Topology in Molecular Biology
110 L.H. Kauffman and S. Lambropoulou H. Seifert, Abh. Math. Sem. Univ. Hamburg, 11 , 84–101 (1936) J. Sawollek, Tait’s flyping ...
6 Linear Behavior of the Writhe Versus the Number of Crossings in Rational Knots and Links C. Cerf and A. Stasiak Summary.Using ...
112 C. Cerf and A. Stasiak Studies of random knots that are not confined to a lattice also revealed the same phenomenon. The ave ...
6 Writhe Versus the Number of Crossings 113 crossings. Examples of nullifications are shown in Figs. 6.2–6.4. A discussion about ...
114 C. Cerf and A. Stasiak If one considers all alternating knots and links, there is no simple function that can relate the wri ...
6 Writhe Versus the Number of Crossings 115 a a (odd) +1 crossings nullification a (even) +1 crossings nullification a (even) -1 ...
116 C. Cerf and A. Stasiak b (even) a (even) -1 crossings +1 crossings nullification b (even) a +1 crossings (odd)^ +1 crossings ...
6 Writhe Versus the Number of Crossings 117 crossings gives rise to the unknot. One cannot nullify the last crossing without dis ...
118 C. Cerf and A. Stasiak aOdd,bEven The closure of this tangle gives rise to a family of knots withnpositive cross- ings:ain t ...
6 Writhe Versus the Number of Crossings 119 1 negative crossing from the horizontal row. Thuswx=−(a−1)−1=−a andwy=− 1 −(b−1) =−b ...
120 C. Cerf and A. Stasiak The same remark holds, i.e., (6.9) and (6.11) are identical but the first one (case B.3) refers to kn ...
6 Writhe Versus the Number of Crossings 121 a b c nullification a (odd) +1 crossings b (odd) +1 crossings c (even) -1 crossings ...
122 C. Cerf and A. Stasiak 6.4 Discussion ................................................. 6.4.1 When isPWra Linear Function of ...
6 Writhe Versus the Number of Crossings 123 more negative crossings of the same type. The predicted writhe is unchanged, leading ...
124 C. Cerf and A. Stasiak The two linear functions ofnare thus shifted by 2b. Sincebis an even integer, the shift is a multiple ...
6 Writhe Versus the Number of Crossings 125 tangle (a)(b)(c)...(r) having a fixed number of crossings onr−1rows,PWr presents a l ...
7 Combinatories and Topology of theβ-Sandwich andβ-Barrel Proteins A.E. Kister, M.V. Kleyzit, T.I. Gelfand, and I.M. Gelfand Sum ...
128 A.E. Kister et al. There is both a local and a global point of view regarding the relation- ship between the linear sequence ...
7 Combinatories and Topology of theβ-Sandwich andβ-Barrel Proteins 129 The search is carried out with predefined sets of several ...
130 A.E. Kister et al. adopted in the SCOP and CATH databases [3, 14]. Proteins grouped together based on their common architect ...
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