Two synthetic DNA molecules that can be knotted have been employed as substrates for E. coli DNA topoisomerases I and III. Both molecules contain 104 nucleotides, including sequences that can form two single-turn helical domains, connected by single-stranded oligo(dT) linkers in an X-Y-X'-Y' pairing motif. One of the knots can be ligated to form cyclic molecules with the topologies of a circle, a trefoil knot with negative nodes, or a figure-8 knot. Cyclic molecules constructed from the other molecule can form a circle, a figure-8 knot, and trefoil knots with either positive or negative nodes. The topologically negative nodes in these knots are derived from right-handed B-DNA, and the positive nodes are derived from left-handed Z-DNA. The topoisomerases can catalyze the interconversion of the different topological forms of these molecules, as a function of solution conditions and the extent to which they favor B-DNA or Z-DNA. The enzymes appear to catalyze a single strand-passage event at a time. The topoisomerases can catalyze strand passage events involving both positive and negative nodes as substrates. Gel retention experiments show that both knots can bind up to four molecules of E. coli DNA topoisomerase I. The thermal denaturation of the domains of a trefoil knot closely related to these knots suggests that the two helical domains are uncoupled, so the single-stranded linkers in the knots are not taut. Chemical ligation experiments yield a distribution of products similar to those of enzymatic ligation, showing that the ATP cofactor in DNA knot ligation does not appear to skew the products markedly. Knots that are stressed by being placed in unfavorable solution conditions have been shown to be a highly sensitive system for detecting topoisomerase activity.