Automated incorporation of pairwise dependency in transcription factor binding site prediction using dinucleotide weight tensors

Gene regulatory networks are ultimately encoded by the sequence-specific binding of (TFs) to short DNA segments. Although it is customary to represent the binding specificity of a TF by a position-specific weight matrix (PSWM), which assumes each position within a site contributes independently to the overall binding affinity, evidence has been accumulating that there can be significant dependencies between positions. Unfortunately, methodological challenges have so far hindered the development of a practical and generally-accepted extension of the PSWM model. On the one hand, simple models that only consider dependencies between nearest-neighbor positions are easy to use in practice, but fail to account for the distal dependencies that are observed in the data. On the other hand, models that allow for arbitrary dependencies are prone to overfitting, requiring regularization schemes that are difficult to use in practice for non-experts. Here we present a new regulatory motif model, called dinucleotide weight tensor (DWT), that incorporates arbitrary pairwise dependencies between positions in binding sites, rigorously from first principles, and free from tunable parameters. We demonstrate the power of the method on a large set of ChIP-seq data-sets, showing that DWTs outperform both PSWMs and motif models that only incorporate nearest-neighbor dependencies. We also demonstrate that DWTs outperform two previously proposed methods. Finally, we show that DWTs inferred from ChIP-seq data also outperform PSWMs on HT-SELEX data for the same TF, suggesting that DWTs capture inherent biophysical properties of the interactions between the DNA binding domains of TFs and their binding sites. We make a suite of DWT tools available at dwt.unibas. ch, that allow users to automatically perform ‘motif finding’, i.e. the inference of DWT motifs from a set of sequences, binding site prediction with DWTs, and visualization of DWT ‘dilogo’ motifs. Author Summary Gene regulatory networks are ultimately encoded in constellations of short binding sites in the DNA and RNA that are recognized by regulatory factors such as transcription factors (TFs). For several decades, computational analysis of regulatory networks has relied on a model of TF sequence-specificity, the position-specific weight-matrix (PSWM), that assumes different positions in a binding site contribute independently to the total binding energy of the TF. However, in recent years evidence has been accumulating that, at least for some TFs, this assumption does not hold. Here we present a new model for the sequence-specificity of TFs, the dinucleotide weight tensor (DWT), that takes arbitrary dependencies between positions in binding sites into account and show that it consistently outperforms PSWMs on high-throughput datasets on TF binding. Moreover, in contrast to previous approaches, DWTs are directly derived from first principles within a Bayesian framework, and contain no tunable parameters. This allows them to be easily applied in practice and we make a suite of tools available for computational analysis with DWTs.