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![Bubble Sort Implementation
Here is an ascending-order implementation of the bubblesort algorithm for integer arrays:
void BubbleSort(int List[] , int Size) {
int tempInt; // temp variable for swapping list elems
for (int Stop = Size - 1; Stop > 0; Stop--) {
for (int Check = 0; Check < Stop; Check++) { // make a pass
if (List[Check] > List[Check + 1]) { // compare elems
tempInt = List[Check]; // swap if in the
List[Check] = List[Check + 1]; // wrong order
List[Check + 1] = tempInt;
}
}
}
}
Bubblesort compares and swaps adjacent elements; simple but not very efficient.
Efficiency note: the outer loop could be modified to exit if the list is already sorted.](https://image.slidesharecdn.com/bioinformatics-t4-alignmentsv2014-141020123044-conversion-gate02/85/Bioinformatics-t4-alignments-v2014-26-320.jpg)
![Needleman-Wunsch.pl
# initialization
my @matrix;
$matrix[0][0]{score} = 0;
$matrix[0][0]{pointer} = "none";
for(my $j = 1; $j <= length($seq1); $j++) {
$matrix[0][$j]{score} = $GAP * $j;
$matrix[0][$j]{pointer} = "left";
}
for (my $i = 1; $i <= length($seq2); $i++) {
$matrix[$i][0]{score} = $GAP * $i;
$matrix[$i][0]{pointer} = "up";
}](https://image.slidesharecdn.com/bioinformatics-t4-alignmentsv2014-141020123044-conversion-gate02/85/Bioinformatics-t4-alignments-v2014-82-320.jpg)
![Needleman-Wunsch.pl
# fill
for(my $i = 1; $i <= length($seq2); $i++) {
for(my $j = 1; $j <= length($seq1); $j++) {
my ($diagonal_score, $left_score, $up_score);
# calculate match score
my $letter1 = substr($seq1, $j-1, 1);
my $letter2 = substr($seq2, $i-1, 1);
if ($letter1 eq $letter2) {
$diagonal_score = $matrix[$i-1][$j-1]{score} + $MATCH;
}
else {
$diagonal_score = $matrix[$i-1][$j-1]{score} + $MISMATCH;
}
# calculate gap scores
$up_score = $matrix[$i-1][$j]{score} + $GAP;
$left_score = $matrix[$i][$j-1]{score} + $GAP;
# choose best score
if ($diagonal_score >= $up_score) {
if ($diagonal_score >= $left_score) {
$matrix[$i][$j]{score} = $diagonal_score;
$matrix[$i][$j]{pointer} = "diagonal";
}
else {
$matrix[$i][$j]{score} = $left_score;
$matrix[$i][$j]{pointer} = "left";
}
} else {
if ($up_score >= $left_score) {
$matrix[$i][$j]{score} = $up_score;
$matrix[$i][$j]{pointer} = "up";
}
else {
$matrix[$i][$j]{score} = $left_score;
$matrix[$i][$j]{pointer} = "left";
}
}](https://image.slidesharecdn.com/bioinformatics-t4-alignmentsv2014-141020123044-conversion-gate02/85/Bioinformatics-t4-alignments-v2014-85-320.jpg)
![Needleman-Wunsch.pl
my $align1 = "";
my $align2 = "";
my $j = length($seq1);
my $i = length($seq2);
while (1) {
last if $matrix[$i][$j]{pointer} eq "none";
if ($matrix[$i][$j]{pointer} eq "diagonal") {
$align1 .= substr($seq1, $j-1, 1);
$align2 .= substr($seq2, $i-1, 1);
$i--; $j--;
}
elsif ($matrix[$i][$j]{pointer} eq "left") {
$align1 .= substr($seq1, $j-1, 1);
$align2 .= "-";
$j--;
}
elsif ($matrix[$i][$j]{pointer} eq "up") {
$align1 .= "-";
$align2 .= substr($seq2, $i-1, 1);
$i--;
}
}
$align1 = reverse $align1;
$align2 = reverse $align2;
print "$align1n";
print "$align2n";](https://image.slidesharecdn.com/bioinformatics-t4-alignmentsv2014-141020123044-conversion-gate02/85/Bioinformatics-t4-alignments-v2014-90-320.jpg)
![Running ClustalW
****** MULTIPLE ALIGNMENT MENU ******
1. Do complete multiple alignment now (Slow/Accurate)
2. Produce guide tree file only
3. Do alignment using old guide tree file
4. Toggle Slow/Fast pairwise alignments = SLOW
5. Pairwise alignment parameters
6. Multiple alignment parameters
7. Reset gaps between alignments? = OFF
8. Toggle screen display = ON
9. Output format options
S. Execute a system command
H. HELP
or press [RETURN] to go back to main menu
Your choice:](https://image.slidesharecdn.com/bioinformatics-t4-alignmentsv2014-141020123044-conversion-gate02/85/Bioinformatics-t4-alignments-v2014-111-320.jpg)
![Practical guide to pairwise alignment:
the “BLAST 2 sequences” website
• Go to http://www.ncbi.nlm.nih.gov/BLAST
• Choose BLAST 2 sequences
• In the program,
[1] choose blastp (protein search) or blastn (for DNA)
[2] paste in your accession numbers
(or use FASTA format)
[3] select optional parameters, such as
--BLOSU62 matrix is default for proteins
try PAM250 for distantly related proteins
--gap creation and extension penalties
[4] click “align”](https://image.slidesharecdn.com/bioinformatics-t4-alignmentsv2014-141020123044-conversion-gate02/85/Bioinformatics-t4-alignments-v2014-128-320.jpg)
![Practicum 3
• CpG Islands
– Download from ENSEMBL 1000 (random) promoters (3000 bp) (hint:
use Biomart)
– How many times would you expect to observe CG if all nucleotides
were equipropable
– Count the number op times CG is observed for these 1000 genes and
make a histogram from these scores.
– Are there any other dinucleatides over- or underrepresented
– CG repeats are often methylated. In order to study methylation
patterns bisulfide treatment of DNA is used. Bisulfide changes every C
which is not followed by G into T. Generate computationally the
bisulfide treated version of DNA (hint: while (s/C([^G])/T$1/g) {};)
– How would you find primers that discriminate between methylated and
unmethylated DNA ? Given that the genome is 3.109 bp how long do
you need to make a primer to avoid mispriming ?](https://image.slidesharecdn.com/bioinformatics-t4-alignmentsv2014-141020123044-conversion-gate02/85/Bioinformatics-t4-alignments-v2014-135-320.jpg)
Uploaded byProf. Wim Van Criekinge
Bioinformatics t4-alignments v2014
This document discusses dot plots and sequence alignments. It begins with an overview of dot plots, explaining that they are a graphical representation used to visualize similarities between two sequences. It describes how dot plots are constructed and notes that they are useful for finding repeated or inverted repeated structures. The document then discusses how to reduce noise in dot plots and provides examples of dot plots. It also discusses sequence alignments, including global vs local alignments and different algorithms for pairwise and multiple sequence alignment such as Needleman-Wunsch, Smith-Waterman, and ClustalW. It notes why multiple alignments are performed and concludes with discussing how to measure algorithm efficiency.
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Bioinformatics t4-alignments v2014
- 2. FBW 21-10-2014 WimVan Criekinge
- 3. Wel les op4 november en GEEN les op 18 november
- 4. Rat versus mouseRBP Rat versus bacterial lipocalin
- 5. – Henikoff andHenikoff have compared the BLOSUM matrices to PAM by evaluating how effectively the matrices can detect known members of a protein family from a database when searching with the ungapped local alignment program BLAST. They conclude that overall the BLOSUM 62 matrix is the most effective. • However, all the substitution matrices investigated perform better than BLOSUM 62 for a proportion of the families. This suggests that no single matrix is the complete answer for all sequence comparisons. • It is probably best to compliment the BLOSUM 62 matrix with comparisons using 250 PAMS, and Overington structurally derived matrices. – It seems likely that as more protein three dimensional structures are determined, substitution tables derived from structure comparison will give the most reliable data. Overview
- 6. Dotplots • Whatis it ? – Graphical representation using two orthogonal axes and “dots” for regions of similarity. – In a bioinformatics context two sequence are used on the axes and dots are plotted when a given treshold is met in a given window. • Dot-plotting is the best way to see all of the structures in common between two sequences or to visualize all of the repeated or inverted repeated structures in one sequence
- 7. Visual Alignments (DotPlots) • Matrix – Rows: Characters in one sequence – Columns: Characters in second sequence • Filling – Loop through each row; if character in row, col match, fill in the cell – Continue until all cells have been examined
- 8. Dotplot-simulator.pl print "$seq1n"; for(my $teller=0;$teller<=$seq2_length;$teller++){ print substr($seq2,$teller,1); $w2=substr($seq2,$teller,$window); for(my $teller2=0;$teller2<=$seq_length;$teller2++){ $w1=substr($seq1,$teller2,$window); if($w1 eq $w2){print "*";}else{print " ";} } print"n"; }
- 9. Overview Window size= 1, stringency 100%
- 10. Noise in DotPlots • Nucleic Acids (DNA, RNA) – 1 out of 4 bases matches at random • Stringency – Window size is considered – Percentage of bases matching in the window is set as threshold
- 11. Reduction of DotPlot Noise Self alignment of ACCTGAGCTCACCTGAGTTA
- 12. Dotplot-simulator.pl Example: ZK822Genomic and cDNA Gene prediction: How many exons ? Confirm donor and aceptor sites ? Remember to check the reverse complement !
- 13. Chromosome Y selfcomparison
- 14. • Regions ofsimilarity appear as diagonal runs of dots • Reverse diagonals (perpendicular to diagonal) indicate inversions • Reverse diagonals crossing diagonals (Xs) indicate palindromes • A gap is introduced by each vertical or horizontal skip Overview
- 15. • Window sizechanges with goal of analysis – size of average exon – size of average protein structural element – size of gene promoter – size of enzyme active site Overview
- 16. Rules of thumb Don't get too many points, about 3- 5 times the length of the sequence is about right (1-2%) Window size about 20 for distant proteins 12 for nucleic acid Check sequence vs. itself Check sequence vs. sequence Anticipate results (e.g. “in-house” sequence vs genomic, question) Overview
- 17. Available Dot PlotPrograms Dotlet (Java Applet) http://www.isrec.isb-sib. ch/java/dotlet/Dotlet. html
- 18. Sequence Alignments Introduction Algorithms What ? Examples Properties Dynamic Programming for Pairwise Alignment Concept Example Needleman-Wunsch(.pl) Smith-Waterman(.pl) Multiple Alignment MSA Hierarchical Pairwise Alignent ClustalW, PileUp Formatting Interpretation Alternative Methods SIM Blast2 Dali
- 19. Global and localalignment Pairwise sequence alignment can be global or local Global: the sequences are completely aligned (Needleman and Wunsch, 1970) Local: only the best sub-regions are aligned (Smith and Waterman, 1981). BLAST uses local alignment.
- 20. Why we domultiple alignments? – In order to characterize protein families, identify shared regions of homology in a multiple sequence alignment; (this happens generally when a sequence search revealed homologies to several sequences) – Determination of the consensus sequence of several aligned sequences – Help prediction of the secondary and tertiary structures of new sequences; – Preliminary step in molecular evolution analysis using Phylogenetic methods for constructing phylogenetic trees – Garbage in, Garbage out – Chicken/egg
- 21. Why we domultiple alignments? • To find conserved regions – Local multiple alignment reveals conserved regions – Conserved regions usually are key functional regions – These regions are prime targets for drug developments • To do phylogenetic analysis: – Same protein from different species – Optimal multiple alignment probably implies history – Discover irregularities, such as Cystic Fibrosis gene
- 22. VTISCTGSSSNIGAG-NHVKWYQQLPG VTISCTGTSSNIGS--ITVNWYQQLPG LRLSCSSSGFIFSS--YAMYWVRQAPG LSLTCTVSGTSFDD--YYSTWVRQPPG PEVTCVVVDVSHEDPQVKFNWYVDG-- ATLVCLISDFYPGA--VTVAWKADS-- AALGCLVKDYFPEP--VTVSWNSG--- VSLTCLVKGFYPSD--IAVEWWSNG--
- 23. Sequence Alignments Introduction Algorithms What ? Examples Properties Dynamic Programming for Pairwise Alignment Concept Example Needleman-Wunsch(.pl) Smith-Waterman(.pl) Multiple Alignment MSA Hierarchical Pairwise Alignent ClustalW, PileUp Formatting Interpretation Alternative Methods SIM Blast2 Dali
- 24. Algorithms and Programs • Algorithm: a method or a process followed to solve a problem. – A recipe. • An algorithm takes the input to a problem (function) and transforms it to the output. – A mapping of input to output. • A problem can have many algorithms.
- 25. Bubble Sort Algorithm One of the simplest sorting algorithms proceeds by walking down the list, comparing adjacent elements, and swapping them if they are in the wrong order. The process is continued until the list is sorted. More formally: 1. Initialize the size of the list to be sorted to be the actual size of the list. 2. Loop through the list until no element needs to be exchanged with another to reach its correct position. 2.1 Loop (i) from 0 to size of the list to be sorted - 2. 2.1.1 Compare the ith and (i + 1)st elements in the unsorted list. 2.1.2 Swap the ith and (i + 1)st elements if not in order ( ascending or descending as desired). 2.2 Decrease the size of the list to be sorted by 1. Each pass "bubbles" the largest element in the unsorted part of the list to its correct location. A 13 7 43 5 3 19 2 23 29 ?? ?? ?? ?? ??
- 26. Bubble Sort Implementation Here is an ascending-order implementation of the bubblesort algorithm for integer arrays: void BubbleSort(int List[] , int Size) { int tempInt; // temp variable for swapping list elems for (int Stop = Size - 1; Stop > 0; Stop--) { for (int Check = 0; Check < Stop; Check++) { // make a pass if (List[Check] > List[Check + 1]) { // compare elems tempInt = List[Check]; // swap if in the List[Check] = List[Check + 1]; // wrong order List[Check + 1] = tempInt; } } } } Bubblesort compares and swaps adjacent elements; simple but not very efficient. Efficiency note: the outer loop could be modified to exit if the list is already sorted.
- 27. ijs • 6eierdooiers + 105 gram S1 kristalsuiker • 1’ kloppen to “ruban” • Ondertussen 500 ml volle melk laten opwarmen met 105 gram S1 suiker • Toevoegen vanille en/of chocolade (kaneel) • Langzaam de bijna kokende melk onder ruban kloppen (van het vuur) • Terug op het vuur: “Porter a la nappe” • Afkoelen • “Afdraaien” (in ijsmachine) • 15” voor stolling 500 ml room toevoegen
- 28.
- 29. "Great algorithms arethe poetry of computation"
- 30. "Great algorithms arethe poetry of computation" 1946: The Metropolis Algorithm for Monte Carlo. Through the use of random processes, this algorithm offers an efficient way to stumble toward answers to problems that are too complicated to solve exactly. 1947: Simplex Method for Linear Programming. An elegant solution to a common problem in planning and decision-making. 1950: Krylov Subspace Iteration Method. A technique for rapidly solving the linear equations that abound in scientific computation. 1951: The Decompositional Approach to Matrix Computations. A suite of techniques for numerical linear algebra. 1957: The Fortran Optimizing Compiler. Turns high-level code into efficient computer-readable code. 1959: QR Algorithm for Computing Eigenvalues. Another crucial matrix operation made swift and practical. 1962: Quicksort Algorithms for Sorting. For the efficient handling of large databases. 1965: Fast Fourier Transform. Perhaps the most ubiquitous algorithm in use today, it breaks down waveforms (like sound) into periodic components. 1977: Integer Relation Detection. A fast method for spotting simple equations satisfied by collections of seemingly unrelated numbers. 1987: Fast Multipole Method. A breakthrough in dealing with the complexity of n-body calculations, applied in problems ranging from celestial mechanics to protein folding. From Random Samples, Science page 799, February 4, 2000.
- 31. Algorithm Properties •An algorithm possesses the following properties: – It must be correct. – It must be composed of a series of concrete steps. – There can be no ambiguity as to which step will be performed next. – It must be composed of a finite number of steps. – It must terminate. • A computer program is an instance, or concrete representation, for an algorithm in some programming language.
- 32. Measuring Algorithm Efficiency • Types of complexity – Space complexity – Time complexity • Analysis of algorithms – The measuring of the complexity of an algorithm • Cannot compute actual time for an algorithm – We usually measure worst-case time
- 33. Measuring Algorithm Efficiency Three algorithms for computing 1 + 2 + … n for an integer n > 0
- 34. Measuring Algorithm Efficiency The number of operations required by the algorithms
- 35. Measuring Algorithm Efficiency The number of operations required by the algorithms as a function of n
- 36. Big Oh Notation • To say "Algorithm A has a worst-case time requirement proportional to n" – We say A is O(n) – Read "Big Oh of n" • For the other two algorithms – Algorithm B is O(n2) – Algorithm C is O(1) • O is derived from order (magnitude)
- 37. Picturing Efficiency O(n)algorithm
- 38. Picturing Efficiency AnO(n2) algorithm.
- 39. Picturing Efficiency AnotherO(n2) algorithm.
- 40. Sequence Alignments Introduction Algorithms What ? Examples Properties Dynamic Programming for Pairwise Alignment Concept Example Needleman-Wunsch(.pl) Smith-Waterman(.pl) Multiple Alignment MSA Hierarchical Pairwise Alignent ClustalW, PileUp Formatting Interpretation Alternative Methods SIM Blast2 Dali
- 41. The best alignment: The one with the maximum total score
- 42. • Exhaustive … – All combinations: • Algorithm – Dynamic programming (much faster) • Heuristics – Needleman – Wunsh for global alignments (Journal of Molecular Biology, 1970) – Later adapated by Smith-Waterman for local alignment Overview
- 43. • Score ofan alignment: reward matches and penalize mismatches and spaces. – eg, each column gets a (different) value for: • a match: +1, (both have the same characters); • a mismatch : -1, (both have different characters); and • a space in a column: -2. – The total score of an alignment is the sum of the values assigned to its columns.
- 44. A metric … GACGGATTAG, GATCGGAATAG GA-CGGATTAG GATCGGAATAG +1 (a match), -1 (a mismatch),-2 (gap) 9*1 + 1*(-1)+1*(-2) = 6
- 45. Dynamic programming Reducethe problem: the solution to a large problem is to simplify … if we first know the solution to a smaller problem that is a subset of the larger problem Overview P P1 P2 P3 P
- 46. Dynamic Programming •Finding optimal solution to search problem • Recursively computes solution • Fundamental principle is to produce optimal solutions to smaller pieces of the problem first and then glue them together • Efficient divide-and-conquer strategy because it uses a bottom-up approach and utilizes a look-up table instead of recomputing optimal solutions to sub-problems P P1 P2 P3 P
- 47. Dynamic Programming Whatis the best way to get from A to C ? Rules: Three stops Solutions: Try all and select best, requires (combin(13,3)) = 286 calculations A C
- 48. Dynamic Programming Whatis the best way to get from A to C ? If we known that B is on the optimal path ? A B C
- 49. Dynamic Programming Whatis the best way to get from A to B ? 1 2 3 A B C 4 5 6
- 50. Dynamic Programming Whatis the best way to get from B to C ? 2 3 A B 4 C 5 6 1
- 51. Dynamic Programming Howmany paths from A to C via B ? 6 * 6 = 36 1 2 3 A B 4 C 5 6 1
- 52. Dynamic Programming Solvethe subproblem A to B: 6 calculations 1 2 3 A B C 4 5 6
- 53. Dynamic Programming Solvethe subproblem B to C: 6 calculations 2 3 A B 4 C 5 6 1
- 54. Dynamic Programming IfB is on optimal path from A->C, this optimal path = optimal path from A to B + optimal path from B to C 12 calculations needed (not 36 or 286) A B C 5 3
- 55. the best alignmentbetween • a zinc-finger core sequence: –CKHVFCRVCI • and a sequence fragment from a viral polyprotein: –CKKCFCKCV
- 56. C K HV F C R V C I +-------------------- C | 1 1 1 K | 1 K | 1 C | 1 1 1 F | 1 C | 1 1 1 K | 1 C | 1 1 1 V | 1 1 Dynamic Programming
- 57. C K HV F C R V C I +-------------------- C | 1 1 1 K | 1 K | 1 C | 1 1 1 F | 1 C | 1 1 1 K | 1 C | 1 1 1 V | 1 1 Dynamic Programming
- 58. C K HV F C R V C I +-------------------- C | 1 1 1 0 K | 1 0 K | 1 0 C | 1 1 1 0 F | 1 0 C | 1 1 1 0 K | 1 0 C | 1 1 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
- 59. C K HV F C R V C I +-------------------- C | 1 1 1 0 K | 1 0 K | 1 0 C | 1 1 1 0 F | 1 0 C | 1 1 1 0 K | 1 0 C | 2 1 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
- 60. C K HV F C R V C I +-------------------- C | 1 1 1 0 K | 1 0 0 K | 1 0 0 C | 1 1 1 0 F | 1 0 0 C | 1 1 1 0 K | 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
- 61. C K HV F C R V C I +-------------------- C | 1 1 1 1 0 K | 1 1 0 0 K | 1 1 0 0 C | 1 1 1 1 0 F | 1 1 0 0 C | 1 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
- 62. C K HV F C R V C I +-------------------- C | 1 1 1 1 1 0 K | 1 1 1 0 0 K | 1 1 1 0 0 C | 1 1 1 1 1 0 F | 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
- 63. C K HV F C R V C I +-------------------- C | 1 2 1 1 1 0 K | 1 1 1 1 0 0 K | 1 1 1 1 0 0 C | 1 2 1 1 1 0 F | 2 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
- 64. C K HV F C R V C I +-------------------- C | 1 2 2 1 1 1 0 K | 1 2 1 1 1 0 0 K | 1 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 2 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
- 65. C K HV F C R V C I +-------------------- C | 1 3 2 2 1 1 1 0 K | 1 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 2 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
- 66. C K HV F C R V C I +-------------------- C | 1 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 2 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
- 67. C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 2 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
- 68. C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
- 69. C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
- 70. C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
- 71. C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
- 72. C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
- 73. C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
- 74. C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
- 75. C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
- 76. C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
- 77. C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 C K H V F C R V C I C K K C F C - K C V C K H V F C R V C I C K K C F C K - C V C - K H V F C R V C I C K K C - F C - K C V C K H - V F C R V C I C K K C - F C - K C V Dynamic Programming
- 78. C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 C K H V F C R V C I C K K C F C - K C V C K H V F C R V C I C K K C F C K - C V C - K H V F C R V C I C K K C - F C - K C V C K H - V F C R V C I C K K C - F C - K C V Dynamic Programming
- 79. Extensions to basicdynamic programming method use gap penalties – constant gap penalty for gap > 1 – gap penalty proportional to gap size • one penalty for starting a gap (gap opening penalty) • different (lower) penalty for adding to a gap (gap extension penalty) • for nucleic acids, can be used to mimic thermodynamics of helix formation – two kinds of gap opening penalties • one for gap closed by AT, different for GC Dynamic Programming
- 80. • Zie cursusvoor voorbeeld met gap-penalties – zoek de fouten ;-) • Beschikbaar als perl programma waarmee we kunnen experimenteren
- 82. Needleman-Wunsch.pl # initialization my @matrix; $matrix[0][0]{score} = 0; $matrix[0][0]{pointer} = "none"; for(my $j = 1; $j <= length($seq1); $j++) { $matrix[0][$j]{score} = $GAP * $j; $matrix[0][$j]{pointer} = "left"; } for (my $i = 1; $i <= length($seq2); $i++) { $matrix[$i][0]{score} = $GAP * $i; $matrix[$i][0]{pointer} = "up"; }
- 83. Needleman-Wunsch-edu.pl The ScoreMatrix ---------------- Seq1(j)1 2 3 4 5 6 7 Seq2 * C K H V F C R (i) * 0 -1 -2 -3 -4 -5 -6 -7 1 C -1 1 0 -1 -2 -3 -4 -5 2 K -2 0 2 1 0 -1 -2 -3 3 K -3 -1 1 1 0 -1 -2 -3 4 C -4 -2 0 0 0 -1 0 -1 5 F -5 -3 -1 -1 -1 1 0 -1 6 C -6 -4 -2 -2 -2 0 2 1 7 K -7 -5 -3 -3 -3 -1 1 1 8 C -8 -6 -4 -4 -4 -2 0 0 9 V -9 -7 -5 -5 -3 -3 -1 -1
- 84. Needleman-Wunsch-edu.pl The ScoreMatrix ---------------- Seq1(j)1 2 3 4 5 6 7 Seq2 * C K H V F C R (i) * 0 -1 -2 -3 -4 -5 -6 -7 1 C -1 1 0 -1 -2 -3 -4 -5 2 K -2 0 2 1 0 -1 -2 -3 3 K -3 -1 1 1 0 -1 -2 -3 4 C -4 -2 0 0 0 -1 0 -1 5 F -5 -3 -1 -1 -1 1 0 -1 6 C -6 -4 -2 -2 -2 0 2 1 7 K -7 -5 -3 -3 -3 -1 1 1 8 C -8 -6 -4 -4 -4 -2 0 0 9 V -9 -7 -5 -5 -3 -3 -1 -1
- 85. Needleman-Wunsch.pl # fill for(my $i = 1; $i <= length($seq2); $i++) { for(my $j = 1; $j <= length($seq1); $j++) { my ($diagonal_score, $left_score, $up_score); # calculate match score my $letter1 = substr($seq1, $j-1, 1); my $letter2 = substr($seq2, $i-1, 1); if ($letter1 eq $letter2) { $diagonal_score = $matrix[$i-1][$j-1]{score} + $MATCH; } else { $diagonal_score = $matrix[$i-1][$j-1]{score} + $MISMATCH; } # calculate gap scores $up_score = $matrix[$i-1][$j]{score} + $GAP; $left_score = $matrix[$i][$j-1]{score} + $GAP; # choose best score if ($diagonal_score >= $up_score) { if ($diagonal_score >= $left_score) { $matrix[$i][$j]{score} = $diagonal_score; $matrix[$i][$j]{pointer} = "diagonal"; } else { $matrix[$i][$j]{score} = $left_score; $matrix[$i][$j]{pointer} = "left"; } } else { if ($up_score >= $left_score) { $matrix[$i][$j]{score} = $up_score; $matrix[$i][$j]{pointer} = "up"; } else { $matrix[$i][$j]{score} = $left_score; $matrix[$i][$j]{pointer} = "left"; } }
- 86. Needleman-Wunsch.pl #!e:perlbin -w use strict; # usage statement die "usage: $0 <sequence 1> <sequence 2>n" unless @ARGV == 2; # get sequences from command line my ($seq1, $seq2) = @ARGV; # scoring scheme my $MATCH = 1; # +1 for letters that match my $MISMATCH = -1; # -1 for letters that mismatch my $GAP = -1; # -1 for any gap
- 87. Needleman-Wunsch-edu.pl The ScoreMatrix ---------------- Seq1(j)1 2 3 4 5 6 7 Seq2 * C K H V F C R (i) * 0 -1 -2 -3 -4 -5 -6 -7 1 C -1 1 a 0 -1 -2 -3 -4 -5 2 K -2 0 c 2 b 1 0 -1 -2 -3 3 K -3 -1 1 1 0 -1 -2 -3 4 C -4 -2 0 0 0 -1 0 -1 5 F -5 -3 -1 -1 -1 1 0 -1 6 C -6 -4 -2 -2 -2 0 2 1 7 K -7 -5 -3 -3 -3 -1 1 1 8 C -8 -6 -4 -4 -4 -2 0 0 9 V -9 -7 -5 -5 -3 -3 -1 -1 A: matrix(i,j) = matrix(i-1,j-1) + (MIS)MATCH if (substr(seq1,j-1,1) eq substr(seq2,i-1,1) B: up_score = matrix(i-1,j) + GAP C: left_score = matrix(i,j-1) + GAP
- 88. Needleman-Wunsch-edu.pl The ScoreMatrix ---------------- Seq1(j)1 2 3 4 5 6 7 Seq2 * C K H V F C R (i) * 0 -1 -2 -3 -4 -5 -6 -7 1 C -1 1 0 -1 -2 -3 -4 -5 2 K -2 0 2 1 0 -1 -2 -3 3 K -3 -1 1 1 0 -1 -2 -3 4 C -4 -2 0 0 0 -1 0 -1 5 F -5 -3 -1 -1 -1 1 0 -1 6 C -6 -4 -2 -2 -2 0 2 1 7 K -7 -5 -3 -3 -3 -1 1 1 8 C -8 -6 -4 -4 -4 -2 0 0 9 V -9 -7 -5 -5 -3 -3 -1 -1
- 89.
- 90. Needleman-Wunsch.pl my $align1= ""; my $align2 = ""; my $j = length($seq1); my $i = length($seq2); while (1) { last if $matrix[$i][$j]{pointer} eq "none"; if ($matrix[$i][$j]{pointer} eq "diagonal") { $align1 .= substr($seq1, $j-1, 1); $align2 .= substr($seq2, $i-1, 1); $i--; $j--; } elsif ($matrix[$i][$j]{pointer} eq "left") { $align1 .= substr($seq1, $j-1, 1); $align2 .= "-"; $j--; } elsif ($matrix[$i][$j]{pointer} eq "up") { $align1 .= "-"; $align2 .= substr($seq2, $i-1, 1); $i--; } } $align1 = reverse $align1; $align2 = reverse $align2; print "$align1n"; print "$align2n";
- 91. Needleman-Wunsch-edu.pl Seq1:CKHVFCRVCI Seq2:CKKCFC-KCV ++--++--+- score = 0
- 92. • Practicum: usesimilarity function in initialization step -> scoring tables • Time Complexity • Use random proteins to generate histogram of scores from aligned random sequences
- 93. Time complexity withneedleman-wunsch.pl Sequence Length (aa) Execution Time (s) 10 0 25 0 50 0 100 1 500 5 1000 19 2500 559 5000 Memory could not be written
- 94. • -edu version • Monte-carlo version
- 95. Average around -64! -80 -78 -76 -74 -72 ** -70 ******* -68 *************** -66 ************************* -64 ************************************************************ -60 *********************** -58 *************** -56 ******** -54 **** -52 * -50 -48 -46 -44 -42 -40 -38
- 96. If the sequencesare similar, the path of the best alignment should be very close to the main diagonal. Therefore, we may not need to fill the entire matrix, rather, we fill a narrow band of entries around the main diagonal. An algorithm that fills in a band of width 2k+1 around the main diagonal.
- 97. Smith-Waterman.pl • Threechanges – The edges of the matrix are initialized to 0 instead of increasing gap penalties – The maximum score is never less than 0, and no pointer is recorded unless the score is greater than 0 – The trace-back starts from the highest score in the matrix (rather than at the end of the matrix) and ends at a score of 0 (rather than the start of the matrix) • Demonstration
- 98. Sequence Alignments Introduction Algorithms What ? Examples Properties Dynamic Programming for Pairwise Alignment Concept Example Needleman-Wunsch(.pl) Smith-Waterman(.pl) Multiple Alignment MSA Hierarchical Pairwise Alignent ClustalW, PileUp Formatting Interpretation Alternative Methods SIM Blast2 Dali
- 99. The best alignment: The one with the maximum total score Multiple Aligment: n>2
- 100. 2 to 3:hyperlattice
- 101. On its top-leftside, the cube is "covered" by the polyhedron. The edges 1, 2, 3, 6 and 7 are coming from the inside, and edges 4 and 5 can be ignored (and are therefore not labeled in the figure).
- 102. Computational Complexity ofMA by standard Dynamic Programming • Each node in the k-dimensional hyperlattice is visited once, and therefore the running time must be proportional to the number of nodes in the lattice. – This number is the product of the lengths of the sequences. – eg. the 3-dimensional lattice as visualized.
- 103. • The memoryspace requirement is even worse. To trace back the alignment, we need to store the whole lattice, a data structure the size of a multidimensional skyscraper. – In fact, space is the No.1 problem here, bogging down multiple alignment methods that try to achieve optimality. – Furthermore, incorporating a realistic gap model, we will further increase our demands on space and running time
- 104.
- 105. • The mostpractical and widely used method in multiple sequence alignment is the hierarchical extensions of pairwise alignment methods. • The principal is that multiple alignments is achieved by successive application of pairwise methods. – First do all pairwise alignments (not just one sequence with all others) – Then combine pairwise alignments to generate overall alignment Multiple Alignment Method
- 106. • The stepsare summarized as follows: – Compare all sequences pairwise. – Perform cluster analysis on the pairwise data to generate a hierarchy for alignment. This may be in the form of a binary tree or a simple ordering – Build the multiple alignment by first aligning the most similar pair of sequences, then the next most similar pair and so on. Once an alignment of two sequences has been made, then this is fixed. Thus for a set of sequences A, B, C, D having aligned A with C and B with D the alignment of A, B, C, D is obtained by comparing the alignments of A and C with that of B and D using averaged scores at each aligned position. Multiple Alignment Method
- 107.
- 108.
- 109. Multiple Sequence Alignmentprograms • Automatic multiple alignemnt – extend dynamic programming (MSA - Lipman) • limit: computing power: length and number of sequences (e.q. 2000^8) – progressive alignment (Feng & Doolittle) • use “guide tree” (PileUp, ClustalW etc) • Dedicated alignment editing program – Boxshade – SeaView – SeqPup (Java) • Combination (Biology – Computation)
- 110. • ClustalW isa general purpose multiple alignment program for DNA or proteins. • ClustalW is produced by Julie D. Thompson, Toby Gibson of European Molecular Biology Laboratory, Germany and Desmond Higgins of European Bioinformatics Institute, Cambridge, UK. Algorithmic • Improves the sensitivity of progressive multiple sequence alignment through sequence weighting, positions-specific gap penalties and weight matrix choice. Nucleic Acids Research, 22:4673-4680. ClustalW
- 111. Running ClustalW ******MULTIPLE ALIGNMENT MENU ****** 1. Do complete multiple alignment now (Slow/Accurate) 2. Produce guide tree file only 3. Do alignment using old guide tree file 4. Toggle Slow/Fast pairwise alignments = SLOW 5. Pairwise alignment parameters 6. Multiple alignment parameters 7. Reset gaps between alignments? = OFF 8. Toggle screen display = ON 9. Output format options S. Execute a system command H. HELP or press [RETURN] to go back to main menu Your choice:
- 113. PileUp • Beforeyou run PILEUP, it is necessary to study the sequences that will be aligned. • PILEUP is very sensitive to gaps, so if a set of sequences are of different lengths, gaps will be added to the ends of all shorter sequences to make them equal to the longest one in the set. • If you try to align five 300 nucleotide EST's with a single 20,000 nucleotide cosmid, you are adding 5 X 19,700 gaps to the alignment - and PILEUP will crash!
- 114. Formatting Multiple Alignments • The final product of a PILEUP run is a set of aligned sequences, which are stored in a Multiple Sequence File (called .msf by GCG). This msf file is a text file that can be formatted with a text editor, but GCG has some dedicated tools for improving the looks of msf files for easier interpretation and for publication. • Consensus sequences can be calculated and the relationship of each character of each sequence to the consensus can be highlighted using the program PRETTY
- 115. Formatting Multiple Alignments • Shading of regions of high homology can be created using the programs BOXSHADE and PRETTYBOX , but that goes beyond the scope of this tutorial. (Boxshade: http://www.ch.embnet.org/software/BOX_form.html) • In addition to these programs that run on the Alpha, the output of PILEUP (or CLUSTAL) can be moved by FTP from your RCR account to a local Mac or PC. • Since this output is a plain text file, it can be edited with any word processing program, or imported into any drawing program to add boldface text, underlining, shading, boxes, arrows, etc
- 116.
- 117. An example ofMultiple Alignment … immunoglobulin VTISCTGSSSNIGAG-NHVKWYQQLPG VTISCTGTSSNIGS--ITVNWYQQLPG LRLSCSSSGFIFSS--YAMYWVRQAPG LSLTCTVSGTSFDD--YYSTWVRQPPG PEVTCVVVDVSHEDPQVKFNWYVDG-- ATLVCLISDFYPGA--VTVAWKADS-- AALGCLVKDYFPEP--VTVSWNSG--- VSLTCLVKGFYPSD--IAVEWWSNG--
- 118. An example ofMultiple Alignment … immunoglobulin • Their alignment highlights conserved residues (one of the cysteines forming the disulphide bridges, and the tryptophan are notable) • conserved regions (in particular, "Q.PG" at the end of the first 4 sequences), and more sophisticated patterns, like the dominance of hydrophobic residues at fragment positions 1 and 3. • The alternating hydrophobicity pattern is typical for the surface beta-strand at the beginning of each fragment. Indeed, multiple alignments are helpful for protein structure prediction.
- 119. A Practical Approach:Interpretation • Providing the alignment is accurate then the following may be inferred about the secondary structure from a multiple sequence alignment. The position of insertions and deletions (INDELS) suggests regions where surface loops exist. Conserved glycine or proline suggests a beta-turn.
- 120. A Practical Approach:Interpretation • Residues with hydrophobic properties conserved at i, i+2, i+4 separated by unconserved or hydrophilic residues suggest surface beta- strands. A short run of hydrophobic amino acids (4 residues) suggests a buried beta-strand. Pairs of conserved hydrophobic amino acids separated by pairs of unconserved, or hydrophilic residues suggests an alfa-helix with one face packing in the protein core. Likewise, an i, i+3, i+4, i+7 pattern of conserved hydrophobic residues.
- 121. A Practical Approach:Which sequences to use ? • Take out noise (GAPS) • Extra information (structure - function) • Recursive selection – first most similar to have an idea about conserved regions – manual scan for these in more distant members then include these
- 122. Sequence Alignments Introduction Algorithms What ? Examples Properties Dynamic Programming for Pairwise Alignment Concept Example Needleman-Wunsch(.pl) Smith-Waterman(.pl) Multiple Alignment MSA Hierarchical Pairwise Alignent ClustalW, PileUp Formatting Interpretation Alternative Methods SIM Blast2 Dali
- 123. L-align (2 sequences) SIM (www.expasy.ch) LALNVIEW is available for UNIX, Mac and PC on the ExPASy anonymous FTP server. very nice TWEAKING tool (70% criteria)
- 124.
- 125.
- 126.
- 127. How can Iuse NCBI to compare two sequences? Answer: Use the “BLAST 2 Sequences” program
- 128. Practical guide topairwise alignment: the “BLAST 2 sequences” website • Go to http://www.ncbi.nlm.nih.gov/BLAST • Choose BLAST 2 sequences • In the program, [1] choose blastp (protein search) or blastn (for DNA) [2] paste in your accession numbers (or use FASTA format) [3] select optional parameters, such as --BLOSU62 matrix is default for proteins try PAM250 for distantly related proteins --gap creation and extension penalties [4] click “align”
- 131. Question #2: Howcan I use NCBI to compare a sequence to an entire database? BLAST!
- 134. • An introductionto Basic Concepts in Computer Science for Life Scientists • Dotplot patterns: A Literal Look at Pattern Languages
- 135. Practicum 3 •CpG Islands – Download from ENSEMBL 1000 (random) promoters (3000 bp) (hint: use Biomart) – How many times would you expect to observe CG if all nucleotides were equipropable – Count the number op times CG is observed for these 1000 genes and make a histogram from these scores. – Are there any other dinucleatides over- or underrepresented – CG repeats are often methylated. In order to study methylation patterns bisulfide treatment of DNA is used. Bisulfide changes every C which is not followed by G into T. Generate computationally the bisulfide treated version of DNA (hint: while (s/C([^G])/T$1/g) {};) – How would you find primers that discriminate between methylated and unmethylated DNA ? Given that the genome is 3.109 bp how long do you need to make a primer to avoid mispriming ?
- 136. Weblems W4.1: Alignthe amino acid sequence of acetylcholine receptor from human, rat, mouse, dog with ClustalW T-Coffee Dali MSA W4.2: Use BoxShade to create a word file indicating the different conserved resides in colours W4.3: Perform a LocalAlignent using SIM and Lalign on the same sequence and Blast2 W4.4: Do the different methods give different results, what are the default settings they use ? W4.5: How would you identify critical residues for catalytic activity ?