1. CSE 5290: Algorithms for Bioinformatics Fall 2011
Suprakash Datta
Office: CSEB 3043
Phone: ext 77875
Course page:
11/30/2018
CSE 5290, Fall 2011

2. Last time Graph algorithms for sequence assembly
Next: Pattern matching
The following slides are based on slides by the authors of our text.
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CSE 5290, Fall 2011

3. Genomic Repeats Example of repeats: ATGGTCTAGGTCCTAGTGGTC
Motivation to find them:
Genomic rearrangements are often associated with repeats
Trace evolutionary secrets
Many tumors are characterized by an explosion of repeats
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4. Genomic Repeats The problem is often more difficult:
ATGGTCTAGGACCTAGTGTTC
Motivation to find them:
Genomic rearrangements are often associated with repeats
Trace evolutionary secrets
Many tumors are characterized by an explosion of repeats
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5. l-mer Repeats Long repeats are difficult to find
Short repeats are easy to find (e.g., hashing)
Simple approach to finding long repeats:
Find exact repeats of short l-mers (l is usually 10 to 13)
Use l-mer repeats to potentially extend into longer, maximal repeats
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6. l-mer Repeats (cont’d)
There are typically many locations where an l-mer is repeated:
GCTTACAGATTCAGTCTTACAGATGGT
The 4-mer TTAC starts at locations 3 and 17
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7. Extending l-mer Repeats
GCTTACAGATTCAGTCTTACAGATGGT
Extend these 4-mer matches:
Maximal repeat: TTACAGAT
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8. Maximal Repeats
To find maximal repeats in this way, we need ALL start locations of all l-mers in the genome
Hashing lets us find repeats quickly in this manner
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9. Hashing: What is it? What does hashing do?
For different data, generate a unique integer
Store data in an array at the unique integer index generated from the data
Hashing is a very efficient way to store and retrieve data
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10. Hashing: Definitions Hash table: array used in hashing
Records: data stored in a hash table
Keys: identifies sets of records
Buckets:
Hash function: uses a key to generate an index (bucket) to insert at in hash table
Collision: when more than one record is mapped to the same index in the hash table
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11. When does hashing work well?
When there are few collisions!
Good hash functions minimize collisions
Problems
knowing what function to use
What buckets to use
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12. Hashing: Example Where do the animals eat? Records: each animal
Keys: where each animal eats
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13. Hashing DNA sequences
Each l-mer can be translated into a binary string (A, T, C, G can be represented as 00, 01, 10, 11)
After assigning a unique integer per l-mer it is easy to get all start locations of each l-mer in a genome
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14. Hashing: Maximal Repeats
To find repeats in a genome:
For all l-mers in the genome, note the start position and the sequence
Generate a hash table index for each unique l-mer sequence
In each index of the hash table, store all genome start locations of the l-mer which generated that index
Extend l-mer repeats to maximal repeats
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15. Hashing: Collisions Dealing with collisions:
“Chain” all start locations of l-mers (linked list)
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16. Hashing: Summary When finding genomic repeats from l-mers:
Generate a hash table index for each l-mer sequence
In each index, store all genome start locations of the l-mer which generated that index
Extend l-mer repeats to maximal repeats
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17. Pattern Matching
What if, instead of finding repeats in a genome, we want to find all sequences in a database that contain a given pattern?
This leads us to a different problem, the Pattern Matching Problem
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CSE 5290, Fall 2011

18. Pattern Matching Problem
Goal: Find all occurrences of a pattern in a text
Input: Pattern p = p1…pn and text t = t1…tm
Output: All positions 1< i < (m – n + 1) such that the n-letter substring of t starting at i matches p
Motivation: Searching database for a known pattern
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19. Exact Pattern Matching: A Brute-Force Algorithm
PatternMatching(p,t)
n  length of pattern p
m  length of text t
for i  1 to (m – n + 1)
if ti…ti+n-1 = p
output i
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CSE 5290, Fall 2011

20. Exact Pattern Matching: An Example
PatternMatching algorithm for:
Pattern GCAT
Text CGCATC
GCAT
CGCATC
GCAT
CGCATC
GCAT
CGCATC
GCAT
CGCATC
GCAT
CGCATC
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CSE 5290, Fall 2011

21. Exact Pattern Matching: Running Time
PatternMatching runtime: O(nm)
The average case is often O(m)
Rarely will there be close to n comparisons in line 4
Better solution: suffix trees
Can solve problem in O(m) time
Conceptually related to keyword trees
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22. Keyword Trees: Example
Apple
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23. Keyword Trees: Example (cont’d)
Apple
Apropos
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24. Keyword Trees: Example (cont’d)
Apple
Apropos
Banana
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25. Keyword Trees: Example (cont’d)
Apple
Apropos
Banana
Bandana
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26. Keyword Trees: Example (cont’d)
Apple
Apropos
Banana
Bandana
Orange
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27. Keyword Trees: Properties
-Stores a set of keywords in a rooted labeled tree
Each edge labeled with a letter from an alphabet
Any two edges coming out of the same vertex have distinct labels
Every keyword stored can be spelled on a path from root to some leaf
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28. Keyword Trees: Threading (cont’d)
Thread “appeal”
appeal
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29. Keyword Trees: Threading (cont’d)
Thread “appeal”
appeal
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30. Keyword Trees: Threading (cont’d)
Thread “appeal”
appeal
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31. Keyword Trees: Threading (cont’d)
Thread “appeal”
appeal
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32. Keyword Trees: Threading (cont’d)
Thread “apple”
apple
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33. Keyword Trees: Threading (cont’d)
Thread “apple”
apple
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34. Keyword Trees: Threading (cont’d)
Thread “apple”
apple
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35. Keyword Trees: Threading (cont’d)
Thread “apple”
apple
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36. Keyword Trees: Threading (cont’d)
Thread “apple”
apple
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37. Multiple Pattern Matching Problem
Goal: Given a set of patterns and a text, find all occurrences of any of patterns in text
Input: k patterns p1,…,pk, and text t = t1…tm
Output: Positions 1 < i < m where substring of t starting at i matches pj for 1 < j < k
Motivation: Searching database for known multiple patterns
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CSE 5290, Fall 2011

38. Multiple Pattern Matching: Straightforward Approach
Can solve as k “Pattern Matching Problems”
Runtime:
O(kmn)
using the PatternMatching algorithm k times
m - length of the text
n - average length of the pattern
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CSE 5290, Fall 2011

39. Multiple Pattern Matching: Keyword Tree Approach
Or, we could use keyword trees:
Build keyword tree in O(N) time; N is total length of all patterns
With naive threading: O(N + nm)
Aho-Corasick algorithm: O(N + m)
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40. Keyword Trees: Threading
To match patterns in a text using a keyword tree:
Build keyword tree of patterns
“Thread” the text through the keyword tree
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41. Keyword Trees: Threading (cont’d)
Threading is “complete” when we reach a leaf in the keyword tree
When threading is “complete,” we’ve found a pattern in the text
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CSE 5290, Fall 2011

42. Suffix Trees=Collapsed Keyword Trees
Similar to keyword trees, except edges that form paths are collapsed
Each edge is labeled with a substring of a text
All internal edges have at least two outgoing edges
Leaves labeled by the index of the pattern.
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43. Suffix Tree of a Text ATCATG TCATG CATG ATG TG G Keyword Tree
Suffix trees of a text is constructed for all its suffixes
ATCATG TCATG CATG ATG TG G
Keyword Tree
Suffix Tree
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CSE 5290, Fall 2011

44. Suffix Tree of a Text ATCATG TCATG CATG ATG TG G Keyword Tree
Suffix trees of a text is constructed for all its suffixes
ATCATG TCATG CATG ATG TG G
Keyword Tree
Suffix Tree
How much time does it take?
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CSE 5290, Fall 2011

45. Suffix Tree of a Text ATCATG TCATG CATG ATG TG G Keyword Tree
Suffix trees of a text is constructed for all its suffixes
ATCATG TCATG CATG ATG TG G
Keyword Tree
Suffix Tree
quadratic
Time is linear in the total size of all suffixes, i.e., it is quadratic in the length of the text
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46. Suffix Trees: Advantages
Suffix trees of a text is constructed for all its suffixes
Suffix trees build faster than keyword trees
ATCATG TCATG CATG ATG TG G
Keyword Tree
Suffix Tree
quadratic
linear (Weiner suffix tree algorithm)
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47. Use of Suffix Trees Suffix trees hold all suffixes of a text
i.e., ATCGC: ATCGC, TCGC, CGC, GC, C
Builds in O(m) time for text of length m
To find any pattern of length n in a text:
Build suffix tree for text
Thread the pattern through the suffix tree
Can find pattern in text in O(n) time!
O(n + m) time for “Pattern Matching Problem”
Build suffix tree and lookup pattern
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CSE 5290, Fall 2011

48. Pattern Matching with Suffix Trees
SuffixTreePatternMatching(p,t)
Build suffix tree for text t
Thread pattern p through suffix tree
if threading is complete
output positions of all p-matching leaves in the tree
else
output “Pattern does not appear in text”
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49. Suffix Trees: Example
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50. Multiple Pattern Matching: Summary
Keyword and suffix trees are used to find patterns in a text
Keyword trees:
Build keyword tree of patterns, and thread text through it
Suffix trees:
Build suffix tree of text, and thread patterns through it
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51. Approximate vs. Exact Pattern Matching
So far all we’ve seen exact pattern matching algorithms
Usually, because of mutations, it makes much more biological sense to find approximate pattern matches
Biologists often use fast heuristic approaches (rather than local alignment) to find approximate matches
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52. Heuristic Similarity Searches
Genomes are huge: Smith-Waterman quadratic alignment algorithms are too slow
Alignment of two sequences usually has short identical or highly similar fragments
Many heuristic methods (i.e., FASTA) are based on the same idea of filtration
Find short exact matches, and use them as seeds for potential match extension
“Filter” out positions with no extendable matches
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53. Dot Matrices Dot matrices show similarities between two sequences
FASTA makes an implicit dot matrix from short exact matches, and tries to find long diagonals (allowing for some mismatches)
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54. Dot Matrices (cont’d) Identify diagonals above a threshold length
Diagonals in the dot matrix indicate exact substring matching
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55. Diagonals in Dot Matrices
Extend diagonals and try to link them together, allowing for minimal mismatches/indels
Linking diagonals reveals approximate matches over longer substrings
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56. Approximate Pattern Matching Problem
Goal: Find all approximate occurrences of a pattern in a text
Input: A pattern p = p1…pn, text t = t1…tm, and k, the maximum number of mismatches
Output: All positions 1 < i < (m – n + 1) such that ti…ti+n-1 and p1…pn have at most k mismatches (i.e., Hamming distance between ti…ti+n-1 and p < k)
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CSE 5290, Fall 2011

57. Approximate Pattern Matching: A Brute-Force Algorithm
ApproximatePatternMatching(p, t, k)
n  length of pattern p
m  length of text t
for i  1 to m – n + 1
dist  0
for j  1 to n
if ti+j-1 != pj
dist  dist + 1
if dist < k
output i
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58. Approximate Pattern Matching: Running Time
That algorithm runs in O(nm).
Landau-Vishkin algorithm: O(kn)
We can generalize the “Approximate Pattern Matching Problem” into a “Query Matching Problem”:
We want to match substrings in a query to substrings in a text with at most k mismatches
Motivation: we want to see similarities to some gene, but we may not know which parts of the gene to look for
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59. Query Matching Problem
Goal: Find all substrings of the query that approximately match the text
Input: Query q = q1…qw,
text t = t1…tm,
n (length of matching substrings),
k (maximum number of mismatches)
Output: All pairs of positions (i, j) such that the
n-letter substring of q starting at i approximately matches the
n-letter substring of t starting at j,
with at most k mismatches
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60. Approximate Pattern Matching vs Query Matching
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61. Query Matching: Main Idea
Approximately matching strings share some perfectly matching substrings.
Instead of searching for approximately matching strings (difficult) search for perfectly matching substrings (easy).
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62. Filtration in Query Matching
We want all n-matches between a query and a text with up to k mismatches
“Filter” out positions we know do not match between text and query
Potential match detection: find all matches of l-tuples in query and text for some small l
Potential match verification: Verify each potential match by extending it to the left and right, until (k + 1) mismatches are found
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63. Filtration: Match Detection
If x1…xn and y1…yn match with at most k mismatches, they must share an l-tuple that is perfectly matched, with l = n/(k + 1)
Break string of length n into k+1 parts, each each of length n/(k + 1)
k mismatches can affect at most k of these k+1 parts
At least one of these k+1 parts is perfectly matched
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64. Filtration: Match Detection (cont’d)
Suppose k = 3. We would then have l=n/(k+1)=n/4:
There are at most k mismatches in n, so at the very least there must be one out of the k+1 l –tuples without a mismatch
1…l
l +1…2l
2l +1…3l
3l +1…n 1 2 k
k + 1
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65. Filtration: Match Verification
For each l -match we find, try to extend the match further to see if it is substantial
Extend perfect match of length l
until we find an approximate match of length n with k mismatches
query
text
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66. Filtration: Example Shorter perfect matches required
k = 0
k = 1
k = 2
k = 3
k = 4
k = 5
l -tuple
length n
n/2
n/3
n/4
n/5
n/6
Shorter perfect matches required
Performance decreases
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67. Local alignment is to slow…
Quadratic local alignment is too slow while looking for similarities between long strings (e.g. the entire GenBank database)
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68. Local alignment is to slow…
Quadratic local alignment is too slow while looking for similarities between long strings (e.g. the entire GenBank database)
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69. Local alignment is to slow…
Quadratic local alignment is too slow while looking for similarities between long strings (e.g. the entire GenBank database)
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70. Local alignment is to slow…
Quadratic local alignment is too slow while looking for similarities between long strings (e.g. the entire GenBank database)
Guaranteed to find the optimal local alignment
Sets the standard for sensitivity
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71. Local alignment is to slow…
Quadratic local alignment is too slow while looking for similarities between long strings (e.g. the entire GenBank database)
Basic Local Alignment Search Tool
Altschul, S., Gish, W., Miller, W., Myers, E. & Lipman, D.J.
Journal of Mol. Biol., 1990
Search sequence databases for local alignments to a query
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72. Next Pattern matching using BLAST
Some of the following slides are based on slides by the authors of our text.
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CSE 5290, Fall 2011

73. BLAST
Great improvement in speed, with a modest decrease in sensitivity
Minimizes search space instead of exploring entire search space between two sequences
Finds short exact matches (“seeds”), only explores locally around these “hits” 1.
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74. What Similarity Reveals
BLASTing a new gene
Evolutionary relationship
Similarity between protein function
BLASTing a genome
Potential genes
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75. BLAST algorithm
Keyword search of all words of length w from the query of length n in database of length m with score above threshold
w = 11 for DNA queries, w =3 for proteins
Local alignment extension for each found keyword
Extend result until longest match above threshold is achieved
Running time O(nm)
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76. BLAST algorithm (cont’d)
keyword
Query: KRHRKVLRDNIQGITKPAIRRLARRGGVKRISGLIYEETRGVLKIFLENVIRD
GVK 18
GAK 16
GIK 16
GGK 14
GLK 13
GNK 12
GRK 11
GEK 11
GDK 11
Neighborhood
words
neighborhood
score threshold
(T = 13)
extension
Query: 22 VLRDNIQGITKPAIRRLARRGGVKRISGLIYEETRGVLK 60
+++DN +G + IR L G+K I+ L+ E+ RG++K
Sbjct: 226 IIKDNGRGFSGKQIRNLNYGIGLKVIADLV-EKHRGIIK 263
High-scoring Pair (HSP)
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77. Original BLAST Dictionary All words of length w Alignment
Ungapped extensions until score falls below some statistical threshold
Output
All local alignments with score > threshold
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78. Original BLAST: Example
A C G A A G T A A G G T C C A G T
w = 4
Exact keyword match of GGTC
Extend diagonals with mismatches until score is under 50%
Output result
GTAAGGTCC
GTTAGGTCC
C T G A T C C T G G A T T G C G A
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From lectures by Serafim Batzoglou (Stanford)

79. Gapped BLAST : Example Original BLAST exact keyword search, THEN:
A C G A A G T A A G G T C C A G T
Original BLAST exact keyword search, THEN:
Extend with gaps around ends of exact match until score < threshold
Output result
GTAAGGTCCAGT
GTTAGGTC-AGT
C T G A T C C T G G A T T G C G A
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CSE 5290, Fall 2011
From lectures by Serafim Batzoglou (Stanford)

80. Assessing sequence similarity
Need to know how strong an alignment can be expected from chance alone
“Chance” relates to comparison of sequences that are generated randomly based upon a certain sequence model
Sequence models may take into account:
G+C content
“Junk” DNA
Codon bias
Etc.
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81. BLAST: Segment Score
BLAST uses scoring matrices (d) to improve on efficiency of match detection
Some proteins may have very different amino acid sequences, but are still similar
For any two l-mers x1…xl and y1…yl :
Segment pair: pair of l-mers, one from each sequence
Segment score: Sli=1 d(xi, yi)
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82. BLAST: Locally Maximal Segment Pairs
A segment pair is maximal if it has the best score over all segment pairs
A segment pair is locally maximal if its score can’t be improved by extending or shortening
Statistically significant locally maximal segment pairs are of biological interest
BLAST finds all locally maximal segment pairs with scores above some threshold
A significantly high threshold will filter out some statistically insignificant matches
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83. BLAST: Statistics Threshold: Altschul-Dembo-Karlin statistics
Identifies smallest segment score that is unlikely to happen by chance
# matches above q has mean E(q) = Kmne-lq; K is a constant, m and n are the lengths of the two compared sequences
Parameter l is positive root of:
S x,y in A(pxpyed(x,y)) = 1, where px and py are frequencies of amino acids x and y, and A is the twenty letter amino acid alphabet
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