Importance of evenly divided modules. Individual lines show different divisions of a 15-nucleotide motif into three modules. For a random region of 100 nucleotides, only 51,000 molecules would need to be searched to have a 99% chance of finding a motif divided into three 5 mers (heavy line at bottom of graph), but nearly four million molecules (a factor of almost 100) would need to be searched to have the same chance of finding a motif divided into a 13 mer and two monomers (heavy line at top of graph). The other lines show the other 87 ways of dividing the motif. Out of 91 total ways, there is one way to divide it into three 5 mers, there are three ways to divide it into a 13 mer and two monomers: [13, 1, 1], [1, 13, 1], and [1, 1, 13]. Similarly, there are three ways to divide it into any other configuration in which two of the pieces are equal. There are six ways to divide it into any particular configuration where all three pieces are unequal: for example, [9, 4, 2], [9, 2, 4], [4, 9, 2], [4, 2, 9], [2, 9, 4], and [2, 4, 9]. Only the size of the pieces, not their order, affects the probability, so only 19 distinct lines are visible on the graph (some are very close together). The top two lines on the graph (the [13, 1, 1] family and the [12, 2, 1] family) are clear outliers; most divisions are closer to the best case of [5, 5, 5] than to the worst case. This effect becomes more extreme at higher modularity. The horizontal gray bar shows 1000 zeptomole (602,000 sequences).
