Self-similarity of biopolymer backbones in the ribosome

Self-similar properties of the biopolymer backbones in the ribosome are investigated in terms of the fractal dimension. We especially estimate the chain fractal and capacity dimensions of the ribosomal RNAs and proteins, which are constituents of the ribosome. The fractal dimensions of both biopolymers are compared with that of the self-avoiding walk, which is a typical model of a polymer without interaction between monomers. We demonstrate that the fractality found in the ribosomal RNAs is pertinent to explain their structural characteristics: local helix formation and long-range tertiary interaction forming three-dimensional structures. The fractal dimension of the ribosomal protein supports the existence of the long and extended domain, which is hardly seen in the globular protein. The self-similarity also upholds the fact that the ribosomal proteins function primarily to stabilize the structure of the ribosome by both the long-extended domain of the protein penetrating into the inside of the RNA, and the globular domain interacting with the RNA on the exterior of it. These results partially, if not whole, unravel the structural characteristics of the biopolymers in the ribosome.