Topology in Molecular Biology

5 From Tangle Fractions to DNA 105

~

~

~

~

K 1

K 2

K 3

K 4

Fig. 5.33.Multiple recombinations

to actually identify the topological type of these knots. The protein coating
technique made it possible to design an experiment involving successive DNA
recombinations and to examine the topology of the products. In [38] the knot-
ted DNA produced by such successive recombinations was consistent with the
hypothesis that all recombinations were of the type of a positive half twist as
in [+1].Then D.W. Sumners and C. Ernst [36] proposed atangle model for
successive DNA recombinationsand showed, in the case of the experiments in
question, that there was no other topological possibility for the recombination
mechanism than the positive half-twist [+1].This constituted a unique use of
topology as a theoretical underpinning for a problem in molecular biology.
Here is a brief description of the tangle model for DNA recombination. It
is assumed that the initial state of the DNA is described as the numerator
closureN(S)ofasubstrate tangleS.The local geometry of the recombination
is assumed to be described by the replacement of the tangle [0] with a specific