Multi-contact statistics distinguish models of chromosome organization

Chromosome organization in both eukaryotes and prokaryotes is highly regulated. Organizing mechanisms, such as loop-extrusion, have been extensively studied using Hi-C methods, which measure pairwise contacts between chromosomal regions. New multi-contact methods additionally measure which chromosomal contacts occur simultaneously. Here, we develop three predictors of baseline multi-contact frequencies given pairwise contact data, corresponding to distinct physical limits, and argue that a comparison between data and prediction can lead to biological insight. We test these predictors for two simulated polymer models with cross-linking or loop-extrusion, and find that simulated three-point contacts are only predicted by the physically appropriate approximation. Finally, we apply our approach to previously published experimental multi-contact data from human chromosomes. Strikingly, we discover that observed three-point contact frequencies are well predicted by a formula based on loop-extrusion, suggesting that multi-contact data can give insight into chromosome organization mechanisms.