msr: Minimal Structure Reduction In Rknots: Topological Analysis of Knotted Proteins, Biopolymers and 3D Structures

Description

Reduce a polygonal link to its minimal structure by applying Generalized Reidemeister Moves.

Usage

 `1` ```msr(points3D, ends = c(), n = 100) ```

Arguments

 `points3D` an N x 3 matrix of the x, y, z coordinates of a polygonal link `ends` a vector of positive integers defining the separators of the polygonal link `n` the number of iterations

Details

A minimal structure for a polygonal link L is a nested sequence of subsets of L:

L \supset L_1 \supset … \supset L_N

that cannot be extended. Each inclusion corresponds to a Generalized Reidemeister Move.

Value

Returns a list of three elements

 `points3D` an M x 3 matrix of the x, y, z coordinates of the reduced structure `ends` a vector of positive integers (if a non empty `ends` has been provided as an argument defining the separators of the reduced structure `M` the intersection matrix of the reduced structure

Note

This is a low-level function.

Note

The default number of iterations is 100. This value almost always allows to reach the minimal structure. If wished, a partial reduction can be achieved with `n` between 2 and 5. This is particularly suitable for graphical representations of the reduction process.

Author(s)

Federico Comoglio, [email protected]

References

Comoglio F. and Rinaldi M. A Topological Framework for the Computation of the HOMFLY Polynomial and Its Application to Proteins (2011) PLoS ONE 6(4): e18693, doi:10.1371/journal.pone.0018693 ArXiv:1104.3405

Examples

 ```1 2 3 4 5 6 7 8 9``` ```## Not run: knot <- makeExampleKnot() reduced <- msr(points3D = knot) ## 3D plot of both the trefoil and its reduced structure plotKnot3D(knot, ends = c(), radius = 0.01, lwd = 2.5) plotKnot3D(reduced\$points3D, reduced\$ends, colors = 'red', radius = 0.1, lwd = 2.5) ## End(Not run) ```

Rknots documentation built on May 29, 2017, 1:38 p.m.