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Finding Regulatory Motifs in DNA Sequences

Finding Regulatory Motifs in DNA Sequences. Outline. Implanting Patterns in Random Text Gene Regulation Regulatory Motifs The Gold Bug Problem The Motif Finding Problem Brute Force Motif Finding The Median String Problem Search Trees Branch-and-Bound Motif Search

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Finding Regulatory Motifs in DNA Sequences

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  1. Finding Regulatory Motifs in DNA Sequences

  2. Outline • Implanting Patterns in Random Text • Gene Regulation • Regulatory Motifs • The Gold Bug Problem • The Motif Finding Problem • Brute Force Motif Finding • The Median String Problem • Search Trees • Branch-and-Bound Motif Search • Branch-and-Bound Median String Search • Consensus and Pattern Branching: Greedy Motif Search

  3. Outline • PMS: Exhaustive Motif Search

  4. Random Sample atgaccgggatactgataccgtatttggcctaggcgtacacattagataaacgtatgaagtacgttagactcggcgccgccgacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaatactgggcataaggtacatgagtatccctgggatgacttttgggaacactatagtgctctcccgatttttgaatatgtaggatcattcgccagggtccgagctgagaattggatgaccttgtaagtgttttccacgcaatcgcgaaccaacgcggacccaaaggcaagaccgataaaggagatcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaatggcccacttagtccacttataggtcaatcatgttcttgtgaatggatttttaactgagggcatagaccgcttggcgcacccaaattcagtgtgggcgagcgcaacggttttggcccttgttagaggcccccgtactgatggaaactttcaattatgagagagctaatctatcgcgtgcgtgttcataacttgagttggtttcgaaaatgctctggggcacatacaagaggagtcttccttatcagttaatgctgtatgacactatgtattggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatttcaacgtatgccgaaccgaaagggaagctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcttctgggtactgatagca

  5. Implanting Motif AAAAAAAGGGGGGG atgaccgggatactgatAAAAAAAAGGGGGGGggcgtacacattagataaacgtatgaagtacgttagactcggcgccgccgacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaataAAAAAAAAGGGGGGGatgagtatccctgggatgacttAAAAAAAAGGGGGGGtgctctcccgatttttgaatatgtaggatcattcgccagggtccgagctgagaattggatgAAAAAAAAGGGGGGGtccacgcaatcgcgaaccaacgcggacccaaaggcaagaccgataaaggagatcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaatAAAAAAAAGGGGGGGcttataggtcaatcatgttcttgtgaatggatttAAAAAAAAGGGGGGGgaccgcttggcgcacccaaattcagtgtgggcgagcgcaacggttttggcccttgttagaggcccccgtAAAAAAAAGGGGGGGcaattatgagagagctaatctatcgcgtgcgtgttcataacttgagttAAAAAAAAGGGGGGGctggggcacatacaagaggagtcttccttatcagttaatgctgtatgacactatgtattggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatAAAAAAAAGGGGGGGaccgaaagggaagctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcttAAAAAAAAGGGGGGGa

  6. Where is the Implanted Motif? atgaccgggatactgataaaaaaaagggggggggcgtacacattagataaacgtatgaagtacgttagactcggcgccgccgacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaataaaaaaaaagggggggatgagtatccctgggatgacttaaaaaaaagggggggtgctctcccgatttttgaatatgtaggatcattcgccagggtccgagctgagaattggatgaaaaaaaagggggggtccacgcaatcgcgaaccaacgcggacccaaaggcaagaccgataaaggagatcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaataaaaaaaagggggggcttataggtcaatcatgttcttgtgaatggatttaaaaaaaaggggggggaccgcttggcgcacccaaattcagtgtgggcgagcgcaacggttttggcccttgttagaggcccccgtaaaaaaaagggggggcaattatgagagagctaatctatcgcgtgcgtgttcataacttgagttaaaaaaaagggggggctggggcacatacaagaggagtcttccttatcagttaatgctgtatgacactatgtattggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcataaaaaaaagggggggaccgaaagggaagctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcttaaaaaaaaggggggga

  7. ImplantingAAAAAAGGGGGGG with 4 Mutations atgaccgggatactgatAgAAgAAAGGttGGGggcgtacacattagataaacgtatgaagtacgttagactcggcgccgccgacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaatacAAtAAAAcGGcGGGatgagtatccctgggatgacttAAAAtAAtGGaGtGGtgctctcccgatttttgaatatgtaggatcattcgccagggtccgagctgagaattggatgcAAAAAAAGGGattGtccacgcaatcgcgaaccaacgcggacccaaaggcaagaccgataaaggagatcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaatAtAAtAAAGGaaGGGcttataggtcaatcatgttcttgtgaatggatttAAcAAtAAGGGctGGgaccgcttggcgcacccaaattcagtgtgggcgagcgcaacggttttggcccttgttagaggcccccgtAtAAAcAAGGaGGGccaattatgagagagctaatctatcgcgtgcgtgttcataacttgagttAAAAAAtAGGGaGccctggggcacatacaagaggagtcttccttatcagttaatgctgtatgacactatgtattggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatActAAAAAGGaGcGGaccgaaagggaagctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcttActAAAAAGGaGcGGa

  8. Now Where is the Motif? atgaccgggatactgatagaagaaaggttgggggcgtacacattagataaacgtatgaagtacgttagactcggcgccgccgacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaatacaataaaacggcgggatgagtatccctgggatgacttaaaataatggagtggtgctctcccgatttttgaatatgtaggatcattcgccagggtccgagctgagaattggatgcaaaaaaagggattgtccacgcaatcgcgaaccaacgcggacccaaaggcaagaccgataaaggagatcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaatataataaaggaagggcttataggtcaatcatgttcttgtgaatggatttaacaataagggctgggaccgcttggcgcacccaaattcagtgtgggcgagcgcaacggttttggcccttgttagaggcccccgtataaacaaggagggccaattatgagagagctaatctatcgcgtgcgtgttcataacttgagttaaaaaatagggagccctggggcacatacaagaggagtcttccttatcagttaatgctgtatgacactatgtattggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatactaaaaaggagcggaccgaaagggaagctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcttactaaaaaggagcgga

  9. Why Finding the Hidden Motif is Difficult atgaccgggatactgatAgAAgAAAGGttGGGggcgtacacattagataaacgtatgaagtacgttagactcggcgccgccgacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaatacAAtAAAAcGGcGGGatgagtatccctgggatgacttAAAAtAAtGGaGtGGtgctctcccgatttttgaatatgtaggatcattcgccagggtccgagctgagaattggatgcAAAAAAAGGGattGtccacgcaatcgcgaaccaacgcggacccaaaggcaagaccgataaaggagatcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaatAtAAtAAAGGaaGGGcttataggtcaatcatgttcttgtgaatggatttAAcAAtAAGGGctGGgaccgcttggcgcacccaaattcagtgtgggcgagcgcaacggttttggcccttgttagaggcccccgtAtAAAcAAGGaGGGccaattatgagagagctaatctatcgcgtgcgtgttcataacttgagttAAAAAAtAGGGaGccctggggcacatacaagaggagtcttccttatcagttaatgctgtatgacactatgtattggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatActAAAAAGGaGcGGaccgaaagggaagctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcttActAAAAAGGaGcGGa AgAAgAAAGGttGGG ..|..|||.|..||| cAAtAAAAcGGcGGG

  10. Challenge Problem • Find a motif in a sample of 20 “random” sequences (e.g. 600 nucleotides long). • Each sequence contains an implanted pattern of length 15. • Each pattern appears with 4 mismatches. • More generally, an (n, k) motif is a pattern of length n which appears with k mismatches within a DNA sequence. • So our challenge problem is to find a (15,4) motif in a group of 20 sequences.

  11. Why (15,4)-motif is hard to find? • Goal: recover original pattern Pfrom its (unknown!) instances: P1 , P2 , … , P20 • Problem: Although P and Pi are similar for each i(4 mutations for a (15,4) motif), given two different instances Pi and Pj, they may differ twice as much (4 + 4 = 8 mutations for a (15,4) motif). • Conclusions: • Pairwisesimiliarities are misleading. • Multiple similarities are difficult to find.

  12. Combinatorial Gene Regulation • A microarray experiment showed that when gene X is knocked out, 20 other genes are not expressed. • Motivating Question: How can one gene have such drastic effects? DNA Microarray

  13. Regulatory Proteins • Answer: Gene X encodes regulatory protein, a.k.a. a transcription factor (TF). • The 20 unexpressed genes rely on gene X’s TF to induce transcription. • A single TF may regulate multiple genes.

  14. Regulatory Regions • Every gene contains a regulatory region (RR) typically stretching 100-1000 bp upstream of the transcriptional start site. • Located within the RR are the Transcription Factor Binding Sites(TFBS), also known as motifs, which are specific for a given transcription factor. • TFs influence gene expression by binding to a specific TFBS. • A TFBS can be located anywhere within the regulatory region. • TFBS may vary slightly across different regulatory regions since non-essential bases could mutate.

  15. Transcription Factors and Motifs: Example ATCCCG gene TTCCGG gene ATCCCG gene gene ATGCCG gene ATGCCC

  16. Transcription Factors and Motifs: Illustration http://www.cs.uiuc.edu/homes/sinhas/work.html

  17. Motif Logos • Motifs can mutate on unimportant bases. • The five motifs in five different genes have mutations in position 3 and 5. • Representations called motif logos illustrate the conserved and variable regions of a motif. • At right is an example of a motif logo. TGGGGGA TGAGAGA TGGGGGA TGAGAGA TGAGGGA

  18. Motif Logos: An Additional Example (http://www-lmmb.ncifcrf.gov/~toms/sequencelogo.html)

  19. Identifying Motifs • Recall that a TFBS is represented by a motif. • Therefore finding similar motifs in multiple genes’ regulatory regions suggests a regulatory relationship among those genes.

  20. Identifying Motifs: Complications • We do not know the motif sequence in advance. • We do not know where the motif is located relative to the genes’ start. • As we have seen, a motif can differ slightly from one gene to the next. • How do we discern a motif with a real pattern from “random” motifs that don’t represent real correlation between genes?

  21. Detour: A Motif Finding Analogy • The Motif Finding Problem is similar to the problem posed by Edgar Allan Poe (1809 – 1849) in his short story “The Gold Bug.”

  22. The Gold Bug Problem • “Here Legrand, having re-heated the parchment, submitted it to my inspection. The following characters were rudely traced, in a red tint, between the death's head and the goat:” 53++!305))6*;4826)4+.)4+);806*;48!8`60))85;]8*:+*8!83(88)5*!; 46(;88*96*?;8)*+(;485);5*!2:*+(;4956*2(5*-4)8`8*; 4069285);)6 !8)4++;1(+9;48081;8:8+1;48!85;4)485!528806*81(+9;48;(88;4(+?3 4;48)4+;161;:188;+?; • Legrand’s Goal: Decipher the message on the parchment.

  23. Gold Bug Problem: Assumptions • The encrypted message is in English • Each symbol corresponds to one letter in the English alphabet • Conversely, no letter corresponds to more than one symbol • No punctuation marks are encoded

  24. Gold Bug Problem: Naïve Approach • Count the frequency of each symbol in the encrypted message • Find the frequency of each letter in the alphabet in the English language • Compare the frequencies of the previous steps, try to find a correlation and map the symbols to a letter in the alphabet

  25. Gold Bug Problem: Symbol Frequencies • Gold Bug Message: • English Language: e t a o i n s r h l d c u m f p g w y b v k x j q z Most frequentLeast frequent

  26. Gold Bug Problem: Symbol Frequencies • Result of using symbol frequencies: sfiilfcsoorntaeuroaikoaiotecrntaeleyrcooestvenpinelefheeosnlt arhteenmrnwteonihtaesotsnlupnihtamsrnuhsnbaoeyentacrmuesotorl eoaiitdhimtaecedtepeidtaelestaoaeslsueecrnedhimtaetheetahiwfa taeoaitdrdtpdeetiwt • The result does not make sense. • Therefore, we must use some other method to decode the message.

  27. Gold Bug Problem: l-tuple count • A better approach is to examine the frequencies of l-tuples, which are subsequences of 2 symbols, 3 symbols, etc. • “The” is the most frequent 3-tuple in English and “;48” is the most frequent 3-tuple in the encrypted text. • We make inferences of unknown symbols by examining other frequent l-tuples.

  28. Gold Bug Problem: l-tuple count • Mapping “the” to “;48” and substituting all occurrences of the symbols: 53++!305))6*the26)h+.)h+)te06*the!e`60))e5t]e*:+*e!e3(ee)5*!t h6(tee*96*?te)*+(the5)t5*!2:*+(th956*2(5*h)e`e*th0692e5)t)6!e )h++t1(+9the0e1te:e+1the!e5th)he5!52ee06*e1(+9thet(eeth(+?3ht he)h+t161t:1eet+?t

  29. The Gold Bug Message Decoding: Second Attempt • Make inferences: 53++!305))6*the26)h+.)h+)te06*the!e`60))e5t]e*:+*e!e3(ee)5*!t h6(tee*96*?te)*+(the5)t5*!2:*+(th956*2(5*h)e`e*th0692e5)t)6!e )h++t1(+9the0e1te:e+1the!e5th)he5!52ee06*e1(+9thet(eeth(+?3ht he)h+t161t:1eet+?t

  30. The Gold Bug Message Decoding: Second Attempt • Make inferences: 53++!305))6*the26)h+.)h+)te06*the!e`60))e5t]e*:+*e!e3(ee)5*!t h6(tee*96*?te)*+(the5)t5*!2:*+(th956*2(5*h)e`e*th0692e5)t)6!e )h++t1(+9the0e1te:e+1the!e5th)he5!52ee06*e1(+9thet(eeth(+?3ht he)h+t161t:1eet+?t • “thet(ee” most likely means “the tree” • Infer “(“ = “r”

  31. The Gold Bug Message Decoding: Second Attempt • Make inferences: 53++!305))6*the26)h+.)h+)te06*the!e`60))e5t]e*:+*e!e3(ee)5*!t h6(tee*96*?te)*+(the5)t5*!2:*+(th956*2(5*h)e`e*th0692e5)t)6!e )h++t1(+9the0e1te:e+1the!e5th)he5!52ee06*e1(+9thet(eeth(+?3ht he)h+t161t:1eet+?t • “thet(ee” most likely means “the tree” • Infer “(“ = “r” • “th(+?3h” becomes “thr+?3h” • Can we guess “+” and “?”?

  32. Gold Bug Problem: Solution • Using inferences like these to figure out all the mappings, the final message is: AGOODGLASSINTHEBISHOPSHOSTELINTHEDEVILSSEATWENYONEDEGRE ESANDTHIRTEENMINUTESNORTHEASTANDBYNORTHMAINBRANCHSEVENT HLIMBEASTSIDESHOOTFROMTHELEFTEYEOFTHEDEATHSHEADABEELINE FROMTHETREETHROUGHTHESHOTFIFTYFEETOUT

  33. Gold Bug Problem: Solution • Using inferences like these to figure out all the mappings, the final message is: AGOODGLASSINTHEBISHOPSHOSTELINTHEDEVILSSEATWENYONEDEGRE ESANDTHIRTEENMINUTESNORTHEASTANDBYNORTHMAINBRANCHSEVENT HLIMBEASTSIDESHOOTFROMTHELEFTEYEOFTHEDEATHSHEADABEELINE FROMTHETREETHROUGHTHESHOTFIFTYFEETOUT • Punctuation is important: A GOOD GLASS IN THE BISHOP’S HOSTEL IN THE DEVIL’S SEA, TWENTY ONE DEGREES AND THIRTEEN MINUTES NORTHEAST AND BY NORTH, MAIN BRANCH SEVENTH LIMB, EAST SIDE, SHOOT FROM THE LEFT EYE OF THE DEATH’S HEAD A BEE LINE FROM THE TREE THROUGH THE SHOT, FIFTY FEET OUT.

  34. Gold Bug Problem: Prerequisites • There are two prerequisites that we need to solve the gold bug problem: • We need to know the relative frequencies of single letters, as well as the frequencies of 2-tuples and 3-tuples in English. • We also need to know all the words in the English language.

  35. Gold Bug Problem and Motif Finding: Similarities Motif Finding: • Nucleotides in motifs encode for a message in the “genetic” language. • In order to solve the problem, we analyze the frequencies of patterns in the nucleotide sequences • Knowledge of established regulatory motifs is helpful. Gold Bug Problem: • Symbols in “The Gold Bug” encode for a message in English. • In order to solve the problem, we analyze the frequencies of patterns in the text written in English • Knowledge of the words in the English language is helpful.

  36. Gold Bug Problem and Motif Finding: Similarities Motif Finding: • Nucleotides in motifs encode for a message in the “genetic” language. • In order to solve the problem, we analyze the frequencies of patterns in the nucleotide sequences. • Knowledge of established regulatory motifs is helpful. Gold Bug Problem: • Symbols in “The Gold Bug” encode for a message in English. • In order to solve the problem, we analyze the frequencies of patterns in the text written in English. • Knowledge of the words in the English language is helpful.

  37. Gold Bug Problem and Motif Finding: Similarities Motif Finding: • Nucleotides in motifs encode for a message in the “genetic” language. • In order to solve the problem, we analyze the frequencies of patterns in the nucleotide sequences. • Knowledge of established regulatory motifs is helpful. Gold Bug Problem: • Symbols in “The Gold Bug” encode for a message in English. • In order to solve the problem, we analyze the frequencies of patterns in the text written in English. • Knowledge of the words in the English language is helpful.

  38. Gold Bug Problem and Motif Finding: Differences • Motif Finding is more difficult than the Gold Bug problem: • We don’t have the complete dictionary of motifs. • The “genetic” language does not have a standard “grammar.” • Only a small fraction of nucleotide sequences encode for motifs; the size of the data is enormous.

  39. The Motif Finding Problem: Informal Statement • Given a random sample of DNA sequences: cctgatagacgctatctggctatccacgtacgtaggtcctctgtgcgaatctatgcgtttccaaccat agtactggtgtacatttgatacgtacgtacaccggcaacctgaaacaaacgctcagaaccagaagtgc aaacgtacgtgcaccctctttcttcgtggctctggccaacgagggctgatgtataagacgaaaatttt agcctccgatgtaagtcatagctgtaactattacctgccacccctattacatcttacgtacgtataca ctgttatacaacgcgtcatggcggggtatgcgttttggtcgtcgtacgctcgatcgttaacgtacgtc • Find the pattern that is implanted in each of the individual sequences, namely, the motif.

  40. The Motif Finding Problem: Additional Info • The hidden sequence is of length 8. • The pattern is not necessarily the same in each array because random mutations (substitutions) may occur in the sequences, as we have seen.

  41. The Motif Finding Problem • The patterns revealed with no mutations: cctgatagacgctatctggctatccacgtacgtaggtcctctgtgcgaatctatgcgtttccaaccat agtactggtgtacatttgatacgtacgtacaccggcaacctgaaacaaacgctcagaaccagaagtgc aaacgtacgtgcaccctctttcttcgtggctctggccaacgagggctgatgtataagacgaaaatttt agcctccgatgtaagtcatagctgtaactattacctgccacccctattacatcttacgtacgtataca ctgttatacaacgcgtcatggcggggtatgcgttttggtcgtcgtacgctcgatcgttaacgtacgtc acgtacgt Consensus String

  42. The Motif Finding Problem • The patterns with 2 point mutations: cctgatagacgctatctggctatccaGgtacTtaggtcctctgtgcgaatctatgcgtttccaaccat agtactggtgtacatttgatCcAtacgtacaccggcaacctgaaacaaacgctcagaaccagaagtgc aaacgtTAgtgcaccctctttcttcgtggctctggccaacgagggctgatgtataagacgaaaatttt agcctccgatgtaagtcatagctgtaactattacctgccacccctattacatcttacgtCcAtataca ctgttatacaacgcgtcatggcggggtatgcgttttggtcgtcgtacgctcgatcgttaCcgtacgGc

  43. The Motif Finding Problem • The patterns with 2-point mutations: cctgatagacgctatctggctatccaGgtacTtaggtcctctgtgcgaatctatgcgtttccaaccat agtactggtgtacatttgatCcAtacgtacaccggcaacctgaaacaaacgctcagaaccagaagtgc aaacgtTAgtgcaccctctttcttcgtggctctggccaacgagggctgatgtataagacgaaaatttt agcctccgatgtaagtcatagctgtaactattacctgccacccctattacatcttacgtCcAtataca ctgttatacaacgcgtcatggcggggtatgcgttttggtcgtcgtacgctcgatcgttaCcgtacgGc • Can we still find the motif now?

  44. Defining Motifs • To define a motif, lets say we know where the motif starts in the sequence. • The motif start positions in their sequences can be represented as s = (s1,s2,s3,…,st).

  45. Motifs: Profiles and Consensus a G g t a c T t C c A t a c g t Alignment a c g t T A g t a c g t C c A t C c g t a c g G _________________ A3 0 1 0 31 1 0 ProfileC24 0 0 14 0 0 G 0 1 4 0 0 0 31 T 0 0 0 5 1 0 14 _________________ Consensus A C G T A C G T • Line up the patterns by their start indexes s = (s1, s2, …, st) • Construct profile matrix with frequencies of each nucleotide in columns • Consensus nucleotide in each position has the highest score in column

  46. Consensus String • Think of the consensus string as an “ancestor” motif, from which mutated motifs emerged • The distance between a real motif and the consensus sequence is generally less than the distance between two real motifs

  47. Consensus String

  48. Evaluating Motifs • We have a guess about the consensus sequence, but how “good” is this consensus? • We need to introduce a scoring function to compare different consensus strings. • Keep in mind that we really want to choose is the starting positions, but since the consensus is obtained from an array of starting positions, we will determine how to compare consensus strings and then work backward to choosing starting positions.

  49. Parameters: Definitions • t - number of sample DNA sequences • n - length of each DNA sequence • DNA - sample of DNA sequences (stored as a t x n array) • l - length of the motif (l-mer) • si - starting position of an l-mer in sequence i • s=(s1, s2,… st) - array of motif’s starting positions

  50. Parameters: Example cctgatagacgctatctggctatccaGgtacTtaggtcctctgtgcgaatctatgcgtttccaaccat agtactggtgtacatttgatCcAtacgtacaccggcaacctgaaacaaacgctcagaaccagaagtgc aaacgtTAgtgcaccctctttcttcgtggctctggccaacgagggctgatgtataagacgaaaatttt agcctccgatgtaagtcatagctgtaactattacctgccacccctattacatcttacgtCcAtataca ctgttatacaacgcgtcatggcggggtatgcgttttggtcgtcgtacgctcgatcgttaCcgtacgGc l= 8 (length of the motif) DNA t=5 n = 69 s s1 = 26s2 = 21s3= 3 s4 = 56s5 = 60 (starting positions)

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