The writhe of a knot is a mathematical measure of the net direction of crossing, summing clockwise against anticlockwise. The 2D writhe is the measure obtained from each of the crossings taken from a projection of the knot onto a two-dimensional surface. The 3D writhe, also called just 'writhe', is the average of 2D writhes across all possible projections.
It has recently been discovered that (3D) writhe is quantized. The quantum is 4/7.
This discovery was made by the Polish physicist Piotr Pieranski, using computer models of knotting techniques, taking into account how a loose knot can be shrunk to its ideal or minimal configuration. It was then confirmed by abstract mathematical methods by researchers Andrzej Stasiak and Corinne Cerf.
It is possible that this quantization may have implications for both the unfolding of DNA and the possible existence of knotted strings in string theory.
Source: this week's New Scientist (issue 2316). Cerf and Stasiak's work is in Proceedings of the National Academy of Sciences (vol. 97, p. 3795), Pieranski's is to appear in The European Physical Journal E.