Self-similarity in entanglement complexity along the backbones of compact proteins

The mean overcrossing number is a useful descriptor of the nature and complexity of self-entanglements in polymer conformations. We show that this descriptor exhibits a degree of self-similarity along the backbones of protein native states. We have estimated the scaling exponent for the power-law behavior of the mean number of overcrossings as a function of the contour length within a fixed (compact) backbone. The reported scaling behavior is found in self-entanglements and not in descriptors of molecular size. The result provides a useful criterion for the elucidation of protein conformations.