Conformational properties of compact polymers

Abstract

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 L x L x L lattice with different occupancy fractions by modifying a recently proposed algorithm. The system sizes studied extend up to N=256,000 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.