Transient chromatin properties revealed by polymer models and stochastic simulations constructed from Chromosomal Capture data

Chromatin organization can be probed by Chromosomal Capture (5C) data, from which the encounter probability (EP) between genomic sites is presented in a large matrix. This matrix is averaged over a large cell population, revealing diagonal blocks called Topological Associating Domains (TADs) that represent a sub-chromatin organization. To study the relation between chromatin organization and gene regulation, we introduce a computational procedure to construct a bead-spring polymer model based on the EP matrix. The model permits exploring transient properties constrained by the statistics of the 5C data. To construct the polymer model, we proceed in two steps: first, we introduce a minimal number of random connectors inside restricted regions to account for diagonal blocks. Second, we account for long-range frequent specific genomic interactions. Using the constructed polymer, we compute the first encounter time distribution and the conditional probability of three key genomic sites. By simulating single particle trajectories of loci located on the constructed polymers from 5C data, we found a large variability of the anomalous exponent, used to interpret live cell imaging trajectories. The present polymer construction provides a generic tool to study steady-state and transient properties of chromatin constrained by some physical properties embedded in 5C data.Author summary: Chromatin organization remains poorly understood and polymer models are used to reconstruct such organization, to reveal hidden structures and to quantify genomic interactions. We use a generalized Rouse model (a linear chain of beads connected by springs) with additional interacting molecules that allow stable loop formation. The polymer models are constructed using the minimal number of binding molecules, positioned according to the encounter probability matrix obtained from experimental chromosomal capture data. We determine the conditional encounter probability of 3 key loci regulating gene inactivation from our calibrated polymer model. Using polymer simulations, we generate single particle trajectories and explore their transient properties. The present results suggest that the heterogeneity of anomalous exponents measured in live cell imaging is due to the large combinatorics in reconstructing the chromatin organization from Chromosomal Capture data. The present method and algorithms are generic and can be used to reconstruct a polymer model at a given scale from any Chromosomal Capture data.