  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.
