Alignment Problem. (Optimal) pairwise alignment consists of considering all possible alignments of two sequences and choosing the optimal one. Sub-optimal (heuristic) alignment algorithms are also very important: e.g. BLAST. Key Issues. Types of alignments (local vs. global)
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Global versus Local Alignments
Sanger (1982) introduced chain-termination sequencing.
Main idea: Obtain fragments of all possible lengths, ending in A, C, T, G.
Using gel electrophoresis, we can separate fragments of differing lengths, and then assemble them.
Can sequence ~500bp with 98.5% accuracy
Sequencing machines are limited to about ~500-750bp, so we must break up DNA into short and long fragments, with reads on either end.
Reads are then assembled into contigs, then scaffolds.
NIH used a Clone-By-Clone strategy; Celera used shotgun assembly.
Celera used 300 sequencing machines in parallel to obtain 175,000 reads per day.
Efforts were combined, resulting in 8x coverage of the human genome; consensus sequence is 2.91 billion base pairs.
The Big Picture
Suppose we had a way to probe fragments of length k that were present in our sequence, from a hybridization assay.
Commercial products: Affymetrix GeneChip, Agilent, Amersham, etc.
Theorem (Euler 1736): A graph has a path visiting every edge exactly once if and only if it is connected and has 2 or fewer vertices of odd degree.