A flexible thread, coiled into a loop, was locked in a tiny box with liquid. It can either absorb water and swell like a sponge, or expel the moisture and shrink into a tight ball. The choice between these states depends on whether the thread has a knot – and which one.
The reason lies in entropy, a measure of disorder. A knot limits the possible bends of the thread, shifting the balance between order and chaos. Even a simple trefoil knot markedly shifts the critical point where the sponge turns into a ball.
Surprisingly, this molecular geometry isn't just for artificial carbon-based polymers. Inside cells, DNA and proteins constantly get tangled into knots, and their shape regulates biological processes. By controlling knots, you could create nanomachines that change shape on command.
The protein carbonic anhydrase carries a trefoil knot that keeps the molecule from unfolding under heat – like a molecular stopper.