Estimating Motifs Under Order Restrictions

Erik W van Zwet 1 , Katherina J Kechris 2 , Peter J Bickel 3  and Michael B. Eisen 4
  • 1 Mathematical Institute, Leiden University
  • 2 Department of Biochemistry and Biophysics, University of California, San Francisco
  • 3 Department of Statistics, University of California, Berkeley
  • 4 Department of Molecular and Cell Biology, University of California, Berkeley; Life Sciences Division, Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley

Transcription factors and many other DNA-binding proteins recognize more than one specific sequence. Among sequences recognized by a given DNA-binding protein, different positions exhibit varying degrees of conservation. The reason is that base pairs that are more extensively contacted by the protein tend to be more conserved. This observation can be used in the discovery of transcription factor binding sites. Here we present a rigorous means to accomplish this. In particular, we constrain the order of the information (entropy) in the columns of the position specific weight matrix (PWM) which characterizes the motif being sought. We then show how to compute the maximum likelihood estimate of a PWM under such order restrictions. This computation is easily integrated with the EM algorithm or the Gibbs sampler to enhance performance in the search for motifs in unaligned sequences. We demonstrate our method on a well-known data set of binding sites of the transcription factor Crp in E. coli.

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SAGMB publishes significant research on the application of statistical ideas to problems arising from computational biology. The range of topics includes linkage mapping, association studies, gene finding and sequence alignment, protein structure prediction, design and analysis of microarrary data, molecular evolution and phylogenetic trees, DNA topology, and data base search strategies.

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