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Interphase chromatin as a self-returning random walk: Can DNA fold into liquid trees?

We introduce a self-returning random walk to describe the structure of interphase chromatin. Based on a simple folding algorithm, our de novo model unifies the high contact frequency discovered by genomic techniques, and the high structural heterogeneity revealed by imaging techniques, which two chromatin properties we theoretically prove to be irreconcilable within a fractal polymer framework. Our model provides a holistic view of chromatin folding, in which the topologically associated domains are liquid-tree-like structures, linked and isolated by stretched-out, transcriptionally active DNA to form a secondary structure of chromatin that further folds into a “3D forest” under confinement.