Inherent limitations of probabilistic models for protein-DNA binding specificity

The specificities of transcription factors are most commonly represented with probabilistic models. These models provide a probability for each base occurring at each position within the binding site and the positions are assumed to contribute independently. The model is simple and intuitive and is the basis for many motif discovery algorithms. However, the model also has inherent limitations that prevent it from accurately representing true binding probabilities, especially for the highest affinity sites under conditions of high protein concentration. The limitations are not due to the assumption of independence between positions but rather are caused by the non-linear relationship between binding affinity and binding probability and the fact that independent normalization at each position skews the site probabilities. Generally probabilistic models are reasonably good approximations, but new high-throughput methods allow for biophysical models with increased accuracy that should be used whenever possible.Author summary: Transcription factors (TFs), a class of DNA-binding proteins, play a central role in the regulation of gene expression. TFs control the rate of transcription by binding to the genome in a sequence-specific manner. Thus, one important aspect in the study of gene regulation mechanism is to model the binding specificities of TFs, namely the features of the DNA sequences that a TF prefers to bind. Multiple models have been proposed to characterize the binding specificities of TFs, among which the class of probabilistic models is the most popular. In this study, we point out several major limitations of the well-established probabilistic model by comparing it with the biophysical model. Through simulations we demonstrate that the probabilistic model is only an approximation of the biophysical model. The latter has most of the advantages of the former, and is a more accurate representation of binding specificities. We propose a shift from the probabilistic model to the biophysical model in future studies of protein-DNA interactions.