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Asymptotic formula of polymer looping and applications to chromatin reconstruction from data

The organization and dynamics of the chromatin in the cell nucleus remains unclear. Two ensembles of data are accessible : many stochastic single particle trajectories (SPTs) of a DNA locus and the distribution of polymer loops across cell populations : What can be recovered about the geometrical organization of the DNA from these two ensemble of data ?

We will present our past efforts to study loop distributions by estimating the eigenvalues of the Laplace’s equation in high dimensional space, when a tubular neighborhood of a sub-manifold is removed using the Chavel-Feldman asymptotic expansion. It is also possible to construct a polymer model with a prescribed anomalous exponent starting with the stochastic Rouse model. These results are used to reconstruct the geometrical coarse-grained organization of the chromatin from million-by-million matrix (Hi-C data), to predict gene interactions and to connect the statistics of SPTs with Hi-C.


CMAP UMR 7641 École Polytechnique CNRS, Route de Saclay, 91128 Palaiseau Cedex France, Tél: +33 1 69 33 46 23 Fax: +33 1 69 33 46 46