Linking chromatin interaction network topology to three-dimensional genome conformation: An analytical framework for chromatin structure

Three-dimensional chromatin architecture is shaped by long-range interactions mediated by various proteins, forming a complex chromatin interaction network. However, how the topology of this network controls chromatin architecture remains unclear. Using a minimal cross-linked polymer model, we derive the spatial position distribution of chromatin fragments, the spatial distance distribution between fragments, and the joint distribution of spatial distances for two fragment pairs. Furthermore, we reveal analytical relationships linking chromatin interaction network to parameters of the derived distributions. In particular, the scale parameter of the spatial distance distribution depends solely on network topology, defined as the "effective tether length" (ETL), which can be further decomposed based on connection topology. Our results generalize the work of Gabriele et al. [Science 376, 496 (2022)10.1126/science.abn6583] on the ETL from systems with a single long-range interaction to those with multiple interactions. On the other hand, our derived joint distribution and the corresponding correlation coefficient provide insights into the experimental observation by Fukaya et al. [Cell 166, 358 (2016)10.1016/j.cell.2016.05.025], highlighting how shared enhancer positioning regulates the coordinated dynamics of enhancer-promoter interactions. Our theoretical findings decipher the role of the topological structure of chromatin interaction networks in controlling chromatin architecture.