  Chromosomes in the nucleus assemble into hierarchies of 3D domains that,
during interphase, share essential features with a knot-free condensed polymer
known as the fractal globule (FG). The FG-like chromosome likely affects
macromolecular transport, yet its characteristics remain poorly understood.
Using computer simulations and scaling analysis, we show that the 3D folding
and macromolecular size of the chromosomes determine their transport
characteristics. Large-scale subdiffusion occurs at a critical particle size
where the network of accessible volumes is critically connected. Condensed
chromosomes have connectivity networks akin to simple Bernoulli bond
percolation clusters, regardless of the polymer models. However, even if the
network structures are similar, the tracer's walk dimension varies. It turns
out that the walk dimension depends on the network topology of the accessible
volume and dynamic heterogeneity of the tracer's hopping rate. We find that the
FG structure has a smaller walk dimension than other random geometries,
suggesting that the FG-like chromosome structure accelerates macromolecular
diffusion and target-search.
