An algorithm based on 3-braids to solve tangle equations arising in the action of Gin DNA invertase

摘要

The tangle model of Ernst and Sumners is an effective tool in the topological analysis of enzymes, a particular application of which aims at deducing the mechanism of action of site-specific recombination mediated by the Gin DNA invertase, an enzyme whose action involves 3-string tangles. In order to determine the enzyme's mechanism of action, the tangle model yields equations that involve tangle indeterminates that must be solved for. While some of the available methods for solving such equations judiciously exploit the theory of 2-tangles, an algorithm is introduced in this note, based on 3-braid-theoretical results in [2], which allowed the authors to discover previously unreported solutions for the action of Gin DNA invertase. More generally, the algorithm allows one to solve 3-string tangle equations for 3-braid solutions under the assumption that each of the products of two or more rounds of recombinations is the unknot or a known 2-bridge knot different from the 2-component unlink. Rather than a specific language implementation, we here provide a pseudo-code description of the algorithm that permits its translation into a variety of computer languages and, possibly, its inclusion into more powerful analysis software.