Towards a theoretical understanding of false positives in DNA motif finding

Background: Detection of false-positive motifs is one of the main causes of low performance in de novo DNA motif-finding methods. Despite the substantial algorithm development effort in this area, recent comprehensive benchmark studies revealed that the performance of DNA motif-finders leaves room for improvement in realistic scenarios. Results: Using large-deviations theory, we derive a remarkably simple relationship that describes the dependence of false positives on dataset size for the one-occurrence per sequence motif-finding problem. As expected, we predict that false-positives can be reduced by decreasing the sequence length or by adding more sequences to the dataset. Interestingly, we find that the false-positive strength depends more strongly on the number of sequences in the dataset than it does on the sequence length, but that the dependence on the number of sequences diminishes, after which adding more sequences does not reduce the false-positive rate significantly. We compare our theoretical predictions by applying four popular motif-finding algorithms that solve the one-occurrence-per -sequence problem (MEME, the Gibbs Sampler, Weeder, and GIMSAN) to simulated data that contain no motifs. We find that the dependence of false positives detected by these softwares on the motif-finding parameters is similar to that predicted by our formula. Conclusions: We quantify the relationship between the sequence search space and motif-finding false-positives. Based on the simple formula we derive, we provide a number of intuitive rules of thumb that may be used to enhance motif-finding results in practice. Our results provide a theoretical advance in an important problem in computational biology.