  The problem of detecting a binding site -- a substring of DNA where
transcription factors attach -- on a long DNA sequence requires the recognition
of a small pattern in a large background. For short binding sites, the matching
probability can display large fluctuations from one putative binding site to
another. Here we use a self-consistent statistical procedure that accounts
correctly for the large deviations of the matching probability to predict the
location of short binding sites. We apply it in two distinct situations: (a)
the detection of the binding sites for three specific transcription factors on
a set of 134 estrogen-regulated genes; (b) the identification, in a set of 138
possible transcription factors, of the ones binding a specific set of nine
genes. In both instances, experimental findings are reproduced (when available)
and the number of false positives is significantly reduced with respect to the
other methods commonly employed.
