GEN-ERIC News

“Knot formation is important in many fields,” said Douglas Smith, an assistant professor of physics who was the senior author on the paper. “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 because he was interested in knot theory—the branch of mathematics that uses formulae 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 experimental set up consisted of a plastic box that was spun by a computer-controlled motor. A piece of string was dropped into the box and tumbled around like clothes in a dryer. Knots formed very quickly, within 10 seconds. The researchers repeated the experiment more than 3,000 times varying the length and stiffness of string, box size and speed of rotation. They classified the resulting knots. “It is virtually impossible to distinguish different knots just by looking at them,” said Raymer. “So I developed a computer program to do it. The computer program counts each crossing of the string. It notes whether the crossing is under or over, and whether the string follows a path to the left or to the right. The result is a bunch of numbers that can be translated into a mathematical fingerprint for a knot.