1. In-Class Assignment #1: Research CD2
Follow instructions on distributed assignment sheet

2. Biology 4900
Biocomputing

3. Pairwise Sequence Alignment
Chapter 3
Pairwise Sequence Alignment

4. Pairwise Alignment
Potential relationships between proteins or nucleic acids can be explored by comparing 2 or more sequences of amino acids or nucleotides.
Difficult to do visually.
Computer algorithms help us by:
Accelerating the comparison process
Allowing for “gaps” or indels in sequences (i.e., insertions, deletions)
Identifying substituted amino acids that are structurally or functionally similar (D and E).
One way to do this is with BLAST (Basic Local Alignment Search Tool)
Allows rapid sequence comparison of a query sequence against a database.
The BLAST algorithm is fast, accurate, and web-accessible.
BLAST lets user select from a variety of scoring matrices to evaluate sequence relatedness.
Pevsner, Bioinformatics and Functional Genomics, 2009

5. Sequence Analyses: RNA
Codons (3 RNA bases in sequence) determine each amino acid that will build the protein expressed
Many amino acids are encoded by more than 1 codon (change in 3rd base).  Change of single base may not be significant.

6. Comparing protein sequences
Comparing protein sequences usually more informative than nucleotide sequences.
Changing base at 3rd position in codon does not always change AA (Ex: Both UUU and UUC encode for phenylalanine)
Different AAs may share similar chemical properties (Ex: hydrophobic residues A, V, L, I)
Relationships between related but mismatched AAs in sequence analysis can be accounted for using scoring systems (matrices).
Protein sequence comparisons can ID sequence homologies from proteins sharing a common ancestor as far back as 1 × 109 years ago (vs. 600 × 106 for DNA).

7. Amino acids by similar biophysical properties

8. Amino acids by similar biophysical properties
These have useful fluorescent properties

9. Amino acids by similar biophysical properties

10. Amino acids by similar biophysical properties

11. Amino acids by similar biophysical properties

12. Sequence Identity and Similarity
Identity: How closely two sequences match one another.
Unlike homology, identity can be measured quantitatively
Similarity: Pairs of residues that are structurally or functionally related (conservative substitutions).
>lcl| CLN:A|PDBID|CHAIN|SEQUENCE
Length=148
Score = 268 bits (684), Expect = 3e-97, Method: Compositional matrix adjust.
Identities = 130/148 (88%), Positives = 143/148 (97%), Gaps = 0/148 (0%)
Query AEQLTEEQIAEFKEAFALFDKDGDGTITTKELGTVMRSLGQNPTEAELQDMINEVDADGN 60
A+QLTEEQIAEFKEAF+LFDKDGDGTITTKELGTVMRSLGQNPTEAELQDMINEVDADGN
Sbjct ADQLTEEQIAEFKEAFSLFDKDGDGTITTKELGTVMRSLGQNPTEAELQDMINEVDADGN 60
Query GTIDFPEFLSLMARKMKEQDSEEELIEAFKVFDRDGNGLISAAELRHVMTNLGEKLTDDE 120
GTIDFPEFL++MARKMK+ DSEEE+ EAF+VFD+DGNG ISAAELRHVMTNLGEKLTD+E
Sbjct GTIDFPEFLTMMARKMKDTDSEEEIREAFRVFDKDGNGYISAAELRHVMTNLGEKLTDEE 120
Query VDEMIREADIDGDGHINYEEFVRMMVSK 148
VDEMIREA+IDGDG +NYEEFV+MM +K
Sbjct VDEMIREANIDGDGQVNYEEFVQMMTAK 148
88% of sequences include the same amino acids (Identities). This increases to 97% (Positives) when you include amino acids that are different, but with similar properties.
Pevsner, Bioinformatics and Functional Genomics, 2009

13. Sequence Homology
Homology: Two sequences are homologous if they share a common ancestor.
No “degrees of homology”: only homologous or not
Almost always share similar 3D structure
Ex. myoglobin and beta globin
Sequences can change significantly over time, but 3D structure changes more slowly
Beta-globin sub-unit of adult hemoglobin (2H35.pdb, in blue), superimposed over myoglobin (3RGK.pdb, in red).
These sequences probably separated 600 million years ago.
Pevsner, Bioinformatics and Functional Genomics, 2009

14. Percent Identity and Homology
For an alignment of 70 amino acids, 40% sequence identity is a reasonable threshold for homology.
Above 20% (more than 70 amino acids) may indicate homology.
Below 20% probably indicates chance alignment.
Pevsner, Bioinformatics and Functional Genomics, 2009

15. Orthologs and Paralogs
Orthologs: Homologous sequences in different species that arose from a common ancestral gene during speciation.
Ex. Humans and rats diverged around 80 million years ago  divergence of myoglobin genes occurred.
Orthologs frequently have similar biological functions.
Human and rat myoglobin (oxygen transport)
Human and rat CaM
Paralogs: Homologous sequences that arose by a mechanism such as gene duplication.
Within same organism/species
Ex. Myoglobin and beta globin are paralogs
Have distinct but related functions.
Pevsner, Bioinformatics and Functional Genomics, 2009

16. Conservative Substitutions in Matrices
Scoring may also vary based on conserved substitutions of amino acids: i.e., amino acids with similar properties will not lose as many points as AAs with very different properties.
Basic AAs: K, R, H
Acidic AAs: D, E
Hydroxylated AAs: S, T
Hydrophobic AAs: G, A, V, L, I, M, F, P, W, Y
These relationships would be considered when calculating “Positives” in BLAST alignment.
Pevsner, Bioinformatics and Functional Genomics, 2009

17. Dayhoff Model: Building a Scoring Matrix
1978, Margaret Dayhoff provided one of the first models of a scoring matrix
Model was based on rules by which evolutionary changes occur in proteins
Catalogued 1000’s of proteins, considered which specific amino acid substitutions occurred when 2 homologous proteins aligned
Assumes substitution patterns in closely-related proteins can be extrapolated to more distantly-related proteins
An accepted point mutation (PAM) is an AA replacement accepted by natural selection
Based on observed mutations, not necessarily on related AA properties
Probable mutations are rewarded, while unlikely mutations are penalized
Scores for comparison of 2 residues (i, j) based on the following equation:
Here, qi,j is the probability of an observed substitution (from mutation probability matrix), while p is the likelihood of observing the replacement AA (i) as a result of chance (normalized frequency of AA table).
Pevsner, Bioinformatics and Functional Genomics, 2009

18. PAM250 Mutation Probability Matrix
Original AA
Ala Arg Asn Asp Cys Gln Glu Gly His Ile Leu Lys Met Phe Pro Ser Thr Trp Tyr Val A R N D C Q E G H I L K M F P S T W Y V Ala A Arg R Asn N Asp D Cys C Gln Q Glu E Gly G His H Ile I Leu L Lys K Met M Phe F Pro P Ser S Thr T Trp W Tyr Y Val V
Replacement AA
Think of these values as percentages (columns sum to 100).
For example, there is an 18% (0.18) probability of R being replaced by K.
This probability matrix needs to be converted into a scoring matrix.

19. Normalized Frequencies of Amino Acids
**How often a given amino acid appears in a protein (determined by empirical analyses)

20. Purpose of PAM Matrices
Derive a scoring system to determine relatedness of 2 sequences.
PAM mutation probability matrix must be converted to a scoring matrix (log odds matrix).

21. PAM250 Log-Odds Matrix
Cys C 12
Ser S
Thr T
Pro P
Ala A
Gly G
Asn N
Asp D
Glu E
Gln Q
His H
Arg R
Lys K
Met M
Ile I
Leu L
Val V
Phe F
Tyr Y
Trp W
C S T P A G N D E Q H R K M I L V F Y W
Cys Ser Thr Pro Ala Gly Asn Asp Glu Gln His Arg Lys Met Ile Leu Val Phe Tyr Trp
This is the PAM250 scoring matrix, calculated as follows:

22. Pairwise Alignment and Homology
Think of PAM value as total number of mutations. This included multiple mutations over time at a single position.
Currently, we accept that once the percent distance reaches ~85%, homology is indeterminate.
PAM250 works best for more distantly related protein sequences.
Seq1 AGDFWYGGDGEYLLV
Seq2 AGQFWYGGEGEKLLV
Seq3 AGEFWYGGEGEKLLV
Seq1 and Seq2 separated by 3 units, while Seq1 and Seq3 separated by 4 PAM units

23. Practical Lessons from the Dayhoff Model
Less mutable amino acids likely play more important structural and functional roles
Mutable amino acids fulfill functions that can be filled by other amino acids with similar properties
Common substitutions tend to require only a single nucleotide change in codon
Amino acids that can be created from more than 1 codon are more likely to be created as a substitute (See p. 63, textbook)
Changes to sequence that do not alter structure and function of protein likely to be more tolerated in nature
Pevsner, Bioinformatics and Functional Genomics, 2009

24. BLOSUM62 Scoring Matrix BLOck SUbstitution Matrix
By Henikoff and Henikoff (1992)
Default scoring matrix for pairwise alignment of sequences using BLAST (local alignments)
Based on empirical observations of distantly-related proteins organized into blocks
In BLOSUM62, proteins are arranged in blocks sharing at least 62% identity
Pevsner, Bioinformatics and Functional Genomics, 2009

25. General Trends in Scoring Matrices
BLOSUM90
PAM30
BLOSUM62
PAM120
BLOSUM45
PAM250
Less divergent
More divergent
Human vs. chimp
Human vs. bacteria
Choose a matrix that is consistent with the level sequence identity you are investigating. I.E., if you are looking at/for more closely related sequences, use BLOSUM90. If you are not sure, use BLOSUM62.

26. Sequence Alignments: General Concepts
Global Alignment: Tries to match the entire length of the sequence.
Local Alignment: Tries to find the longest section that matches.
Both are examples of dynamic programming: precise but slow

27. -GADEG-YFGPVILAADGEVA GGA-EGDYFGPAI--AEGEVA
Global Alignment
Input: two sequences over the same alphabet (either nucleotide or amino acid sequences)
Output: The alignment of the sequences
Example:
GADEGYFGPVILAADGEVA and GGAEGDYFGPAIAEGEVA
A possible alignment might look like this:
-GADEG-YFGPVILAADGEVA
GGA-EGDYFGPAI--AEGEVA
ins
del
ins
del
del
mut
mut

28. Global Alignment – A Simple Scoring Scheme
Each position is scored independently:
Match: +1
Mismatch: -1
Insertions or deletions (gaps): -2
The alignment score is the sum of the position scores
-GADEG-YFGPVILAADGEVA
GGA-EGDYFGPAI--AEGEVA
Global Alignment Score: (14 ×(+1)) + (5 × (-2)) + (2 × (-1)) = 2
-----GADEG-YFGPVILAADGEVA---
DLGNVGA-EGDYFGPAI--AEGEVARPL
Global Alignment Score: (14 ×(+1)) + (12 × (-2)) + (2 × (-1)) = -12
-----GADEG-YFGPVILAADGEVA---
dlgnvGA-EGDYFGPAI--AEGEVArpl
Local Alignment Score: (14 ×(+1)) + (4 × (-2)) + (2 × (-1)) = 4

29. Calculate the score in BLOSUM-62 for a gap with 7 residues…
Matrices and Gap Costs
The raw score of an alignment is the sum of the scores for aligning pairs of residues and the scores for gaps.
Gapped BLAST and PSI-BLAST use "affine gap costs" which charge the score -a for the existence of a gap, and the score -b for each residue in the gap. Thus a gap of k residues receives a total score of -(a+bk); specifically, a gap of length 1 receives the score -(a+b).
Your total raw score for the alignment is reduced when you introduce gaps into the query sequence.
Calculate the score in BLOSUM-62 for a gap with 7 residues…

30. Global Sequence Alignments
Global Alignment: Entire sequence of each protein or DNA.
Needleman and Wunsch (1970)
Reduces problem to series of smaller alignments on a residue-by-residue basis.
How this approach works
Setting up a matrix
Score the matrix
ID the optimal alignment

31. Global Sequence Alignments: Setting up a Matrix
Create 2D Matrix of 2 sequences to align
Seq 2
Seq 2
Seq 1
Seq 1
Perfect Alignment
Mismatch Alignment (lower score)
Seq 2
Seq 2
Seq 1
Seq 1
Deletion, Seq 2
Insertion, Seq 2

32. Global Sequence Alignments: Setting up a Matrix
In simple identity matrix, matches scored as (+1), everything else is (0)
Here you can see how BLOSUM62 Scoring Matrix is applied to replace to simple matrix
Seq 2
Seq 2
Seq 1
Seq 1
Simple Identity Matrix
BLOSUM62 Scoring Matrix

33. Global Seq. Alignments: Identity to Scoring Matrix
We need to find a way to convert the identity matrix into a meaningful scoring system (match, mismatch, gap in 1 or 2)
Seq 2 (j)
Seq 2
Seq 1
Seq 1 (i)
Simple Identity Matrix
Needleman-Wunsch-Sellers Scoring Matrix

34. Global Seq. Alignments: Identity to Scoring Matrix
Gap penalty values, matches, coordinate system
Gap penalty
Seq 2 (j)
Gap penalty
Seq 1 (i)
Match = +1
Else = -2
Matches
Needleman-Wunsch-Sellers Scoring Matrix

35. Global Seq. Alignments: Scoring Matrix Calculations
Seq 2 (j) +1
Seq 1 (i)
Needleman-Wunsch-Sellers Scoring Matrix
Calculate Mi,j = MAXIMUM[ Mi-1, j-1 + Si,j (match/mismatch in the diagonal), Mi,j-1 + w (gap in sequence #1), Mi-1,j + w (gap in sequence #2)]
Note that in the example, Mi-1,j-1 will be red, Mi,j-1 will be blue and Mi-1,j will be green.
Using this information, the score at position 1,1 (i, j) in the matrix can be calculated. Since the first residue in both sequences is an F, S1,1 = +1, and by the assumptions stated earlier, w = -2. Thus, Mi,j = MAX[Mi-1,j-1 + 1, Mi,j-1 - 2, Mi-1,j - 2] = MAX[+1, -4, -4].
MAX function means we retain the highest (MAX) score of all possible scores.

36. Global Seq. Alignments: Scoring Matrix Calculations
Seq 2 (j) +1 -1
Seq 1 (i)
Needleman-Wunsch-Sellers Scoring Matrix
Calculate Mi,j+1 = MAXIMUM[ Mi, j-1 + Si,j+1 (match/mismatch in the diagonal), Mi,j + w1 (gap in sequence #1), Mi-1,j+1 + w2 (gap in sequence #2)]
The score at position 1,2 (i, j+1) in the matrix can be calculated. Since the residues are mismatched, Si+1,j = -2, and by the assumptions stated earlier, w = -2. Thus, Mi,j = MAX[Mi-1,j-1 + 1, Mi,j-1 - 2, Mi-1,j - 2] = MAX[-4, -1, -6].

37. Global Seq. Alignments: Scoring Matrix Calculations
Seq 2 (j) +1
Seq 1 (i) -1
Needleman-Wunsch-Sellers Scoring Matrix
Calculate Mi+1,j = MAXIMUM[ Mi, j-1 + Si,j (match/mismatch in the diagonal), Mi+1,j-1 + w1 (gap in sequence #1), Mi-1,j + w2 (gap in sequence #2)]
The score at position 2,1 (i+1, j) in the matrix can be calculated. Since the residues are mismatched, Si+1,j = -2, and by the assumptions stated earlier, w = -2. Thus, Mi,j = MAX[Mi,j-1 - 2, Mi+1,j-1 - 2, Mi,j - 2] = MAX[-4, -6, -1].

38. Scored Matrix
Seq 2 (j)
Red Arrows indicate Pathways to calculated Max values
Seq 1 (i)
Overall score of optimal alignment

39. Optimal Alignment: Trace-back Procedure
Seq 2 (j)
Trace-back arrows can only follow pathways identified when calculating Max values
Seq 1 (i)
Start here

40. Completed Global Pairwise Alignment
Seq 2 (j)
Seq 2 (j)
Seq 1 (i)
Seq 1 (i)
Seq 1 (i)
F K H M E D - P L - E
F M - D T P L N E
Seq 2 (j)
Note that final pairwise alignment score (-4) is equal to the value calculated based on total numbers of matches, mismatches, insertions and deletions
Global Alignment Score: (6 ×(+1)) + (5 × (-2)) = -4

41. Local Sequence Alignment
Local Alignment: Longest matching regions (subsets) between 2 sequences.
Smith and Waterman Algorithm (1981)
Scoring is similar to global alignment
Set up a matrix
Score the matrix
No negative values allowed: If negative values are the only choices, then answer defaults to zero (0).
Mismatches and gaps at ends score 0.
ID the optimal alignment
More sensitive but much slower than heuristic methods (FASTA, BLAST)

42. Smith and Waterman Local Sequence Alignment
Can use any scoring matrix you want (ex. Substitute BLOSUM62)
No negative values allowed: Default is 0
Alignment can start anywhere in sequence: not restricted to ends and no penalties at ends
Trace-back starts with the highest number, works backwards the same as with global alignment
Seq 2
G A A G A
G T T T A A G

43. Heuristic (word or k-tuple based) algorithms
Uses initial query to make reasonable guesses about sequence alignments, then evaluates those considered “most likely”
Alignment then extended until:
One of the sequences ends
Score falls below some threshold
In BLAST, search depends on word size
KENFDKARFSGTWYAMAKKDPEG 50 RBP (query)
MKGLDIQKVAGTWYSLAMAASD. 44 lactoglobulin (hit)
extend
extend
Hit!

44. FASTA (Pearson and Lippman 1988)
Combines Smith and Waterman algorithm with word (k-tup) search  faster, heuristic approach
Query sequence divided into small words (usually k=2 for proteins)
Words used to initially compare and match sequences
If words located on same diagonal, surrounding region is then selected for analysis
Seq 1 Search words (k-tup = 2)
FY YG GK
KL LH HM
ME EG GD
Seq 1 FYGKLHMEGD
Seq 2 FWGKLHMEGSNE

45. FASTA (Pearson and Lippman 1988)
(a) Identify common k-words between sequences A and B
(b) Score diagonals with k-word matches, identify 10 best diagonals (dense regions of k-word overlap)
Rescore initial regions with a substitution score matrix
(c) Join initial regions using gaps, penalize for gaps
(d) Perform dynamic programming to find final alignments

46. Statistical Significance of Pairwise Alignments
Is an alignment similar based on statistical significance, or are similarities due to chance?
How do we define significant? Statistics.
Start with Null Hypothesis (H0) that 2 sequences are not related.
Suggest an alternative hypothesis (H1) that 2 sequences are related.
Select an arbitrary value defining statistical significance (α=0.05): This is the probability that the Null hypothesis can be rejected (i.e., there is less than 5% probability that a match occurs as a result of chance).

47. Statistical Mean and Standard Deviation
Mean (average) is the sum of a set of numbers (x1 + x2 + … xn), divided by the total instances in the set (n)
Standard Deviation (s) is the square root of the squared sum of the difference between a given value (xi) and the sample mean (x-bar) divided by the total instances in the set (n)

48. Statistical Measures of Algorithms
Objective of alignment algorithms is to maximize sensitivity and specificity of alignments.
Sensitivity: Measure of how well algorithm correctly predicts sequences that are related.
Specificity: Measure of how well algorithm correctly predicts sequences that are unrelated.

49. Statistical Comparison of 2 Sequences
Compare a large number of “random” sequences
Many different proteins
Randomly generated sequences
Scrambled variations of 1 of your 2 sequences
Calculate a Z score from the difference between the score of your aligned sequences (x) and the mean of the random sequences (μ), divided by the standard deviation of the random sequences (σ).

50. Convert Z Score to Probability of Chance Alignment
Z score represents distance between sequence alignment score and population mean (per SD) estimated from random sequences
The Z score can be converted to probability.
Example: For Z = 2.0 (at α = 0.05), 97.98% of all values fall within 2.0 standard deviations (Z=2.0), therefore your sequence score could occur by chance only 2.02% of the time.