Fast Westfall-Young permutation procedure for combinatorial regulation discovery

Three or more transcription factors (TFs) often work together, and the combinatorial regulations are essential in cellular machinery. However, it is impossible to discover statistically significant sets of TF binding motifs due to the necessity of the multiple testing procedure. To improve the sensitivity of widely used Bonferroni correction or its modified methods, such as Holm procedure, Westfall-Young permutation procedure (WY-procedure) has often been applied. However, few studies have used WY-procedure for the discoveries of the combinatorial effects of the motifs because of the extremely large computational time. In this paper, we propose an efficient branch-and-bound algorithm to perform WY-procedure to enumerate statistically significant motif combinations. When we use WY-procedure for the combinatorial regulation discovery, finding the minimum P-value from each permuted dataset consumes an enormous amount of time. We show that a combination that has the possibility to achieve the minimum P-value appears with high frequency over the threshold in dataset. This property enables a frequent itemset mining algorithm to efficiently select the candidates to achieve the minimum P-value. Our demonstrations using yeast and human transcriptome datasets show that the proposed algorithm is orders-of-magnitude faster than WY-procedure, and can practically list statistically significant motif combinations even when any combinations are considered.