Coherent band pathways between knots and links
Dorothy Buck, Kai Ishihara
TL;DR
This paper classifies and analyzes minimal coherent band pathways between knots and links, applying the findings to understand DNA recombination processes and the properties of recombinant DNA molecules.
Contribution
It introduces a classification of coherent band pathways between knots and links and applies these results to DNA recombination analysis.
Findings
Classified coherent band pathways between knots and links.
Determined minimal pathways for small crossing number knots and links.
Applied results to DNA recombination event analysis.
Abstract
We categorise coherent band (aka nullification) pathways between knots and 2-component links. Additionally, we characterise the minimal coherent band pathways (with intermediates) between any two knots or 2-component links with small crossing number. We demonstrate these band surgeries for knots and links with small crossing number. We apply these results to place lower bounds on the minimum number of recombinant events separating DNA configurations, restrict the recombination pathways and determine chirality and/or orientation of the resulting recombinant DNA molecules.
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Taxonomy
TopicsGeometric and Algebraic Topology · semigroups and automata theory · Surface Chemistry and Catalysis