  Monte Carlo simulations of coarse-grained polymers provide a useful tool to
deepen the understanding of conformational and statistical properties of
polymers both in physical as well as in biological systems. In this study we
sample compact conformations on a cubic LxLxL lattice with different occupancy
fractions by modifying a recently proposed algorithm. The system sizes studied
extend up to N=256000 monomers, going well beyond the limits of older
publications on compact polymers. We analyze several conformational properties
of these polymers, including segment correlations and screening of excluded
volume. Most importantly we propose a scaling law for the end-to-end distance
distribution and analyze the moments of this distribution. It shows
universality with respect to different occupancy fractions, i.e. system
densities. We further analyze the distance distribution between intrachain
segments, which turns out to be of great importance for biological experiments.
We apply these new findings to the problem of chromatin folding inside
interphase nuclei and show that -- although chromatin is in a compacted state
-- the classical theory of compact polymers does not explain recent
experimental results.
