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Implementation of space-saving three DNA sequences alignment

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We will discuss a space-saving technique for pairwise sequence alignment based on divide-and-conquer in the lectures. The technique can be easily extended to multiple sequence alignment. Your task is to design an O(mn) space, O(mn*k) time SP alignment algorithm for three DNA sequences of lengths m, n, and k, respectively. Implement your algorithm in C/C++/Java, and test it on real data.

You may find discussions on the space-saving technique for pairwise sequence comparison in the books by Jones and Pevzner, by Gusfield, and by Jiang, Xu, and Zhang. The following original papers provide more detailed information:

D.S. Hirschberg. Algorithms for the longest common subsequence problem. J.ACM, 24:664-75, 1977.

E. W. Myers and W. Miller. Optimal alignments in linear space. Comp. Appl. Biosciences, 4:11-17, 1988. At UCR Science Lib: call number is QH324.2 .C66

Chao, Hardison and Miller. Recent developments in linear-space alignment methods: a survey. Journal of Computational Biology. Vol. 1-4, pp. 271-291. 1994.

(i) For simplicity, let's consider global alignment and the basic SP score model where gaps are not specially treated.

(ii) Your program should work for any score function on nucleotides. In other words, the user should be able to input a score function in the form of a 5x5 matrix indexed by A, C, G, T, and space. The SP-score of a column of letters/spaces is the sum of the scores of each pair of letters/spaces in the column.

To test your program, use the Blast scores: Match = 5, Mismatch = -4, and Indel = -8. The score between two spaces is 0.

(iii) Test your program on the following four sets of sequences:

 1.
 NM_013096.  Rattus norvegicus hemoglobin alpha, adult chain 2 (Hba-a2),
             mRNA. 556 bps.
 NM_008218.  Mus musculus hemoglobin alpha, adult chain 1 (Hba-a1), 
             mRNA. 569 bps.
 NM_000558.  Homo sapiens hemoglobin, alpha 1 (HBA1), mRNA. 627 bps.
 
 2.
 NM_010019.  Mus musculus death-associated protein kinase 2 (Dapk2),
            mRNA, 1792 bps.
 NM_001243563. Sus scrofa death-associated protein kinase 2 (DAPK2),
            mRNA, 1825 bps.
 NM_014326. Homo sapiens death-associated protein kinase 2 (DAPK2), 
            mRNA, 2628 bps.
            
 3.
 NM_000545. Homo sapiens HNF1 homeobox A (HNF1A), mRNA. 3417 bps
 NM_008261. Mus musculus hepatic nuclear factor 4 (Hnf4). 4391 bps
 NM_000457. Homo sapiens hepatocyte nuclear factor 4, alpha (HNF4A), 
            transcript variant 2, mRNA. 4737 bps
            
 4.
 NM_000492. Homo sapiens cystic fibrosis transmembrane conductance
            regulator (ATP-binding cassette sub-family C, member 7) 
            (CFTR), mRNA. 6132 bps
 NM_031506. Rattus norvegicus cystic fibrosis transmembrane 
            conductance regulator homolog (Cftr), mRNA. 6287 bps.
 NM_021050. Mus musculus cystic fibrosis transmembrane conductance
            regulator homolog (Cftr), mRNA. 6305 bps.

You may retrieve the sequences at http://www.ncbi.nlm.nih.gov/nucleotide/ using the accession numbers NM_000558.3, etc. Select "nucleotide" in the search option box. The sequence data is given at the bottom of the search result page. Note that the last dataset may take your algorithm quite some time to run, especially on an old computer.

For this question, submit a report (hard copy) along with HW3 with -------------- (a) a high-level description of your algorithm (i.e. high-level pseudo-code), and the data structures used, (b) your source code, and (c) the result of your program on each dataset, including the score of the optimal alignment obtained, the length of the alignment, the number of columns with perfectly matched nucleotides in the alignment, and the running time and memory (on a PC or laptop with specification of CPU and memory). Please do not include the actual alignment in the report (because it is going to be quite loooong :-). (d) Do you see any obvious conserved regions captured in your alignments?

Although this question is optional for HW2, it could be a very good idea that you complete the dynamic programming routine for computing the optimal score of a 3-sequence alignment in O(m*n) space, and test it on some small data to make sure that it is correct. The recurrence relation is given in Chapter 6.10 of the textbook. Note that this algorithm will need the dynamic programming algorithm for pairwise sequence alignment to initialize its matrix.

Also, although your goal is to implement the O(mn)-space algorithm, it will be useful for you to implement the standard O(mnk)-space dynamic programming algorithm for 3-sequence alignment and use it as a subroutine in the divide-and-conquer process when one of the sequences degenerates to one or zero letters.

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