Natural similarity measures between position frequency matrices with an application to clustering

Transcription factors (TFs) play a key role in gene regulation by binding to target sequences. In silico prediction of potential binding of a TF to a binding site is a well-studied problem in computational biology. The binding sites for one TF are represented by a position frequency matrix (PFM). The discovery of new PFMs requires the comparison to known PFMs to avoid redundancies. In general, two PFMs are similar if they occur at overlapping positions under a null model. Still, most existing methods compute similarity according to probabilistic distances of the PFMs. Here we propose a natural similarity measure based on the asymptotic covariance between the number of PFM hits incorporating both strands. Furthermore, we introduce a second measure based on the same idea to cluster a set of the Jaspar PFMs.