This document discusses various statistical methods used in bioinformatics, including dot matrix analysis and dynamic programming algorithms. Dot matrix analysis can be used to compare DNA or protein sequences visually and look for repeats or alignments. Dynamic programming algorithms like those used in BLAST are commonly used to generate optimal global and local sequence alignments by calculating alignment scores based on substitution matrices like PAM and BLOSUM.

1. Statistical methods in
Bioinformatics

2. Dot Matrix
•First described by Gibbs and McIntyre (1970)
•Dot matrix analysis of DNA sequence (W=11, S=7)
Phage P22 c2 repressor
Phage lambda cI

3. Dot Matrix
•Dot matrix analysis of amino acid sequence (W=1, S=1)
Phage lambda cI
Phage P22 c2 repressor

4. Filtering in Dot Matrix
•Filtering can be applied using Sliding windows
Window size Match requirement
(Stringency)
DNA 15 10
Protein 2/3 2
•For DNA Long Windows, higher Stringency
For Proteins Short Windows, Low Stringency
For Protein Domains Long Windows, Low Stringency

5. Dot Matrix Programs
•DNA strider
•DOTTER
•COMPARE
•DOPLOT
For sequence repeats,
•LALIGN
•PLALIGN

6. LALIGN/PALIGN

7. Dot plot for Repeat analysis
(Window=1, Stringency=1)

8. Dot plot for Repeat analysis
(Window=23, Stringency=7)

9. Dynamic programming
•Compares every pair of characters in the two sequences and
generates an alignment
•Alignment includes matches, mismatches and gaps
•Alignments obtained depend on the choice of scoring system

10. Programs for alignment of sequences

11. Scoring using Gap penalty

12. Derivation of Dynamic programming
algorithm

13. Dynamic programming Algorithm

14. Dynamic programming Algorithm

15. Dynamic programming Algorithm

16. Dynamic programming Algorithm

17. Dynamic programming Algorithm

18. Dynamic programming Algorithm

19. Dynamic programming Algorithm

20. Formal description of Algorithm

21. Global and Local alignments

22. Global and Local alignments

23. Scoring matrices
•Certain amino acid substitutions common in related proteins
from different species
Proteins still function with these
substitutions

24. Scoring matrices

25. Scoring matrices
•Probability of changing
A B
is identical to
B A

26. PAM (Percent Accepted Mutation)
•Based on evolutionary principles
•Each matrix gives the changes expected for a given period
of evolutionary time
•Each change at a particular site is assumed to be
independent of previous mutational events
•Estimations are based on 1572 changes in 71 groups of
protein sequences that were at least 85% similar

27. Scoring matrices

28. PAM (Percent Accepted Mutation)
PAM1 matrix estimates what rate of substitution would be
expected if 1% of the amino acids had changed
Similarity Matrix used
40% PAM120
50% PAM80
60% PAM60
14-27% PAM250

29. BLOSUM (Blocks Amino acid
Substitution Matrices)
Matrix values are based on amino acid substitutions in a large
set of ~2000 conserved amino acid patterns (blocks)
Note: patterns are found by MOTIFMOTIF program

30. BLOSUM
– Derivation of the Matrix values

31. PAM 250

32. BLOSUM62

33. BLAST home page

34. BLAST

35. BLAST results

36. BLAST results

37. BLAST results