Multicontact statistics distinguish models of chromosome organization

Chromosome organization can be modeled using various approaches, ranging from mechanistic bottom-up models to models inferred directly from experimental data. Many such models can recapitulate experimental Hi-C data for pairwise contact probabilities, meaning that these data cannot always be used to distinguish different models. Here, we consider two illustrative example models for bacterial chromosome organization: one a bottom-up model for loop extrusion, the other a data-driven maximum entropy model inferred from Hi-C data. We find that despite predicting similar pairwise contact frequencies, the models predict qualitatively different features on three-point contact maps. We explain these differences by constructing analytical approximations for three-point contact probabilities in each model. Finally, we apply our analytical approximations to previously published experimental multicontact data from human chromosomes, and find that these data are well described by the loop extruder approximation. Our work illustrates how multicontact statistics can be used to compare and test models for chromosome organization.