The distribution of p-values is different for each PWM, so q-values are computed separately for each motif. The FDR should be considered separately for each motif. Note thoug,h that the q-values provided by FIMO are compensating for applying the p-value threshold for a single motif at each point in your sequences. In a previous posting you noted that you are scanning with 4000 motifs, so you are introducing a second, distinct, source of multiple tests issues, which are not considered by FIMO. You may want to consider applying a
Bonferroni correction to the FIMO q-values, say multiplying them by 1e4 or 1e3 (roughly 1/4000) .