Abstract
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.
Highlights
Chromatin is organized in heterogeneous sub-regions of various sizes, as recently revealed by Chromosome Capture (5C) data [1, 2]
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
By exploring the statistics of simulated single particle trajectories (SPTs), we further show that the large heterogeneity of the anomalous exponent present in live cell imaging can be explained by random binding locations on the chromatin that can vary from cell to cell
Summary
Chromatin is organized in heterogeneous sub-regions of various sizes, as recently revealed by Chromosome Capture (5C) data [1, 2]. Mammalian chromatin at a resolution of 3kb, [3, 4] contains an organization at 1Mbp scale, where several sub-structures are enriched with intra-connectivity, reflecting an increased encounter probability (EP) between genomic segments. This increased EP is described in the two-dimensional encounter frequency (EF) matrix, containing diagonal blocks called Topologically Associating Domains (TADs) [3, 5]. TADs represent average chromatin conformations, characterized by a higher numbers of binding molecules compared to non-TAD regions
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