The Genom of Homo sapiens.pdf

EULERIAN ASSEMBLY AND MULTIPLE ALIGNMENT 20970012006001000Sum of Pair Distance Score500400300Aligning Alignment Distance Score8006004002002001000 50 100 150 200 250 300 350 400 450 500Number of Sequences00 50 100 150 200 250 300 350 400 450 500Number of SequencesFigure 5. SP and AA scores (distance score) with respect to the number of sequences. The squares and triangles indicate differentpair-wise similarities (square, 90%, triangle, 70%). Both SP and AA scores are computed from a single alignment test. Solid lines connectpoints from EulerAlign, and dashed lines connect points from ClustalW.mance of EulerAlign: (1) sum of pairs (SP) score, a popularand simple measure, and (2) aligning alignment(AA) score, comparison of an alignment to the true alignment;by simulating sequences, the true alignment (ratherthan the mathematically optimal alignment) is known.We used ClustalW (Higgins and Sharp 1989; Thompsonet al. 1994), a well-studied and popular MSA software, asthe reference. Figure 5 shows the comparison betweenEulerAlign and ClustalW on sequence sets generated bythe evolutionary model with different mutation rates:5.2% and 16.4%, respectively, corresponding to 90% and70% pair-wise sequence similarities. The comparison onthe equidistance model is not shown, simply because EulerAlignis designed for that model and hence achieves abetter result. The linear growth of the computational timewith respect to the number of aligned sequences by EulerAlignis shown in Figure 6a, and a significant comparisonto the quadratic growth by ClustalW is shown in Figure6b. We used distance scores; hence, the smaller thescore the better the result. All tests are done on a SUNUltraSPARC 750MHz workstation.Application on Arabidopsis SequencesArabidopsis thaliana is widely used as a model organismfor genetic study in plant biology. As an applicationon real genomic sequences, we used EulerAlign to constructalignments for several sets of short specific sequencessampled from 96 Arabidopsis individuals byPCR experiments with certain primers. These alignmentsare then used to study the genetic variations and henceevolutionary relationships in the Arabidopsis population.Sequence data are kindly provided by M. Nordborg atUSC. Presented with base-calling errors, an accuratemultiple alignment is crucial for efficiently detecting realgenetic variations other than sequencing errors. The maindifference between genetic variations and sequencing errorsis that sequencing errors are more independently andrandomly distributed (although of course a function ofposition in the sequence fragment).To reduce base-calling errors, each individual is sequencedfrom both forward and backward strands, andeach base-call has a quality value assigned by Phred (Ew-1401500012010090%1000090%806080%80%70%50004070%20Ours00 50 100 150 200 250 300 350 400 450 500Number of Sequences( a )00 50 100 150 200 250 300 350 400 450 500Number of Sequences( b )Figure 6. (a) Linear time cost (in seconds) by EulerAlign with respect to the number of sequences; three lines correspond to 90%,80%, and 70% pair-wise similarities. (b) Comparison to the quadratic time cost by ClustalW (dashed lines). The tested numbers ofsequences are 10, 15, 50, 100, 250, and 500.