Modeling High-Order Chromatin Structure in Single Cells

Abstract

Chromosome conformation capture techniques have discovered territorial organization of chromatin at an ensemble-averaged level. However, how chromatin folds at the single-cell level still remains elusive. Here, we introduce a self-returning random walk to describe the high-order structure of chromatin in single cells. Based on a simple folding algorithm, our 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 associating domains are liquid-tree-like structures, linked and isolated by stretched out, transcriptionally active chromatin backbone to form a secondary structure of chromatin that further folds into a “3D forest” under confinement. Our theoretical predictions compare favorably with experimental observations of chromatin scaling and packing heterogeneity, which leads to the hypothesis that well-organized 3D structures such as domains and compartments are intrinsic chromatin characteristics at the single-cell level rather than merely statistical patterns of a large population. Based on a global folding parameter, the model reveals a unique structure-function relation that couples many chromatin structural properties under genomic response to environmental stress. Our results suggest the existence of universal folding principles for chromatin to fulfill its regulatory functions.