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Touchdown PCR involves decreasing the annealling temperature by 1 degree C every second cycle to a 'touchdown' annealing temp which is then used for 10 or so cycles. It was originally intended to bypass more complicated optimization processes for determining optimal annealing temperatures. The idea is that any differences in Tm between correct and incorrect annealing gives a 2-fold difference in product amount per cycle (4-fold per degree C). You therefore enrich for the correct product over any incorrect products.
Another use for this procedure is in determining DNA sequence for a known peptide sequence. The strategy here is to use two sets of degenerate primers that match potential coding sequences at the two ends of a peptide of known sequence. In practice, this requires that you know a stretch of peptide sequence of only 13 amino acids, with left and right primers of 18 nt (6 a.a.) and a space in between of one or more nt. Using these degenerate primers, you do a touchdown PCR. You will get a huge number of products, but you can select the desired product based on size since you know the exact interprimer distance from the peptide sequence. The advantage of this technique is that the touchdown PCR enriches for products containing correct matches between primers and template. If you clone and sequence a dozen PCR products, you can determine the correct coding sequence for the peptide, design an oligo for hybridization, etc. The technique is especially useful for peptide sequences full of ser, lys, and arg (six codons each).