A novel family of space-filling curves in their relation to chromosome conformation in eukaryotes

Spatial conformation of DNA chains during interphase in eukaryotic cell nucleus is relatively dense, yet unknotted and exhibits self-similar fractal properties. In this respect it resembles the space-filling curves of Hilbert, but differs in the experimentally accessible contact probability of distant loci. Here we construct space-filling curves with fractal domain boundaries of dimension close to that of the embedding space and show how these match the statistical properties and the contact probability of the DNA conformation. The present mathematical model should shed light on the statistical ensemble of unknotted dense polymers and ease the modeling of genome folding and related biological processes.