"Knot formation is important in many fields," said University of California-San Diego Assistant Professor Douglas Smith, senior author of the study. "For example, knots often form in DNA, which is a long string-like molecule. Cells have enzymes that undo the knots by cutting the DNA strands so that they can pass through each other. Certain anti-cancer drugs stop tumor cells from dividing by blocking the unknotting of DNA."

Dorian Raymer, a research assistant working with Smith, initiated the study while he was an undergraduate because he was interested in knot theory -- the branch of mathematics that uses formulas to distinguish unique knots.

"Very little experimental work had been done to apply knot theory to the analysis and classification of real, physical knots," said Smith. "For mathematicians, the problem is very abstract. They imagine the types of knots that can form and then classify them. In our experiments, we produced thousands of different knots, used mathematical knot theory to analyze them and then developed a simple physics model to explain our findings."

The findings appear in the Proceedings of the National Academy of Sciences.