HELIOS: High-speed sequence alignment in optics
Fig 3
Step-by-step progress of the S1-align operation of the HELIOS method for optical sequence alignment.
(A) Two input sequences, i.e S1 and S2, are given to the HELIOS method, assuming the third character (i.e. ‘A’ in S1 and E in S2) is mutated. (B) S1 and S2 are coded based on the proposed coding procedure, assuming k = 2 and R = 1. While the self-label codes of the third character are different for S1 and S2, the nearby-label codes of the fifth characters (i.e. ‘S’) are different as well, due to the mutated character, assuming k = 2. Afterward, the coded S2 is shifted one time horizontally towards the left and right of the coded S2 assuming R = 1. Then, the main S1 is compared with the main S2 and all its shifts, and hence, (C) the comparison results are presented for each comparison. (D) Next, the comparison output vector is formed by aggregating all the comparison results, where the matched characters result in nonzero entries. As represented with the zero entry, the mutated character in position 3 within the input sequences is successfully located due to the different self-label codes, while the 5th character is false mismatched due to the different nearby-label codes. (E) To compensate for this false mismatch, the ith entry of the output is determined according to aggregating the ith and the (i + k)th entries of the comparison outcome vector. Hence, the 5th entry is recovered by the corresponding nonzero value at the 7th entry; while proper detection of character mutation at the 3rd entry is not affected.