1. BNFO 602 Lecture 2
Usman Roshan

2. DNA Sequence Evolution
-3 mil yrs
-2 mil yrs
-1 mil yrs
today
TAGGCCTT
(Human)
TAGCCCTTA
(Monkey)
A_C_CTT
(Cat)
A_CACTTC
(Lion)
_G_GCTT
(Mouse)
_GGGCTT
TAGACCTT
A_CACTT
AAGGCTT
T_GACTT
AAGACTT
AAGACTT
T_GACTT
AAGGCTT
_GGGCTT
TAGACCTT
A_CACTT
ACCTT
(Cat)
ACACTTC
(Lion)
TAGCCCTTA
(Monkey)
TAGGCCTT
(Human)
GGCTT
(Mouse)
_GGGCTT
TAGACCTT
A_CACTT
AAGGCTT
T_GACTT
AAGACTT
T_GACTT
AAGGCTT
AAGACTT
AAGACTT

3. Sequence alignments They tell us about
Function or activity of a new gene/protein
Structure or shape of a new protein
Location or preferred location of a protein
Stability of a gene or protein
Origin of a gene or protein
Origin or phylogeny of an organelle
Origin or phylogeny of an organism
And more…

4. Pairwise alignment X: ACA, Y: GACAT Match=8, mismatch=2, gap-5
ACA-- -ACA- --ACA ACA----
GACAT GACAT GACAT G--ACAT
Score =

5. Optimal alignment
An alignment can be specified by the traceback matrix.
How do we determine the traceback for the highest scoring alignment?
Needleman-Wunsch algorithm for global alignment
First proposed in 1970
Widely used in genomics/bioinformatics
Dynamic programming algorithm

6. Needleman-Wunsch Input:
X = x1x2…xn, Y=y1y2…ym
(X is seq2 and Y is seq1)
Define V to be a two dimensional matrix with len(X)+1 rows and len(Y)+1 columns
Let V[i][j] be the score of the optimal alignment of X1…i and Y1…j.
Let m be the match cost, mm be mismatch, and g be the gap cost.

7. Dynamic programming Initialization:
for i = 1 to len(seq2) { V[i][0] = i*g; }
For i = 1 to len(seq1) { V[0][i] = i*g; }
Recurrence:
for i = 1 to len(seq2){
for j = 1 to len(seq1){
V[i-1][j-1] + m(or mm)
V[i][j] = max { V[i-1][j] + g
V[i][j-1] + g
if(maximum is V[i-1][j-1] + m(or mm)) then T[i][j] = ‘D’
else if (maximum is V[i-1][j] + g) then T[i][j] = ‘U’
else then T[i][j] = ‘L’ }

8. Traceback code aligned_seq1 = "" aligned_seq2 = "" i = len(seq1)
j = len(seq2)
while(i !=0 or j != 0):
if(T[i][j] == “L”):
aligned_seq1 = “-” + aligned_seq1
aligned_seq2 = seq2[j-1] + aligned_seq2
j = j - 1
elif(T[i][j] == "U"):
aligned_seq2 = "-" + aligned_seq2
aligned_seq1 = seq1[i-1] + aligned_seq1
i = i - 1
else:

9. Example V G A C A T A C T Input: seq2: ACA seq1: GACAT m = 5 mm = -4
gap = -20
seq2 is lined along the rows
and seq2 is along the columns
G A C A T
-20
-40
-60
-80
-100 -4
-15
-35
-55
-75
-24 -8
-10
-30
-50
-44
-19
-12 -5
-25 A C T L U D

10. Affine gap penalties
Affine gap model allows for long insertions in distant proteins by charging a lower penalty for extension gaps. We define g as the gap open penalty (first gap) and e as the gap extension penalty (additional gaps)
Alignment:
ACACCCT ACACCCC
ACCT T AC CTT
Score = Score = 0.9
Trivial cost matrix: match=+1, mismatch=0, gapopen=-2, gapextension=-0.1

11. Affine penalty recurrence
M(i,j) denotes alignments of x1..i and y1..j ending with
a match/mismatch. E(i,j) denotes alignments of x1..i
and y1..j such that yj is paired with a gap. F(i,j) defined
similarly. Recursion takes O(mn) time where m and n
are lengths of x and y respectively.

12. How do we pick gap parameters?

13. Structural alignments
Recall that proteins have 3-D structure.

14. Structural alignment - example 1
Alignment of thioredoxins from
human and fly taken from the
Wikipedia website. This protein
is found in nearly all organisms
and is essential for mammals.
PDB ids are 3TRX and 1XWC.

15. Structural alignment - example 2
Taken from
Unaligned proteins.
2bbm and 1top are
proteins from fly and
chicken respectively.
Computer generated
aligned proteins

16. Structural alignments
We can produce high quality manual alignments by hand if the structure is available.
These alignments can then serve as a benchmark to train gap parameters so that the alignment program produces correct alignments.

17. Benchmark alignments Protein alignment benchmarks
BAliBASE, SABMARK, PREFAB, HOMSTRAD are frequently used in studies for protein alignment.
Proteins benchmarks are generally large and have been in the research community for sometime now.
BAliBASE 3.0

18. Biologically realistic scoring matrices
PAM and BLOSUM are most popular
PAM was developed by Margaret Dayhoff and co-workers in 1978 by examining 1572 mutations between 71 families of closely related proteins
BLOSUM is more recent and computed from blocks of sequences with sufficient similarity

19. PAM
We need to compute the probability transition matrix M which defines the probability of amino acid i converting to j
Examine a set of closely related sequences which are easy to align---for PAM 1572 mutations between 71 families
Compute probabilities of change and background probabilities by simple counting

20. Expected accuracy alignment
The dynamic programming formulation allows us to find the optimal alignment defined by a scoring matrix and gap penalties. This may not necessarily be the most “accurate” or biologically informative.
We now look at a different formulation of alignment that allows us to compute the most accurate one instead of the optimal one.

21. Posterior probability of xi aligned to yj
Let A be the set of all alignments of sequences x and y, and define P(a|x,y) to be the probability that alignment a (of x and y) is the true alignment a*.
We define the posterior probability of the ith residue of x (xi) aligning to the jth residue of y (yj) in the true alignment (a*) of x and y as
Do et. al., Genome Research, 2005

22. Expected accuracy of alignment
We can define the expected accuracy of an alignment a as
The maximum expected accuracy alignment can be obtained by the same dynamic programming algorithm
Do et. al., Genome Research, 2005

23. Example for expected accuracy
True alignment
AC_CG
ACCCA
Expected accuracy=( )/4=1
Estimated alignment
ACC_G
Expected accuracy=( )/4 ~ 0.75

24. Estimating posterior probabilities
If correct posterior probabilities can be computed then we can compute the correct alignment. Now it remains to estimate these probabilities from the data
PROBCONS (Do et. al., Genome Research 2006): estimate probabilities from pairwise HMMs using forward and backward recursions (as defined in Durbin et. al. 1998)
Probalign (Roshan and Livesay, Bioinformatics 2006): estimate probabilities using partition function dynamic programming matrices

25. Example

26. Local alignment Global alignment recurrence:
Local alignment recurrence

27. Local alignment traceback
Let T(i,j) be the traceback matrices and m and n be length of input sequences.
Global alignment traceback:
Begin from T(m,n) and stop at T(0,0).
Local alignment traceback:
Find i*,j* such that T(i*,j*) is the maximum over all T(i,j).
Begin traceback from T(i*,j*) and stop when
T(i,j) <= 0.

28. BLAST Local pairwise alignment heuristic
Faster than standard pairwise alignment programs such as SSEARCH, but less sensitive.
Online server:

29. BLAST
Given a query q and a target sequence, find substrings of length k (k-mers) of score at least t --- also called hits. k is normally 3 to 5 for amino acids and 12 for nucleotides.
Extend each hit to a locally maximal segment. Terminate the extension when the reduction in score exceeds a pre-defined threshold
Report maximal segments above score S.

30. Finding k-mers quickly
Preprocess the database of sequences:
For each sequence in the database store all k-mers in hash-table.
This takes linear time
Query sequence:
For each k-mer in the query sequence look up the hash table of the target to see if it exists
Also takes linear time