Pictorial representation of the PASA algorithm. Overlapping Arabidopsis transcript sequence alignments are ordered by their beginning position and assigned indices 0–8 as shown in (a). The matrix shown in (b) provides the ordered alignments along the rows and columns according to their index positions. The predetermined containments (chain links) and incompatibilities (bricks) present obstacles within the matrix, disallowing any direct comparisons between two alignments during La or Ra calculations. To compute La, each alignment a is compared with all compatible preceding alignments b, generating the value max[Ca, Lb + Ca\b] stored in the upper left of the matrix cell at [row b][column a], with an arrow drawn to the Lb value that yielded the max. La is then the maximum upper left value in column a and is shown circled in yellow. After all La values are computed, the maximum one is found at [row 7][column 8] and the arrows traced back from it (indicated in red) identify the alignments comprising the maximal assembly (alignments 8, 7, 4 and 0) with their contained alignments (5, 6 and 2). The result is the red assembly 1 shown in (a). An examination of assembly 1 indicates that it lacks alignments 1 and 3. The trace back from the forward scan at La where a = 3 provides the maximal assembly containing a originating from the left of a (trace back drawn in blue), but does not identify the alignments to the right of a that are in the a maximal assembly. To find the maximal alignment assembly containing alignment 3, the reverse scan computations were performed, calculating max[Ca, Lb + Ca\b], where b > a, and storing the score in the lower right of cell [row b][column a]. Ra is the maximum lower right value in column a and is shown circled in yellow. The trace forward from Ra, where a = 3, is shown with blue arrows. Combined with the trace back from La where a = 3, this yields the maximal assembly containing alignment 3, shown as assembly 2, namely alignments 0–3, 6–8. This assembly is also the maximal assembly containing alignment 1. In general, maximal assemblies for missing alignments are found in order of decreasing La + Ra – Ca value until all missing alignments are accounted for within maximal alignment assemblies; this was not done here for brevity. Note that alignment 6 is regarded as contained in alignment 1, even though it extends a few bases into intron 4. PASA has a parameter, called ‘fuzz distance’, which specifies the length of mismatches to discount at transcript ends, where sequence alignment quality is often poor.