How does a circular piece of DNA (like a plasmid, maybe?) not get its double-helix all in a twist? With a strand with two ends, it seems OK, but when the two ends have to stay attached to each other, topologically, it looks like it would become a mess.
There are enzymes that cut single strands so the mess can unwind. We have not paid much attention to the topology, but any biochemistry or molecular biology book will tell you the details.