Interconversion by DNA Topoisomerases

On the top of this figure are the three knots discussed here, the trefoil knot (green) with positive nodes (31+), the figure-8 (red) knot (41), and the trefoil knot (blue) with negative nodes (31-). The nucleotide pairs that give rise to the nodes are indicated between strands. The same knots are shown in the bottom portion of the figure, interspersed by circles (aqua) drawn with the node structures of dumbbells. The lines indicating the base pairs have been removed for clarity. The '+' and '-' signs near the nodes indicate their topological signs. The equilibria indicated between structures are catalyzed by the E. coli DNA Topoisomerases I and III. The 31+ knot on the left has all positive signs, and the signs of a single node at a time are switched from positive to negative in each of the structures as one proceeds towards the right of the figure. Changing the sign of a single node in the 31+ knot produces a circle (dumbbell), and changing a second node in the same domain produces a 41 knot. Changing the sign of another positive node in the 41 knot produces the circle (dumbbell) on the right, and changing the sign of the last node generates the 31- knot. It is important to realize that the two circles shown may interconvert without the catalytic activity of a topoisomerase.

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