Local Volume Concentration, Packing Domains and Scaling Properties of Chromatin.

We propose the Self Returning Excluded Volume (SR-EV) model for the structure of chromatin based on stochastic rules and physical interactions that is able to capture the observed behavior across imaging and sequencing based measures of chromatin organization. The SR-EV model takes the return rules of the Self Returning Random Walk, incorporates excluded volume interactions, chain connectivity and expands the length scales range from 10 nm to over 1 micron. The model is computationally fast and we created thousands of configurations that we grouped in twelve different ensembles according to the two main parameters of the model. The analysis of the configurations was done in a way completely analogous to the experimental treatments used to determine chromatin volume concentration, contact probability, packing domain identification and size characterization, and packing scaling behavior. We find a robust agreement between the theoretical and experimental results. The overall organization of the model chromatin is corrugated, with dense packing domains alternating with a very dilute regions in a manner that resembles the mixing of two disordered bi-continuous phases. The return rules combined with excluded volume interactions lead to the formation of packing domains. We observed a transition from a short scale regime to a long scale regime occurring at genomic separations of ~ 4 × 10 base pairs or ~ 100 nm in distance. The contact probability reflects this transition with a change in the scaling exponent from larger than -1 to approximately -1. The analysis of the pair correlation function reveals that chromatin organizes following a power law scaling with exponent in the transition region between the short and long distance regimes.