  Transcription factors (TFs) exert their regulatory action by binding to DNA
with specific sequence preferences. However, different TFs can partially share
their binding sequences due to their common evolutionary origin. This
`redundancy' of binding defines a way of organizing TFs in `motif families' by
grouping TFs with similar binding preferences. Since these ultimately define
the TF target genes, the motif family organization entails information about
the structure of transcriptional regulation as it has been shaped by evolution.
Focusing on the human TF repertoire, we show that a one-parameter evolutionary
model of the Birth-Death-Innovation type can explain the TF empirical
ripartition in motif families, and allows to highlight the relevant
evolutionary forces at the origin of this organization. Moreover, the model
allows to pinpoint few deviations from the neutral scenario it assumes: three
over-expanded families (including HOX and FOX genes), a set of `singleton' TFs
for which duplication seems to be selected against, and a higher-than-average
rate of diversification of the binding preferences of TFs with a Zinc Finger
DNA binding domain. Finally, a comparison of the TF motif family organization
in different eukaryotic species suggests an increase of redundancy of binding
with organism complexity.
