Topology in Molecular Biology
90 L.H. Kauffman and S. Lambropoulou 5.4.2 The Fraction Through Colouring We conclude this section by giving an alternate defini ...
5 From Tangle Fractions to DNA 91 or 0 0 0 0 11 1 1 1 -1^1 1 0 0 0 2 0 1 23 4 3 -3 -6^11 18 T = [2] + 1/([2] + 1/[3]) F(T) = 17/ ...
92 L.H. Kauffman and S. Lambropoulou closureN(T) one obtains a colouring in a modular number system. For exam- ple in Fig. 5.17 ...
5 From Tangle Fractions to DNA 93 Note that we only need to take numerator closures, since the denominator closure of a tangle i ...
94 L.H. Kauffman and S. Lambropoulou and S= [[4],[3],[2]] = [4] + 1 [3] +[2]^1 both close to the same rational knot, shown at th ...
5 From Tangle Fractions to DNA 95 R=[1]+ S=[-3] [2] _^1 ~ Fig. 5.20.An example of the special cut T T open to obtain K = N([1] + ...
96 L.H. Kauffman and S. Lambropoulou special cut ~ ~ = [-1] - open to obtain _^1 T T K = N([1] +T) = T T T Fig. 5.22.A special c ...
5 From Tangle Fractions to DNA 97 open Fig. 5.24.A non-rational cut by the Tait conjecture they will differ by flypes. We analys ...
98 L.H. Kauffman and S. Lambropoulou classification of rational knots and links to determine their chirality. Indeed, we have th ...
5 From Tangle Fractions to DNA 99 5.7 The Oriented Case Oriented rational knots and links arise as numerator closures of oriente ...
100 L.H. Kauffman and S. Lambropoulou Type I Type II Compatible bottom twist Incompatible Fig. 5.28.Compatible and incompatible ...
5 From Tangle Fractions to DNA 101 [0] = [∞]=>< [+1] =χ. Note that connectivity type [0] yields two-component rational li ...
102 L.H. Kauffman and S. Lambropoulou to the change from moduluspin the unoriented case to the modulus 2 pin the oriented case.W ...
5 From Tangle Fractions to DNA 103 5.8 Strongly Invertible Links..................................... An oriented knot or link i ...
104 L.H. Kauffman and S. Lambropoulou L = N([[3], [1], [1], [1], [3]]) Fig. 5.31.An example of a strongly invertible link N ( ) ...
5 From Tangle Fractions to DNA 105 ~ ~ ~ ~ K 1 K 2 K 3 K 4 Fig. 5.33.Multiple recombinations to actually identify the topologica ...
106 L.H. Kauffman and S. Lambropoulou tangleR.The results of the successive rounds of recombination are the knots and links N(S+ ...
5 From Tangle Fractions to DNA 107 there arep′,q′,r′such that for somen(or a range of values ofnto be specified below)Kn=N((p′+q ...
108 L.H. Kauffman and S. Lambropoulou In this version of the tangle model for DNA recombination we have made a blanket assumptio ...
5 From Tangle Fractions to DNA 109 L.H. Kauffman, S. Lambropoulou, On the classification of rational knots, to appear inL’ Ense ...
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