TherMos: Estimating protein–DNA binding energies from in vivo binding profiles

Accurately characterizing transcription factor (TF)-DNA affinity is a central goal of regulatory genomics. Although thermodynamics provides the most natural language for describing the continuous range of TF-DNA affinity, traditional motif discovery algorithms focus instead on classification paradigms that aim to discriminate 'bound' and 'unbound' sequences. Moreover, these algorithms do not directly model the distribution of tags in ChIP-seq data. Here, we present a new algorithm named Thermodynamic Modeling of ChIP-seq (TherMos), which directly estimates a position-specific binding energy matrix (PSEM) from ChIP-seq/exo tag profiles. In cross-validation tests on seven genome-wide TF-DNA binding profiles, one of which we generated via ChIP-seq on a complex developing tissue, TherMos predicted quantitative TF-DNA binding with greater accuracy than five well-known algorithms. We experimentally validated TherMos binding energy models for Klf4 and Esrrb, using a novel protocol to measure PSEMs in vitro. Strikingly, our measurements revealed strong non-additivity at multiple positions within the two PSEMs. Among the algorithms tested, only TherMos was able to model the entire binding energy landscape of Klf4 and Esrrb. Our study reveals new insights into the energetics of TF-DNA binding in vivo and provides an accurate first-principles approach to binding energy inference from ChIP-seq and ChIP-exo data.