4 S.D. Levene
2.1.1 Why Study DNA Topology?
Topological aspects of DNA structure can provide great insight into biochemi-
cal mechanisms of proteins that mediate changes in DNA structure and topol-
ogy. The goal of these studies is generally to understand how the structure of
a DNA-metabolizing enzyme and that of the DNA sequence recognized by the
enzyme interact to participate in a particular chemical reaction. The overall
change in DNA topology that takes place often greatly limits the number of
prospective mechanistic scenarios because any changes in topology must be
consistent with overall changes in DNA geometry.
A limitation of this approach is that although DNA topology and geometry
must be consistent with one another, the latter is rarely uniquely determined.
However, there is at least one important advantage of the topological approach
that outweighs any of its disadvantages: the fact that the topology of a DNA
molecule is fixed and invariant as long as the backbones of both DNA strands
remain unbroken. As long as this constraint is not violated, perturbations
of DNA structure do not affect its global topology. The topological state
of a DNA molecule is independent of temperature, solution conditions, the
presence of particular ions or small DNA-binding molecules, or any other
environmental factors, which offers an enormous experimental advantage.
Finally, an underappreciated aspect of the topological approach is that
topology is extremely useful in ruling out implausible mechanistic scenarios.
One is sometimes faced with the prospect of selecting the most likely mecha-
nism from a long list of candidates. Frequently, the availability of topological
information helps to limit the plausible choices to a small subset or a unique
scheme.
2.1.2 Secondary and Tertiary Structure of DNA
The helical structure of double-stranded DNA is an integral aspect of the
topology of closed DNA molecules. Figure 2.1 shows the three canonical struc-
tures of double-stranded DNA one frequently encounters in textbooks (see [1]
for example). Over the last 20 years it has become clear that local sequence-
dependent variations on these canonical themes exist; therefore, these struc-
tures should be thought of as prototypes of structural families rather than
rigid templates.
The B form of DNA is the structure considered most representative of
DNA molecules in aqueous solution: it is a right-handed double helix with a
period of 10.5 residues (base pairs). Each base pair is nearly perpendicular
to the helix axis and separated from its neighbors by 0.34 nm, giving the
helix a pitch of 3.6 nm. The A-form DNA is a particular structural family
characteristic of DNA molecules under conditions of poor hydration (DNA
fibers at low relative humidity or molecules in solution that contain substantial
amounts of alcohol or other nonaqueous solvents). It is also a right-handed
helical form with a period of 11.0 base pairs and a pitch of 3.2 nm. Unlike the