A 4-string tangle analysis of DNA-protein complexes based on difference topology

Kim, Soo-Jeong

doi:10.1142/s021821651550056x

Cited by 3 publications

(4 citation statements)

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“…We solved all such equations in which the twist knot had fewer than 100,000 crossings by writing a simple C program (code available upon request). This allows us to use the results in Darcy et al (2009) and Kim and Darcy (2015) to prove that the only biologically relevant tangle model representing P is a three-branched structure if P binds three DNA segments or R-standard if P binds to four DNA segments.…”

Section: Mathematical Methodsmentioning

confidence: 99%

“…Technology has significantly advanced, but it is still unsuccessful for large complexes in which proteins bind multiple DNA segments. To study protein-bound DNA, an experimental technique called difference topology combined with the mathematics of tangle analysis has been used (Kimura et al, 1999;Pathania et al, 2002;Petrushenko et al, 2006;Darcy et al, 2009;Kim and Darcy, 2015). Note that this technique focuses on determining the topology of DNA bound in a protein complex.…”

Section: Introductionmentioning

confidence: 99%

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A topological analysis of difference topology experiments of condensin with Topoisomerase II

Kim

Darcy

2020

Biology Open

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An experimental technique called difference topology combined with the mathematics of tangle analysis has been used to unveil the structure of DNA bound by the Mu transpososome. However, difference topology experiments can be difficult and time consuming. We discuss a modification that greatly simplifies this experimental technique. This simple experiment involves using a topoisomerase to trap DNA crossings bound by a protein complex and then running a gel to determine the crossing number of the knotted product(s). We develop the mathematics needed to analyze the results and apply these results to model the topology of DNA bound by 13S condensin and by the condensin MukB.

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Section: Mathematical Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A topological analysis of difference topology experiments of condensin with Topoisomerase II

Kim

Darcy

2020

Biology Open

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“…In the first experiment, the product DNA of Cre recombination is a 3-noded knot (trefoil), which means there are three crossings between E &L and E & R. In the second experiment, the product DNA of Cre recombination is also a 3-noded knot (trefoil), which implies there are three crossings between L &E and L&R. In the third experiment, the product DNA of Cre recombination is 4-noded link, which means there are four crossings between R &E and R &L. From putting all results together, one can conclude that the DNA topology within the Mu transpososome has 3-branched(this is biologically reasonable assumption [12]) five noded configuration such that two crossings between E &R and L&R, one crossing between E &L. Remark that Pathania et al performed more experiments considering the orientation of Cre binding sites and linear DNA with Enhancer site. See [12,13,4,9,10,3] for more detail.…”

Section: Difference Topology Experiments Of Mu-transpososomementioning

confidence: 99%

“…When a circular DNA binds to a protein, the conformation of the DNA-protein complex is simply a ball (protein) with a circular string (DNA) which is very similar to the shape of a tangle. A tangle model for DNA-protein complexes are introduced by C. Ernst and D. Sumners in late 80's (see Figure 15) and mathematical analysis of a tangle model is very useful for understanding biological activities of the complex [3,4,5,6,7,9,10,15,16,20,12,17,18].…”

Section: Introductionmentioning

confidence: 99%

Topological Analysis of Mu-Transposition

Kim¹

2013

Journal of the Korea Society for Industrial and Applied Mathema

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An n-string tangle is a three dimensional ball with n-strings which are properly embedded in the ball. In early 90's, C. Ernst and D. Sumners first used a tangle to describe a DNA-protein complex. In this model, DNA is represented by a string and protein is represented by a ball. Mu is a protein which binds to DNA at three sites and a DNA-Mu complex is called Mu-transpososome. Knowing the DNA topology within Mu-transpososome is very important to understand DNA transposition by Mu protein. In 2002, Pathania et al. determined that the DNA configuration within the Mu transpososome is three branched and five noded [12]. In 2007, Darcy et al. analyzed this by using mathematical tangle and concluded that the three branched and five noded DNA configuration is the only biologically reasonable solution [4]. In this paper, based on the result of Pathania et al. and Darcy et al., the author determines the DNA topology within the DNA-Mu complex after the whole Mu transposition process. Furthermore, a new experiment is designed which can support the Pathania et al.'s result. The result of this new experiment is predicted through mathematical knot thory.

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A topological analysis of difference topology experiments of condensin with Topoisomerases II

Kim

Darcy

2019

Preprint

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7An experimental technique called difference topology combined with the mathematics of tangle analysis has been used to unveil the structure of DNA bound by the Mu transpososome. However, difference topology experiments can be difficult and time-consuming.We discuss a modification that greatly simplifies this experimental technique. This simple experiment involves using a topoisomerase to trap DNA crossings bound by a protein complex and then running a gel to determine the crossing number of the knotted product(s). We develop the mathematics needed to analyze the results and apply these results to model the topology of DNA bound by 13S condensin and by the condensin MukB. 8 9 10 11 12 13 KEYWORDS: difference topology experiment, DNA topology, tangle analysis, condensin 14 15 SUMMARY STATEMENT 16 Tangles are used to model protein-DNA complexes: A 3-dimensional ball represents protein while strings embedded in this ball represent 17 protein-bound DNA. We use this simple model to analyze experimental results. 18 19 Proteins bind DNA in many genetic activities such as replication, transcription, packaging, repair, and rearrangement. Understanding the 20 DNA conformation within protein-DNA complexes is useful for modeling and analyzing reactions (Crisona et al., 1999; Harshey and 21

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A 4-string tangle analysis of DNA-protein complexes based on difference topology

Cited by 3 publications

References 28 publications

A topological analysis of difference topology experiments of condensin with Topoisomerase II

A topological analysis of difference topology experiments of condensin with Topoisomerase II

Topological Analysis of Mu-Transposition

A topological analysis of difference topology experiments of condensin with Topoisomerases II

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