A Random Effect Model for Reconstruction of Spatial Chromatin Structure

Abstract

A gene may be controlled by distal enhancers and repressors, not merely by regulatory elements in its promoter. Spatial organization of chromosomes is the mechanism that brings genes and their distal regulatory elements into close proximity. Recent molecular techniques, coupled with Next Generation Sequencing (NGS) technology, enable genome-wide detection of physical contacts between distant genomic loci. In particular, Hi-C is an NGS-aided assay for the study of genome-wide spatial interactions. The availability of such data makes it possible to reconstruct the underlying three-dimensional (3D) spatial chromatin structure. In this article, we present the Poisson Random effect Architecture Model (PRAM) for such an inference. The main feature of PRAM that separates it from previous methods is that it addresses the issue of over-dispersion and takes correlations among contact counts into consideration, thereby achieving greater consistency with observed data. PRAM was applied to Hi-C data to illustrate its performance and to compare the predicted distances with those measured by a Fluorescence In Situ Hybridization (FISH) validation experiment. Further, PRAM was compared to other methods in the literature based on both real and simulated data.

Principal curve approaches for inferring 3D chromatin architecture

“…Poisson models C ij ∼ P ois(λ ij ) are widely adopted , Zou et al, 2016, Park and Lin, 2017, where λ ij = λ ij (x 1 , . .…”

“…The absence of gold standards makes such assessment challenging. In comparing competing 3D genome reconstructions several authors have appealed to simulation (Zhang et al, 2013, Zou et al, 2016, Park and Lin, 2017, however, real data referents are preferable. To that end, many of the same reconstruction algorithm developers have made recourse to fluorescence in situ hybridization (FISH) imaging as a basis for gauging accuracy.…”

“…This proceeds by comparing distances between imaged probes with corresponding reconstruction-based distances. But such methods are necessarily limited by the sparse number of probes (∼ 2 − 6; see Lieberman-Aiden et al, , Shavit et al, 2014, Park and Lin, 2017 and the modest resolution thereof, many straddling over 1 megabase (Mb). The recent advent of multiplex FISH transforms 3D genome reconstruction accuracy evaluation by providing an order of magnitude more probes and hence two orders of magnitude more inter-probe distances than conventional FISH.…”

“…These parameters can be difficult to specify and their inclusion substantially increases the computational burden. Other approaches (Zhang et al, 2013, Park and Lin, 2017, Rieber and Mahony, 2017 do not formally incorporate contiguity but impose it post hoc, creating chromatin reconstructions by "connecting the dots" of the 3D solution according to the ordering of corresponding genomic bins.…”

An Empirical Bayes Approach for the Identification of Long-range Chromosomal Interaction from Hi-C Data

“…Depending on the resolution of the data, and the scale of the biological questions, there are many ways of modeling the 3D physical interaction between potential regulatory elements. Researchers have made important findings in analyzing Hi-C data, including the inference on the large-scale structure of the genome such as the topologically associated domains (TADs, e.g., Rieber and Mahony 2017), the A/B compartments (Zheng and Zheng, 2017) and the 3D spatial structure (Park and Lin, 2017), and the identification of the individual genomic loci pairs with physical interactions (peak calling, e.g., Ay et al 2014;Jin et al 2013).…”