be descriptively used for any TN structure.

Like the earlier SBS structures of Rodley et al and Sasisekharan, which it strongly resembles, the Delmonte Paranaemic model is hypothetical, and did not arise from direct physical investigations into DNA structure.

All three SBS models have important asymmetries and irregularities which distinguish them from the "traditional" double-helix. Each has a repeating motif of 10 base pairs, within which each base pair has a completely unique geography compared to the other nine. In the case of the Rodley and Sasisekharan models, this can be understood by keeping in mind the reversal of the direction of helical winding every 5 base pairs. Thus, one might imagine an atom-sized miniature man walking about in the model. Wherever he was, he would be able to readily determine the direction of helical winding, and also the points where that direction changed. Each base pair of each right-handed section could therefore be easily identified as being the first, second, third, fourth or fifth in that section, and likewise for the base pairs of each left-handed section.

It has been observed in several separate studies (reviewed by Delmonte and Mann) that DNase-1, inexplicably, has a remarkably faithful and reproducible tendency to cut DNA into pieces of exactly 10 base pairs in length. Delmonte and Mann refer to this as the "phasing problem", and they note that it extends to DNA in nucleoprotein as well. When DNase-1 is used to cleave DNA in reconstituted nucleosomes, the resultant fragments are large and heterogeneous (160-300 base pairs in length), but the differences in fragment size remain 10 base pairs. That is, the sizes of the cleavage fragments, in base pairs, might be 160 or 170, but not 161, 162, 163...168 or 169.

This creates a conceptual problem for a DNA science based upon the "traditional" double helix, in that the double helix is a thoroughly-symmetrical cylinder. Our imaginary miniature man, when wandering aimlessly inside the double helix, will have no idea where he is from moment-to-moment, because every side is like every other side, and every base pair like every other base pair. Likewise, DNAse-1 also cannot possibly "know" where in the DNA it is located at any given time, which puts us at a loss to explain how it is able to intelligently cut at 10 base pair intervals. The possibility that the enzyme is positioning itself according to some recognizable peculiarity of the base sequence has been considered and ruled out, leaving no alternative explanation except a structural one. The Paranaemic model, like the earlier SBS models, provides a ready structural explanation, by virtue of its 10-base-pair repeating motif.

Another unexpected finding, by McGhee and Felsenfeld (also reviewed by Delmonte and Mann , is that the pattern of methylation of DNA guanine residues by the methylating agent, dimethyl sulfate, is not affected by the DNA being bound to histones. The very fact of such histone binding, in and of itself, implies that there is a face of the DNA which is not solvent-accessible. If DNA had the "traditional" double-helical structure, then that face should not become methylated, or at least not to the extent that the solvent-accessible side is. The experimental finding, however, is that methylation proceeds identically whether or not the DNA is bound to histone. "Traditional" theory does not provide a good explanation for this.

The Paranaemic structure, however, can explain the finding. This structure may be thought of as an undulating ribbon with a definite front and back (illustrated below). If we arbitrarily assign the name "back" to the side which comes into contact with histone, than it may be concluded that the part consequently labeled "front" is that part whose guanine residues become methylated in the presence of dimethyl sulfate. In the Delmonte structure there is, in principle, no base pair whose "front" is any less accessible to the surrounding solvent than that of any other base pair, and therefore the methylation pattern of DNA complexed with histone might not be different than that of naked DNA.

The unique feature of the Delmonte structure is its dimensions, which accord with those determined experimentally for DNA by James and Mazia, at the dawn of the era of molecular biology. These investigators employed the Langmuir trough, within which a molecular monolayer of DNA can be spread and measured. From the measured surface area and height of the monolayer, the dimensions of the DNA duplex could be calculated to be about 1.2 nm x 2.2 nm, i.e., decidedly non-symmetrical.

There is not, as yet, a virtual structure file for the Delmonte structure, but there is a large physical model:

FIGURE 19 - CLIVE'S PARANEMIC DRAWING
FIGURE 19 - CLIVE'S PARANEMIC DRAWING
FIGURE 19 - CLIVE'S PARANEMIC DRAWING
FIGURE 19 - CLIVE'S PARANEMIC DRAWING
FIGURE 19 - CLIVE'S PARANEMIC DRAWING
FIGURE 19 - CLIVE'S PARANEMIC DRAWING
FIGURE 19 - CLIVE'S PARANEMIC DRAWING

The sugar phosphate backbones are both right-handed helices, but they do not intertwine with one another. Each has a cylindrical diameter of 1.1 nm, giving rise to dimensions of 1.1 nm x 2.2 nm for the duplex, corresponding to the measurements derived from the Langmuir trough experiment. The length of a 10 base-pair segment is 3.34 nm, about the same as other DNA structures.

Although the flat, two-dimensional illustrations might not make it apparent, this structure, when viewed in 3D, is actually quite similar to the older SBS structures of Rodley and Sasisekharan, and can perhaps be thought of as arising by a "homogenization" thereof. Thus, where the older models consisted of a pattern of alternating right-handed and left-handed segments, with abrupt transitions in between, the Delmonte model has uniformly smooth transitions from base pair to base pair.

Summary

For the following reasons, an ongoing consideration of non-helical DNA structure is indicated:

1. The conceptual problems inherent in a replication scheme for a duplex structure whose strands are plectonemically locked together by hundreds of thousands of helical twists (as in bacteria), or even millions of helical twists (as in eukaryotes), are solved by topoisomerases and gyrases, but in theory only. There is no direct evidence that either enzyme type is involved in normal DNA replication in vivo.

2. The topological properties of circular DNA (as portrayed in Fig. 8 above) all result from changes in superhelical winding, in accordance with the topology equation L_k=T+W. These changes can all be explained without resorting to the presumption that DNA has a net helical twist. All that is required is the understanding that under physiological conditions, DNA "prefers" the right-handed secondary helical conformation (i.e., the Watson-Crick double-helix), with base pair spacing of 3.4 Å, but that under conditions favoring unwinding, DNA will eventually come to "prefer" the left-handed Z structure, because of its more loosely-wound spacing of 3.7 Å. At any given pH, one or the other direction of secondary winding will be energetically most favorable, and the less favorable winding will unwind itself as much as possible, driving the formation of tertiary superhelical twists in the opposite sense.

3. The single most important physical finding, with respect to the question of helicity vs non-helicity in circular duplex chromosomes, is the apparent resistance to strand separation under conditions which promote denaturation. Wu, however, has demonstrated that the strands can indeed be separated, and by the simple expedient of agarose gel electrophoresis. All that is required is that the electrophoresis be done at a time when one of the strands has significant amounts of bound m-RNA, which imparts to that strand a different electrophoretic mobility.

4. Another key question, upon whose answer the entire theory of non-helicity rests, is whether the separated single strands of a plasmid can be re-annealed to give a properly base-paired structure, with full restoration of the known physical properties of the native chromosome. One publication says that this cannot be done, but that experimental protocol can be persuasively shown to have been fatally flawed, in that the conditions of re-annealing had been previously proven to be inadequate for the creation of a base-paired structure. Additionally, another researcher reported an entirely contrary finding, namely that the separated single strands of a plasmid could be successfully re-annealed back to the original base-paired structure, but the work was never formally published. This latter experiment, which took many months to do in the past, can now be repeated in a matter of days, and at a fraction of the original cost, but no one has taken the trouble to do so.

5. A detailed solution to the problem of protamine-DNA structure in the sperm head has never been possible with helical DNA as the starting point. It has been shown, however, that when a non-helical DNA structure is accepted as a starting point, the remaining details of the protamine-DNA structure puzzle virtually solve themselves.