Position weight matrices are the de facto most commonly used models for describing sequence affinities of DNA-binding proteins. It's also well known that most PWM hits on the genome show no evidence of binding from genome-wide binding assays such as ChIP/DNase/DamID. A commonly offered explanation for these "PWM false positives" is competition effects with other DNA-binding proteins such as transcription factors and nucleosomes.
1) Do these "PWM false positives" show binding in in vitro assays using only naked DNA and the protein under study?
2) Are there alternative statistical models of protein-DNA binding (short of doing a full molecular dynamics simulation) that have been shown to significantly outperform PWMs, again for in vitro data that does not consider competition effects?