Phylogenetic Analysis

1. Phylogenetic Analysis

2. Review of Linux • ls • cd • mkdir • less • cp • mv • cat • pwd • >

3. Perl • Variables • $DNA="A"; • @DATA=('A', 'B'); • %TABLE=(A=>'A', N=>'[AC]',); • Statements • print • length • open • close • substr • push • pop • shift • unshift

4. #!/usr/bin/perl –w $word = 'MNIDDKL'; if($word eq 'QSTVSGE') { print "QSTVSGE\n"; } elsif($word eq 'MRQQDMISHDEL') { print "MRQQDMISHDEL\n"; } elsif ( $word eq 'MNIDDKL' ) { print "MNIDDKL-the magic word!\n"; } else { print "Is \”$word\“ a peptide?\n"; } exit;

5. $x = 10; $y = -20; if ($x <= 10) { print "1st true\n";} if ($x > 10) {print "2nd true\n";} if ($x <= 10 || $y > -21) {print "3rd true\n";} if ($x > 5 && $y < 0) {print "4th true\n";} if (($x > 5 && $y < 0) || $y > 5) {print "5th true\n";}

6. $position = 0; while ( $position < length $DNA) { $base = substr($DNA, $position, 1); if ( $base eq 'C' or $base eq 'G') { ++$count_of_CG; } $position++; } for ( $position = 0 ; $position < length $DNA ; ++$position ) { $base = substr($DNA, $position, 1); if ( $base eq 'C' or $base eq 'G') { ++$count_of_CG; } }

7. The Most Common Sequence Formats

8. Converting Formats • Don’t re-compute your MSA if it is not in the right format • Convert your file using one of the online conversion tools • The 3 most popular reformatting utilities: • Fmtseq The most complete • RESDSEQ Very popular and robust • SeqCheck Can clean FASTA sequences

10. Editing your MSA • If your MSA looks bad . . . • Don’t torture the online server • Edit the MSA yourself locally • Never, ever, ever (ever) use a standard word processor • Always use a dedicated MSA editor • The most popular online tool is Jalview • You can get it at www.jalview.org

12. MSA => LOGO Graph • A LOGO graph summarizes an MSA • Tall letters indicate highly conserved positions • Short letters indicate poorly conserved positions • LOGO graphs are ideal for identifying conserved patterns • weblogo.berkeley.edu/

13. Molecular Evolution and Phylogenetic Reconstruction

14. Evolutionary Tree of Bears and Raccoons

15. Human Evolutionary Tree (cont’d) http://www.mun.ca/biology/scarr/Out_of_Africa2.htm

16. Human Migration Out of Africa 1. Yorubans 2. Western Pygmies 3. Eastern Pygmies 4. Hadza 5. !Kung 1 2 3 4 5 http://www.becominghuman.org

17. Reading Your Tree • There’s a lot of vocabulary in a tree • Nodes correspond to common ancestors • The root is the oldest ancestor • Often artificial • Only meaningful with a good outgroup • Trees can be un-rooted • Branch lengths are only meaningful when the tree is scaled • Cladograms are often scaled • Phenograms are usualy unscaled

18. Rooted and Unrooted Trees • In the unrooted tree the position of the root (“oldest ancestor”) is unknown. Otherwise, they are like rooted trees

19. Type of Trees (Cladogram)

20. Type of Trees (Phylogram)

21. Orthology and Paralogy 直系（垂直）同源和旁系（平行）同源 • Orthologous genes • Separated by speciation • Often have the same function • Paralogous genes • Separated by duplications • Can have different functions • In the graph: • A is paralogous with B • A1 is orthologous with A2

22. Which Sequences ? • Orthologous sequences • Produce a species tree • Show how the considered species have diverged • Paralogous sequences • Produce a gene tree • Show the evolution of a protein family

23. Building the Right MSA • Your MSA should have as few gaps as possible. Most time should remove columns with gaps. • Some variability but not too much! • Some conservation but not too much!

24. Building the Right Tree • There are three types of tree-reconstruction methods • Distance-based methods • Statistical methods • Parsimony methods • Statistical methods are the most accurate • Maximum likelihood of success • Bayesian methods • Statistical methods take more time • Limited to small datasets

25. j i Distance in Trees: an Exampe d1,4 = 12 + 13 + 14 + 17 + 12 = 68

26. Compute a Distance Matrix Evolutionary Distance - number of substitutions per 100 amino acids (for proteins) or nucleotides (for DNA) A C T G T A G G A A T C G C A A T G A A A G A A T C G C 3 observed changes A C T G T A G G A A T C G C A C T G C A G G A A T A G C A A T G A A A G A A T C G C 6 actual changes

27. j i Edit Distance vs Tree Distance d1,4 = 12 + 13 + 14 + 17 + 12 = 68 D1,4 may be smaller than 68, as some changes may not be observed

28. Fitting Distance Matrix • Given n species, we can compute the n x n distance matrixDij • Evolution of these genes is described by a tree that we don’t know. • We need an algorithm to construct a tree that best fits the distance matrix Dij

29. Tree reconstruction for any 3x3 matrix is straightforward We have 3 leaves i, j, k and a center vertex c Reconstructing a 3 Leaved Tree Observe: dic + djc = Dij dic + dkc = Dik djc + dkc = Djk

30. dic + djc = Dij + dic + dkc = Dik 2dic + djc + dkc = Dij + Dik 2dic + Djk = Dij + Dik dic = (Dij + Dik – Djk)/2 Similarly, djc = (Dij + Djk – Dik)/2 dkc = (Dki + Dkj – Dij)/2 Reconstructing a 3 Leaved Tree(cont’d)

31. Additive Distance Matrices Matrix D is ADDITIVE if there exists a tree T with dij(T) = Dij NON-ADDITIVE otherwise

32. The Four Point Condition (cont’d) Compute: 1. Dij + Dkl, 2. Dik + Djl, 3. Dil + Djk 2 3 1 2 and 3 represent the same number: the length of all edges + the middle edge (it is counted twice) 1 represents a smaller number: the length of all edges – the middle edge

33. The Four Point Condition: Theorem • The four point condition for the quartet i,j,k,l is satisfied if two of these sums are the same, with the third sum smaller than these first two • Theorem : An n x n matrix D is additive if and only if the four point condition holds for every quartet 1 ≤ i,j,k,l ≤ n

34. Distance Based Phylogeny Problem • Goal: Reconstruct an evolutionary tree from a distance matrix • Input: n x n distance matrix Dij • Output: weighted tree T with n leaves fitting D • If D is additive, this problem has a solution and there is a simple algorithm to solve it

35. Find neighboring leavesi and j with parent k Remove the rows and columns of i and j Add a new row and column corresponding to k, where the distance from k to any other leaf m can be computed as: Using Neighboring Leaves to Construct the Tree Dkm = (Dim + Djm – Dij)/2 Compress i and j into k, iterate algorithm for rest of tree

36. Finding Neighboring Leaves • To find neighboring leaves we simply select a pair of closest leaves.

37. Finding Neighboring Leaves • To find neighboring leaves we simply select a pair of closest leaves. • WRONG

38. Finding Neighboring Leaves • Closest leaves aren’t necessarily neighbors • i and j are neighbors, but (dij= 13) > (djk = 12) • Finding a pair of neighboring leaves is • a nontrivial problem!

39. Neighbor Joining Algorithm • In 1987 Naruya Saitou and Masatoshi Nei developed a neighbor joining algorithm for phylogenetic tree reconstruction • Finds a pair of leaves that are close to each other but far from other leaves: implicitly finds a pair of neighboring leaves • Advantages: works well for additive and other non-additive matrices, it does not have the flawed molecular clock assumption

40. Overview • Based on the current distance matrix calculate the matrix Q (defined later). • Find the pair of taxa for which has its lowest value Qij. Add a new node to the tree, joining these taxa to the rest of the tree. • Calculate the distance from each of the taxa in the pair to this new node. • Calculate the distance from each of the taxa outside of this pair to the new node. • Start the algorithm again, replacing the pair of joined neighbors with the new node and using the distances calculated in the previous step.

41. Basic Algorithm

43. D Q

44. D Q

45. D Q

46. Another Example

47. Q(ij)=(N-2)d(ij) - [r(i) + r(j)]

48. Q

49. D(AU) =d(AB) / 2 + [r(A)-r(B)] / 2(N-2) = 1 D(BU) =d(AB) -D(AU) = 4 Tree (So far)

50. d(CU) = [d(AC) + d(BC) - d(AB)] / 2 = 3 d(DU) = [d(AD) + d(BD) - d(AB) ]/ 2 = 6 d(EU) = [d(AE) + d(BE) - d(AB) ]/ 2 = 5 d(FU) = [d(AF) + d(BF) - d(AB) ]/ 2 = 7 New Matrix