  We present a minimal computational model, which allows very fast, on-the-fly
construction of three dimensional haploid interphase genomes from single cell
Hi-C contact maps using the HOOMD-blue molecular dynamics package on graphics
processing units. Chromosomes are represented by a string of connected beads,
each of which corresponds to 100,000 base pairs, and contacts are mediated via
a structure-based harmonic potential. We suggest and test two minimization
protocols which consistently fold into conformationally similar low energy
states. The latter are similar to previously published structures but are
calculated in a fraction of the time. We find evidence that mere fulfillment of
contact maps is insufficient to create experimentally relevant structures.
Particularly, an excluded volume term is required in our model to induce the
formation of chromosome territories. We also observe empirically that contact
maps do not capture the chirality of the underlying structures. Depending on
starting configurations and protocol details, one of two mirror images emerges.
Finally, we analyze the occurrence of knots in a particular chromosome. The
same knot appears in (almost) all structures irrespective of minimization
protocols or even details of underlying potentials providing further evidence
for the existence of knots in interphase chromatin.
