The topological properties of circular DNA are complex.  In standard texts, these properties are invariably explained in terms of a helical model for DNA, but in 2008 it was noted that each topoisomer, negative or positive, adopts a unique and surprisingly wide distribution of three-dimensional conformations.
When the sedimentation coefficient, s, of circular DNA is ascertained over a large range of pH, the following curves are seen. Three curves are shown here, representing three species of DNA.  From top-to-bottom they are:  "Form IV" (green), "Form I" (blue) and "Form II" (red).
"Form I" (blue curve) 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 (red curve) is seen.
Form IV (green curve) 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 doesnt 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, green 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 (&Delta;).  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.
Briefly, the alterations of s seen in the pH titration curve above are widely thought 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 pH still, the chromosome, which is now denaturing in earnest, tends to unwind entirely, which it cannot do so (because L 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.