Take a long thread, close it into a ring, and tie a knot in it. The knot slides along the thread until it hits something. Now imagine the thread is made of two different segments: one stiff and slippery, the other soft and sticky. When heated, the sticky segment softens, and the knot can slide off it, like a sled sliding off a melting hill. That is exactly the picture observed in a computer experiment with tiny molecular rings.
The authors built a model of a polymer ring (a long chain of repeating units) from two types of monomers: type A repels itself, while type B attracts itself. The interaction between A and B is neutral. The result is a chain with alternating "prickly" and "sticky" segments. They tied different knots in the rings, from a simple trefoil to a complex cinquefoil, and watched how their shape changed as the temperature varied from very low to very high. They used a clever Monte Carlo algorithm (a random walk method) that allowed them to scan all possible states of the system without getting stuck in energy wells.
A surprising thing emerged: at the same heating, the ring could either shrink or expand depending on how many sticky links it had. If the sticky block was short, the knot sat on it at low temperature, pulling the ring tight. Upon heating, the sticky links lost their grip, the knot slipped off, and the ring swelled. But if there were slightly more sticky links, the picture reversed: the cold ring was swollen, and it shrank upon heating. This "reversible" effect resembles a spring that is compressed and then released, but here it is all determined by the battle between attraction energy and the disorder (entropy) introduced by the knot.
Sailors' knots have their counterparts in the molecular world. For example, the trefoil knot, the simplest nontrivial knot, is found in the DNA of some viruses.
In Neal Stephenson's novel The Diamond Age, smart materials assemble from molecular blocks. Controlling knots on polymer chains is a step toward such programmable substances that change shape on command.