Abstract
Recent experimental and theoretical efforts have highlighted the fact that binding of transcription factors to DNA can be more accurately described by continuous measures of their binding affinities, rather than a discrete description in terms of binding sites. While the binding affinities can be predicted from a physical model, it is often desirable to know the distribution of binding affinities for specific sequence backgrounds. In this paper, we present a statistical approach to derive the exact distribution for sequence models with fixed GC content. We demonstrate that the affinity distribution of almost all known transcription factors can be effectively parametrized by a class of generalized extreme value distributions. Moreover, this parameterization also describes the affinity distribution for sequence backgrounds with variable GC content, such as human promoter sequences. Our approach is applicable to arbitrary sequences and all transcription factors with known binding preferences that can be described in terms of a motif matrix. The statistical treatment also provides a proper framework to directly compare transcription factors with very different affinity distributions. This is illustrated by our analysis of human promoters with known binding sites, for many of which we could identify the known regulators as those with the highest affinity. The combination of physical model and statistical normalization provides a quantitative measure which ranks transcription factors for a given sequence, and which can be compared directly with large-scale binding data. Its successful application to human promoter sequences serves as an encouraging example of how the method can be applied to other sequences.