• Kyungpook Mathematical Journal
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• v.52 no.2
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• pp.201-208
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• 2012

By the works of Kondo and Sakai, it is known that Alexander polynomials of knots which are transformed into the trivial knot by a single crossing change are characterized. In this note, we will characterize Alexander polynomials of knots which are transformed into the trefoil knot (and into the figure-eight knot) by a single crossing change.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.661-671
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• 2007

We investigate the number of knots and links in linear embeddings of $K_6$, the complete graph with 6 vertices. Concretely, we show that any linear embedding of $K_6$ contains either only one Hopf link, or three Hopf links and one trefoil knot.

• Proceedings of the Korea Crystallographic Association Conference
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• 2003.05a
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• pp.17-17
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• 2003

tRNA (m¹ G37) methyltransferase (TrmD) catalyze s the trans for of a methyl group from S-adenosyl-L-methionine (AdoMet) to G/sup 37/ within a subset of bacterial tRNA species, which have a residue G at 36th position. The modified guanosine is adjacent to and 3' of the anticodon and is essential for the maintenance of the correct reading frame during translation. We have determined the first crystal structure of TrmD from Haemophilus influenzae, as a binary complex with either AdoMet or S-adenosyl-L-homocysteine (AdoHcy), as a ternary complex with AdoHcy/phosphate, and as an apo form. The structure indicates that TrmD functions as a dimer (Figure 1). It also suggests the binding mode of G/sup 36/G/sup 37/ in the active site of TrmD and catalytic mechanism. The N-terminal domain has a trefoil knot, in which AdoMet or AdoHcy is bound in a novel, bent conformation. The C-terminal domain shows a structural similarity to DNA binding domain of trp or tot repressor. We propose a plausible model for the TrmD₂-tRNA₂ complex, which provides insights into recognition of the general tRNA structure by TrmD (Figure 2).