  It is widely believed that the folding of the chromosome in the nucleus has a
major effect on genetic expression. For example co-regulated genes in several
species have been shown to colocalize in space despite being far away on the
DNA sequence. In this manuscript, we present a new method to model the
three-dimensional structure of the chromosome in live cells, based on DNA-DNA
interactions measured in high-throughput chromosome conformation capture
experiments (Hi-C) and genome architecture mapping experiments (GAM). Our
approach incorporates a polymer model, and directly uses the contact
probabilities measured in Hi-C and GAM experiments rather than estimates of
average distances between genomic loci. Specifically, we model the chromosome
as a Gaussian polymer with harmonic interactions and extract the coupling
coefficients best reproducing the experimental contact probabilities. In
contrast to existing methods, we give an exact expression of the contact
probabilities at thermodynamic equilibrium. The Gaussian effective model (GEM)
reconstructed with our method reproduces experimental contacts with high
accuracy. We also show how Brownian Dynamics simulations of our reconstructed
GEM can be used to study chromatin organization, and possibly give some clue
about its dynamics.
