Reliable scaling of Position Weight Matrices for binding strength comparisons between transcription factors

Scoring DNA sequences against Position Weight Matrices (PWMs) is a widely adopted method to identify putative transcription factor binding sites. While common bioinformatics tools produce scores that can reflect the binding strength between a specific transcription factor and the DNA, these scores are not directly comparable between different transcription factors. Here, we provide two different ways to find the scaling parameter $\lambda$ that allows us to infer binding energy from a PWM score. The first approach uses a PWM and background genomic sequence as input to estimate $\lambda$ for a specific transcription factor, which we applied to show that $\lambda$ distributions for different transcription factor families correspond with their DNA binding properties. Our second method can reliably convert $\lambda$ between different PWMs of the same transcription factor, which allows us to directly compare PWMs that were generated by different approaches. These two approaches provide consistent and computationally efficient ways to scale PWMs scores and estimate transcription factor binding sites strength.