12 S.D. Levene
Fig. 2.6.(a) The set of all prime topologies containing up to nine irreducible knot
crossings and dimeric catenanes with up to eight irreducible crossings generated
using the programKnot Plot. Each structure is labeled above and to the left ac-
cording to Alexander and Briggs notation in the case of knots and Rolfsen notation
in the case of catenanes. (b) Some knots and catenanes of biological importance,
left side (from top to bottom): +3 trefoil knot, 4-noded knot, +5-noded torus knot,
2-catenane (or Hopf link), 4-noded torus catenane, 6-noded torus catenane. Right
side: 5-noded twist knot, +7-noded torus knot, 7-noded twist knot, 8-noded torus
catenane, trimeric (three-component) singly linked catenane
computational analysis, the more than one million possible knots containing
up to 16 irreducible crossings have been cataloged [23]. A gallery of all knots
with up to nine irreducible crossings and all dimeric catenanes with up to
eight crossings is shown in Fig. 2.6 along with several biologically important
examples. These species are readily separated by gel electrophoresis (Fig. 2.7).
Only a limited subset of DNA knots and catenanes have been encoun-
tered in biological contexts, implying that these topological forms do not
result from random linking and unlinking of DNA. Instead, knots and cate-
nanes are generated via pathways that reflect the specific mechanisms of pro-
teins involved in DNA metabolism. The power of DNA topology therefore
resides in its ability to illuminate the mechanism of a particular biological
process via analysis of the topological forms that these processes generate.
The high topological specificity of DNA knotting and linking greatly limits
the number of possible mechanistic scenarios and very effectively eliminates
implausible ones.