• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.349-369
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• 2017

In last 30 years, mathematical tangle theory is applied to molecular biology, especially to DNA topology. The recent issues and research results of this topic are reviewed in this paper. We introduce a tangle which models an enzyme-DNA complex. The studies of 2-string tangle equations related to Topoisomerase II action and site-specific recombination is discussed. And 3-string tangle analysis of Mu-DNA complex, n-string tangle analysis ($n{\geq}4$) of DNA-enzyme synaptic complexes are also discussed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.2
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• pp.87-102
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• 2013

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.

• The Pure and Applied Mathematics
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• v.25 no.2
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• pp.95-113
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• 2018

A mathematical knot is an embedded circle in ${\mathbb{R}}^3$. A fundamental problem in knot theory is classifying knots up to its numbers of crossing points. Knots are often distinguished by using a knot invariant, a quantity which is the same for equivalent knots. Knot polynomials are one of well known knot invariants. In 2006, J. Przytycki showed the effects of a n - move (a local change in a knot diagram) on several knot polynomials. In this paper, the authors review about knot polynomials, especially Jones polynomial, and give an alternative proof to a part of the Przytychi's result for the case n = 3 on the Jones polynomial.

• Food Science of Animal Resources
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• v.44 no.2
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• pp.483-497
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• 2024

This study investigated the effects of ultra-ground seaweed powders (USP) on the physicochemical properties (proximate composition, mineral contents, pH, color, shear force, sensory evaluation, electronic nose, and electronic tongue) of restructured black goat jerky. Restructured black goat jerky was prepared using three different treatments, i.e., 3% (w/w) each of ultra-ground sea tangle (ST; Undaria pinnatifida), sea mustard (SM; Saccharina japonica), and sea string (SS; Gracilaria verrucosa) powders. Moisture and ash contents were significantly higher in the USP-treated group than in the control (p<0.05). Potassium, calcium, and zinc contents were significantly higher in the SM than in the other USP-treated groups (p<0.05). In contrast, pH values were significantly higher in the ST and SM than in the control and SS (p<0.05). CIE L^*, CIE a^*, CIE b^*, and shear force were significantly lower in the USP-treated groups than in the control (p<0.05). Sensory evaluation revealed no significant difference in taste, texture, seaweed-like odor, and goaty flavor (p<0.05). Principal component analysis (PCA) and peak graph analysis of the electronic nose showed that the SS differed the most from the control compared with the other USP-treated groups, owing to the seaweed odor of ultra-ground SS powder. The PCA and ranking analysis of the electronic tongue showed that the umami taste of the SM was higher than that of the control and other USP-treated groups. Therefore, the potassium, calcium, zinc contents, and umami taste of reconstituted black goat jerky were significantly higher in the SM than in the control and other USP-treated groups.