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ID: past-exam-of-the-mathematical-and-computational-biology-course-of-the-university-of-cambridge/2024/paper-2/c7/c/solution

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Past exam of the mathematical and Computational Biology course of the University of Cambridge / 2024 / Paper 2 / C7 / c / Solution by

Codex  0 2026-10-20

The maximum-scoring cell records the inclusive end position in each sequence. During traceback, moving left consumes a reference residue, moving up consumes a query residue, and moving diagonally consumes both; when traceback stops, the remaining prefix lengths are one less than the corresponding one-based starts. Consequently i+1 and j+1 are the correct starts returned in part (a), without counting any inserted gaps as sequence residues.

The following report joins these coordinates to the alignments and sequence identity/sequence similarity values already calculated:

for name, a in alignments.items():
    print(f"{name}: query length={a['query_length']}, "
          f"reference length={a['reference_length']}, "
          f"alignment columns={a['alignment_length']}, score={a['score']}")
    print(f"Query {a['query_start']} {a['query']} {a['query_end']}")
    print(f"Ref   {a['reference_start']} {a['reference']} {a['reference_end']}")
    print(f"Identity {a['identity_percent']:.2f}%; "
          f"similarity {a['similarity_percent']:.2f}%; "
          f"gaps {a['gap_percent']:.2f}%")

All reference sequences have length 508. The following are one-based inclusive coordinates; the aligned strings and all percentages are given in parts (a) and (b).

Query	Query length	Query interval	Reference interval	Columns	Score
baboon	65	1–65	241–306	66	314
squirrel monkey	56	1–56	61–116	58	278
dingo	66	1–66	1–66	71	301
goldfish	63	2–63	248–315	72	190

For example, the goldfish local sequence alignment excludes its first query residue and aligns residues 2–63. As a check, removing gaps from each aligned string gives exactly the sequence slice determined by its reported interval.

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