A polymer model for the quantitative reconstruction of 3d chromosome architecture from HiC and GAM data

In this article, we present a polymermodel of the chromosome that can be parameterized to quantitatively reproduce contact probabilities measured in high-throughput chromosome conformation capture (Hi-C) or genome architecture mapping (GAM) experiments. Specifically, our Gaussian effective model (GEM) introduces harmonic potentials to represent interactions detected during such experiments. As a central property, we derive an exact relation between the couplings of these potentials and the resulting contact probabilities. This relation is used here to solve the inverse problem of constructing a GEM which best reproduces the contact probabilities measured experimentally. For that purpose, we present a minimization scheme that searches for the GEM that has contact probabilities as close as possible to the experimental ones. We apply this method to several data sets generated from experiments using the Hi-C or GAM techniques. To illustrate potential applications of our method, we show how the reconstructed couplings can be used to investigate the chromosome organization by Brownian Dynamics.