Needleman Wunsch Sequence Alignment

1
Needleman Wunsch Sequence Alignment

• The NeedlemanWunsch algorithm performs a global
  alignment on two sequences (called A and B here).
  
• It is commonly used in bioinformatics to align
  protein or nucleotide sequences.
• The algorithm was proposed in 1970 by Saul
  Needleman and Christian Wunsch in their paper A
  general method applicable to the search for
  similarities in the amino acid sequence of two
  proteins, J Mol Biol. 48(3)443-53.
• The NeedlemanWunsch algorithm is an example of
  dynamic programming, and was the first
  application of dynamic programming to biological
  sequence comparison.

2
Needleman Wunsch Sequence Alignment

• Scores for aligned characters are specified by a
  similarity matrix. Here, S(i,j) is the similarity
  of characters i and j. It uses a linear gap
  penalty, called d.
• For example, if the similarity matrix was
• A G C T
• A 10 -1 -3 -4
• G -1 7 -5 -3
• C -3 -5 9 0
• T -4 -3 0 8
• Then the alignment
• AGACTAGTTAC
• CGA - - -GACGT
• with a gap penalty of -5, would have the
  following score...
• S(A,C) S (G,G) S(A,A) 3d S(G,G) S(T,A)
  S(T,C) S(A,G) S(C,T)
• -3 7 10 -35 7 -4 0 -1 0 1

3
Needleman Wunsch Sequence Alignment

• To find the alignment with the highest score, a
  two-dimensional array (or matrix) is allocated.
  This matrix is often called the F matrix, and its
  (i,j)th entry is often denoted Fij (j along
  horizontal axis and i along vertical axis)
• There is one column for each character in
  sequence A, and one row for each character in
  sequence B.
• Thus, if we are aligning sequences of sizes n and
  m, the running time of the algorithm is O(nm) and
  the amount of memory used is in O(nm).
• As the algorithm progresses, the Fij will be
  assigned to be the optimal score for the
  alignment of the first j characters in A and the
  first i characters in B.
• The principle of optimality is then applied as
  follows.
• Basis F0j d j Fi0 d i
• Recursion, based on the principle of optimality
• Fij max(Fi - 1,j - 1 S(Bi,Aj),Fi,j - 1 d,Fi
  - 1,j d)

4
Needleman Wunsch Sequence Alignment

• The pseudo-code for the algorithm to compute the
  F matrix therefore looks like this (array and
  sequence indexes start at 0)
• for i0 to length(B)-1
• F(i,0) lt- di
• for j0 to length(A)-1
• F(0,j) lt- dj
• for i1 to length(B)
• for j 1 to length(A)
• Choice1 lt- F(i-1,j-1) S(B(i), A(j))
• Choice2 lt- F(i-1, j) d
• Choice3 lt- F(i, j-1) d
• F(i,j) lt- max(Choice1, Choice2, Choice3)
• Once the F matrix is computed, the bottom right
  hand corner of the matrix is the maximum score
  for any alignment.
• To compute which alignment actually gives this
  score, you can start from the bottom right cell,
  and compare the value with the three possible
  sources(Choice1, Choice2, and Choice3 above) to
  see which it came from.
• If Choice1, then A(j) and B(i) are aligned,
• If Choice2, then A(j) is aligned with a gap, and
• If Choice3, then B(i) is aligned with a gap.

5
Needleman Wunsch Sequence Alignment

• AlignmentA lt- "" AlignmentB lt- "
• i lt- length(B) j lt- length(A)
• while (i gt 0 AND j gt 0)
• Score lt- F(i,j) ScoreDiag lt- F(i - 1, j - 1)
• ScoreLeft lt- F(i, j - 1) ScoreUp lt- F(i - 1,
  j)
• if (Score ScoreDiag S(A(j), B(i)))
• AlignmentA lt- A(j) AlignmentA AlignmentB lt-
  B(i) AlignmentB
• i lt- i 1 j lt- j 1
• else if (Score ScoreLeft d)
• AlignmentA lt- A(j) AlignmentA AlignmentB lt-
  "-" AlignmentB
• j lt- j - 1
• else if (Score ScoreUp d)
• AlignmentA lt- "-" AlignmentA AlignmentB lt-
  B(i) AlignmentB
• i lt- i - 1
• while (j gt 0) AlignmentA lt- A(j) AlignmentA
  AlignmentB lt- "-" AlignmentB j lt- j - 1
• while (i gt 0) AlignmentA lt- "-" AlignmentA
  AlignmentB lt- B(i) AlignmentB i lt- i - 1

6
Needleman Wunsch Sequence Alignment

• Project Deliverables
• Given the computation flow of the NWSA algorithm,
  architect a pipelined VHDL implementation such
  that a single pipeline stage contains a single
  processing element (PE).
• 1. Find the number and width of data elements
  that move between PEs.
• 2. Also assume that the testbench code includes
  the read/write memory.
• a. Assume a fixed length of the A string A
  does not change.
• b. B strings are sent from the memory to the
  PEs as inputs. Once a B string is consumed, the
  next B string is fed into the system from the
  memory.
• c. The final score values are sent back to
  memory as outputs. Each score corresponds to a
  single B string.
• d. Explicit instantiations of memory elements
  are not required supply input values from
  testbench, and read output values into the
  testbench.
• e. Each PE also stores the compass value (cv) to
  remember where it got its score from (0
  diagonal, 1 up, 2 left).
• 3. Describe your pipelined design implementation
  in your report.
• 4. Give printouts of the VHDL codes, including
  testbench in the report.
• 5. Attach the waveform printouts in the report.