Braid Solutions to the Action of the Gin Enzyme

Abstract

The topological analysis of enzymes, an active research topic, has allowed the application of the tangle model of Ernst and Sumners to deduce the action mechanism of several enzymes, modeled as 2-string tangles. By first deriving some results in the theory of 3-braids, in this paper we analyze knotted and linked products of site-specific recombination mediated by the Gin DNA invertase, an enzyme that involves 3-string tangles. Provided that the 3-tangles involved are 3-braids, we determine four families of solutions to its action, two families for each of the directly and inversely repeated site cases. For each case, one of the given solutions had not previously been reported in the related literature. These solutions were found using a computer algorithm, based on our theoretical results, which allows one to solve tangle equations under the assumption that the product of two or more rounds of recombinations is known.

An algebraic view of bacterial genome evolution

“…Tangles continue to be used to describe the synaptic structure giving rise to recombination, for example extending the model to include 3-string tangles [Emert and Ernst, 2000, Kim and Darcy, 2009, Cabrera-Ibarra and Lizárraga-Navarro, 2010, and have also been used to make predictions of the possible knots that may arise under different hypotheses about the substrate arrangement [Valencia and Buck, 2011]. Other algebraically related approaches to DNA configurations have been attempted, including the use of the action of affine Lie groups through a translation of knot surgery into tilings of the plane on which the Lie group acts [Bodner et al, 2012], as well as the study of self-assembly of DNA polyhedra [Hu et al, 2011].…”

Determining the topology of stable protein–DNA complexes

“…Mathematical analysis can be applied directly to study the topological mechanism of proteins that knot/catenate circular DNA [11,[19][20][21][22][23][24][25][26][27][28][29]. The configuration of DNA bound by Tn3 resolvase ( Figure 1B) was proposed using the experimentally determined product topologies [9,10,[12][13][14][15].…”