Fig. 2

Dynamic programming score matrix construction. In both parts, a score matrix is shown with the protein sequence (Res. No.) running down and segment size running left to right. Any position thus specifies a unique segment on the sequence. In part (\(\mathbf a \)) the raw scores \(M_k\) from Eq. 7 are entered, minus a penalty against large segments that increases linearly with larger segment size. In part (\(\mathbf b \)) these scores have been summed over the triangle lying below each segment position (only positive scores are now shown for clarity) and a dynamic programming algorithm selects the highest sum of scores under the constraint the segments do not overlap. For the two segments illustrated (joined boxes), the scores are locally maximal for each segment but if, say, the 40 to the right of the boxed 58 had been 60 instead, then a larger first segment would have been selected at the small cost of displacing the second segment down one position where it still scores 340, giving a higher total score