Loop competition and extrusion model predicts CTCF interaction specificity

Three-dimensional chromatin looping interactions play an important role in constraining enhancer-promoter interactions and mediating transcriptional gene regulation. CTCF is thought to play a critical role in the formation of these loops, but the specificity of which CTCF binding events form loops and which do not is difficult to predict. Loops often have convergent CTCF binding site motif orientation, but this constraint alone is only weakly predictive of genome-wide interaction data. Here we present an easily interpretable and simple mathematical model of CTCF mediated loop formation which is consistent with Cohesin extrusion and can predict ChIA-PET CTCF looping interaction measurements with high accuracy. Competition between overlapping loops is a critical determinant of loop specificity. We show that this model is consistent with observed chromatin interaction frequency changes induced by CTCF binding site deletion, inversion, and mutation, and is also consistent with observed constraints on validated enhancer-promoter interactions.