Statistical detection of co-operative transcription factors with similarity adjustment

Motivation: Statistical assessment of cis-regulatory modules (CRMs) is a crucial task in computational biology. Usually, one concludes from exceptional co-occurrences of DNA motifs that the corresponding transcription factors are co-operative. However, similar DNA motifs tend to co-occur in random sequences due to high probability of over-lapping occurrences. Therefore, it is important to consider similarity of DNA motifs in the statistical assessment. Results: Based on previous work, we propose to adjust the window size for co-occurrence detection. Using the derived approximation, one obtains different window sizes for different sets of DNA motifs depending on their similarities. This ensures that the probability of co-occurrences in random sequences are equal. Applying the approach to selected similar and dissimilar DNA motifs from human trans-cription factors shows the necessity of adjustment and confirms the accuracy of the approximation by comparison to simulated data. Furthermore, it becomes clear that approaches ignoring similari-ties strongly underestimate p-values for co-operativity of transcription factors with similar DNA motifs. In addition, the approach is extended to deal with overlapping win-dows. We derive Chen-Stein error bounds for the approximation. Comparing the error bounds for similar and dissimilar DNA motifs shows that the approximation for similar DNA motifs yields large bounds. Hence, one has to be careful using overlapping windows. Based on the error bounds, one can pre-compute the approximation errors and select an appropriate overlap-scheme before running the analysis. Availability: Software to perform the calculation for pairs of Position Frequency Matrices (PFMs) is available a