Abstract
A thermodynamic method for computing the stability and dynamics of chromatin loops is proposed. The CTCF-mediated interactions as observed in ChIA-PET experiments for human B-lymphoblastoid cells are evaluated in terms of a polymer model for chain folding physical properties and the experimentally observed frequency of contacts within the chromatin regions. To estimate the optimal free energy and a Boltzmann distribution of suboptimal structures, the approach uses dynamic programming with methods to handle degeneracy and heuristics to compute parallel and antiparallel chain stems and pseudoknots. Moreover, multiple loops mediated by CTCF proteins connected together and forming multimeric islands are simulated using the same model. Based on the thermodynamic properties of those topological three-dimensional structures, we predict the correlation between the relative activity of chromatin loop and the Boltzmann probability, or the minimum free energy, depending also on its genomic length. Segments of chromatin where the structures show a more stable minimum free energy (for a given genomic distance) tend to be inactive, whereas structures that have lower stability in the minimum free energy (with the same genomic distance) tend to be active.
