10 S.D. Levene
Fig. 2.4.Topology of closed circular DNA. (a) Sign convention for DNA crossings
in closed-circular DNA. The convention corresponds to the normal right-hand rule
in chemistry and physics: a left-handed crossing is counted as negative whereas a
right-handed crossing is counted as positive. (b) Conversion of relaxed DNA into
negatively and positively supercoiled DNA. The descriptor of supercoiling, the link-
ing number, can be computed from one-half the sum of signed crossings of the black
and red strands. In the case of relaxed DNA there is no writhe and the linking num-
ber, Lk, is equal to the twist number, Tw. In negatively supercoiled DNA, reduction
of Lk below Tw gives rise to right-handed interwound supercoils, or negative writhe.
Conversely, incrementing Lk above Tw generates left-handed interwound supercoils
and positive writhe
Almost all DNA in the cells of terrestrial organisms is underwound or
negatively supercoiled, which means that the Lk of DNA molecules is reduced
below the value that pertains to the same DNA in the absence of torsional
stress, designated Lk 0. Exceptions to this rule are found among archeabacteria
that require positively supercoiled genomes in order to survive in extreme
conditions of temperature and pressure near geothermal vents at the ocean
floor. The distortion of DNA structure generated by negative (deficits in Lk
relative to Lk 0 ,∆Lk<0) or positive (surpluses in Lk relative to Lk 0 ,∆Lk>
0) supercoiling manifests itself in the formation of branched, interwound DNA
superhelices (Fig. 2.5). A detailed analysis of the properties of supercoiled
DNA based on Monte Carlo simulations of closed wormlike chains has been
presented previously [21]. This model depends on only three parameters:P,