Abstract
The goal of this paper is to determine the braid index of two types of complicated DNA polyhedral links introduced by chemists and biologists in recent years. We shall study it in a more broad context and actually consider so-called Jaeger's links (more general Traldi's links) which contain, as special cases, both four types of simple polyhedral links whose braid indexes have been determined and the above two types of complicated DNA polyhedral links. Denote by and the braid index and crossing number of an oriented link , respectively. Roughly speaking, in this paper, we prove that for any link in a family including Jaeger's links and contained in Traldi's links, which is obtained by combining the MFW inequality and an Ohyama's result on upper bound of the braid index. Our result may be used to to characterize and analyze the structure and complexity of DNA polyhedra and entanglement in biopolymers.
Highlights
The braid index of links has some applications in chemistry and molecular biology
In recent 20 years, many DNA polyhedral links such as DNA cube [2], DNA tetrahedron [3], DNA octahedron [4], DNA truncated octahedron [5], DNA bipyramid [6], DNA dodecahedron [7], DNA icosahedron and buckyballs [8] etc, have been synthesized in laboratories or schemes for synthesizing them have been designed by chemists and biologists
Our research demonstrates that using the braid index or crossing index to describe the complexity of some polyhedral links are equivalent and it may open a door to characterize, analyze the structure and complexity of DNA
Summary
The braid index of links has some applications in chemistry and molecular biology. For four types of simple polyhedral links, their braid indexes have been determined in [9]. The purpose of this paper is to determine braid index of another two types of more complicated polyhedral links appeared in [8,10,11,12,13] and [14], respectively. We shall study it in a more broad context and consider so-called Jaeger’s links and more general Traldi’s links
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