A unified approach for quantifying and interpreting DNA shape readout by transcription factors

Transcription factors (TFs) interpret DNA sequence by probing the chemical and structural properties of the nucleotide polymer. DNA shape is thought to enable a parsimonious representation of dependencies between nucleotide positions. Here, we propose a unified mathematical representation of the DNA sequence dependence of shape and TF binding, respectively, which simplifies and enhances analysis of shape readout. First, we demonstrate that linear models based on mononucleotide features alone account for 60-70% of the variance in minor groove width, roll, helix twist, and propeller twist. This explains why simple scoring matrices that ignore all dependencies between nucleotide positions can partially account for DNA shape readout by a TF Adding dinucleotide features as sequence-to-shape predictors to our model, we can almost perfectly explain the shape parameters. Building on this observation, we developed a post hoc analysis method that can be used to analyze any mechanism-agnostic protein-DNA binding model in terms of shape readout. Our insights provide an alternative strategy for using DNA shape information to enhance our understanding of how cis-regulatory codes are interpreted by the cellular machinery.