Context-specific independence mixture modeling for positional weight matrices

Motivation: A positional weight matrix (PWM) is a statistical representation of the binding pattern of a transcription factor estimated from known binding site sequences. Previous studies showed that for factors which bind to divergent binding sites, mixtures of multiple PWMs increase performance. However, estimating a conventional mixture distribution for each position will in many cases cause overfitting. Results: We propose a context-specific independence (CSI) mixture model and a learning algorithm based on a Bayesian approach. The CSI model adjusts complexity to fit the amount of variation observed on the sequence level in each position of a site. This not only yields a more parsimonious description of binding patterns, which improves parameter estimates, it also increases robustness as the model automatically adapts the number of components to fit the data. Evaluation of the CSI model on simulated data showed favorable results compared to conventional mixtures. We demonstrate its adaptive properties in a classical model selection setup. The increased parsimony of the CSI model was shown for the transcription factor Leu3 where two binding-energy subgroups were distinguished equally well as with a conventional mixture but requiring 30% less parameters. Analysis of the human-mouse conservation of predicted binding sites of 64 JASPAR TFs showed that CSI was as good or better than a conventional mixture for 89% of the TFs and for 70% for a single PWM model.