Recovering Chromatin Conformations from Contact Probabilities

Abstract

The packaging of chromatin within the nucleus of eukaryotic cells is achieved through several levels of spatial organization. The lowest levels give rise to nucleosomes and the 30-nm chromatin fiber while the higher levels involve folding of the chromatin fiber into chromosomes. These higher levels, often referred to as the higher order organization of chromatin, are still poorly understood but are actively being investigated through a new class of experiments known as chromatin conformation capture (3C), and its high-throughput derivative called Hi-C. These experiments detect contacts between different genomic loci, yielding contact probabilities (CPs) that may be used to elucidate the higher order organization of chromatin. Here we present a computational method for recovering chromatin conformation ensembles from reference CPs (Meluzzi D and Arya G. Nucleic Acids Research. 2013 41:63). The conformations are generated by simulating a bead-chain polymer model that represents the 30-nm chromatin fiber. Selected parameters of this polymer model are optimized iteratively until the CPs estimated from the conformation ensembles match the reference CPs. To minimize the size of ensembles required to reliably compute the CPs, we have developed a method that estimates CPs by fitting the extended generalized lambda distribution to simulated inter-bead distances. We show that our overall approach enables the recovery of conformation ensembles for genomic lengths on the order of 1 Mbp and that these ensembles can be used to investigate the shape and spatial properties of biologically relevant chromatin domains.