On the value of intra-motif dependencies of human insulator protein CTCF

The modularity of the ZOOPS model allows for combining an arbitrary motif model with parameters Θm with an arbitrary flanking model with parameters Θf. The binary latent variable ui handles the situation that the i-th sequence contains (ui = 1) or contains not (ui = 0) a binding site. We model the position of the binding site of width W by the latent variable vi ∈ {1, . . . , Li −W + 1}. The binding site may occur on both strands, so we introduce a third latent variable si ∈ {F,R}, indicating whether the binding site occurs on the forward strand (si = F ) or on the reverse complement strand (si = R). We denote the latent variables of the complete data set by ~u = (u1, . . . , uN ), ~v = (v1, . . . , vN ), and ~s = (s1, . . . , sN ). The conditional likelihood of X given the latent variables (~u,~v,~s) and parameters Θm,Θf is given by