  The problem of motif detection can be formulated as the construction of a
discriminant function to separate sequences of a specific pattern from
background. In computational biology, motif detection is used to predict DNA
binding sites of a transcription factor (TF), mostly based on the weight matrix
(WM) model or the Gibbs free energy (FE) model. However, despite the wide
applications, theoretical analysis of these two models and their predictions is
still lacking. We derive asymptotic error rates of prediction procedures based
on these models under different data generation assumptions. This allows a
theoretical comparison between the WM-based and the FE-based predictions in
terms of asymptotic efficiency. Applications of the theoretical results are
demonstrated with empirical studies on ChIP-seq data and protein binding
microarray data. We find that, irrespective of underlying data generation
mechanisms, the FE approach shows higher or comparable predictive power
relative to the WM approach when the number of observed binding sites used for
constructing a discriminant decision is not too small.
