Hilbert curve or Hilbert space-filling curve is a continuous fractal space-filling curve that densely fills higher-dimensional space without crossing itself. It was first described by the German mathematician David Hilbert in 1891. In a recent article Aiden et al. describe a new method called as Hi-C for reconstructing the three-dimensional architecture of the human genome which not only reveals folding principles of the human genome but also resembles a polymer analog of Hilbert’s curve at the megabase scale. Their finding suggest that Chromosomes are organized in a fractal knot-free conformation or fractal globule that is densely packed while easily folded and unfolded contrary to what was previously hypothesized as an equilibrium globule. This study has shown that each Chromosome is organized into two separate compartments, keeping active genes accessible while sequestering unused DNA in a denser storage compartment. Each chromosome alternates between regions of active, gene-rich DNA and inactive, gene-poor stretches.

Abstract

We describe Hi-C, a method that probes the three-dimensional architecture of whole genomes by coupling proximity-based ligation with massively parallel sequencing. We constructed spatial proximity maps of the human genome with Hi-C at a resolution of 1 megabase. These maps confirm the presence of chromosome territories and the spatial proximity of small, gene-rich chromosomes. We identified an additional level of genome organization that is characterized by the spatial segregation of open and closed chromatin to form two genome-wide compartments. At the megabase scale, the chromatin conformation is consistent with a fractal globule, a knot-free, polymer conformation that enables maximally dense packing while preserving the ability to easily fold and unfold any genomic locus. The fractal globule is distinct from the more commonly used globular equilibrium model. Our results demonstrate the power of Hi-C to map the dynamic conformations of whole genomes.