1 / 76

Finding Motifs in DNA

Finding Motifs in DNA. References: 1. Bioinformatics Algorithms, Jones and Pevzner, Chapter 4. 2. Algorithms on Strings, Gusfield, Section 7.11. 3. Beginning Perl for Bioinformatics, Tisdall, Chapter 9. 4. Wikipedia. Summary. Introduce the Motif Finding Problem

Antony
Download Presentation

Finding Motifs in DNA

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Finding Motifs in DNA References: 1. Bioinformatics Algorithms, Jones and Pevzner, Chapter 4. 2. Algorithms on Strings, Gusfield, Section 7.11. 3. Beginning Perl for Bioinformatics, Tisdall, Chapter 9. 4. Wikipedia

  2. Summary • Introduce the Motif Finding Problem • Explain its significance in bioinformatics • Develop a simple model of the problem • Design algorithmic solutions: • Brute Force • Branch and Bound • Greedy • Compare results of each method.

  3. News: October 6, 2009 IBM Developing Chip to Sequence DNA DNA DNA DNA Gene Discovery May Advance Head and Neck Cancer Therapy DNA on bloody clothes matches missing US diplomat 3 Scientists Share Nobel Chemistry Prize for DNA Work S1P Gene Regulating Lipid May Help Develop New Drugs against Cancer Need a New Heart? Grow Your Own Updated map of human genome to help fight against disease

  4. The Motif Finding Problem • motif noun 1. a recurring subject, theme, idea, etc., esp. in a literary, artistic, or musical work. 2. a distinctive and recurring form, shape, figure, etc., in a design, as in a painting or on wallpaper. 3. a dominant idea or feature: the profit motif of free enterprise.

  5. Example: Fruit Fly • Set of immunity genes. • DNA pattern: TCGGGGATTTCC • Consistently appears upstream of this set of genes. • Regulates timing/magnitude of gene expression. • “Regulatory Motif” • Finding such patterns can be difficult.

  6. Construct an Example: 7 DNA Samples cacgtgaagcgactagctgtactattctgcat cgtccgatctcaggattgtctggggcgacgat gggggcggtgcgggagccagcgctcggcgttt gcaaggcgtcaaattgggaggcgcattctgaa ccacaagcgagcgttcctcgggattggtcacg aggtataatgcgaacagctaaaactccggaaa cccccgcaatttaactagggggcgcttagcgt Pattern acctggcc

  7. Insert Pattern at random locations: cacgtgaacctggccagcgactagctgtactattctgcat cgtccgatctcaggattgtctacctggccggggcgacgat gacctggccggggcggtgcgggagccagcgctcggcgttt gcaaggacctggcccgtcaaattgggaggcgcattctgaa ccacaagcgagcgttcctcgggattggacctggcctcacg aggtataatgcgaaacctggcccagctaaaactccggaaa cccccgcaaacctggcctttaactagggggcgcttagcgt

  8. Add Mutations: cacgtgaacGtggccagcgactagctgtactattctgcat cgtccgatctcaggattgtctacctgAccggggcgacgat gGcctggccggggcggtgcgggagccagcgctcggcgttt gcaaggacctggTccgtcaaattgggaggcgcattctgaa ccacaagcgagcgttcctcgggattggaActggcctcacg aggtataatgcgaaacctTgcccagctaaaactccggaaa cccccgcaaacTtggcctttaactagggggcgcttagcgt

  9. Finally, find the hidden pattern: cacgtgaacgtggccagcgactagctgtactattctgcat cgtccgatctcaggattgtctacctgaccggggcgacgat ggcctggccggggcggtgcgggagccagcgctcggcgttt gcaaggacctggtccgtcaaattgggaggcgcattctgaa ccacaagcgagcgttcctcgggattggaactggcctcacg aggtataatgcgaaaccttgcccagctaaaactccggaaa cccccgcaaacttggcctttaactagggggcgcttagcgt

  10. cacgtgaacgtggccagcgactagctgtactattctgcat cgtccgatctcaggattgtctacctgaccggggcgacgat ggcctggccggggcggtgcgggagccagcgctcggcgttt gcaaggacctggtccgtcaaattgggaggcgcattctgaa ccacaagcgagcgttcctcgggattggaactggcctcacg aggtataatgcgaaaccttgcccagctaaaactccggaaa cccccgcaaacttggcctttaactagggggcgcttagcgt

  11. Three Approachs • Brute Force: • check every possible pattern. • Branch and Bound: • prune away some of the search space. • Greedy: • commit to “nearby” options, never look back.

  12. Brute Force • Given that the pattern is of length = L. • Generate all DNA patterns of length L. • (Called “L-mers”). • Match each one to the DNA samples. • Keep the L-mer with the best match. • “Best” is Based on a scoring function.

  13. Scoring: Hamming Distance an L-mer gtgtaggt L=8 dna sequence gtgtaggt gtgtaggt gtgtaggt accgtaccggtaacaagtaccgtacgggtaacaagtaccgtaggtgtaacaagt 8 mismatches 4 mismatches 2 mismatches Try all starting positions Find the position with the fewest mismatches

  14. Scoring try all possible L-mers t = 8 DNA samples 3 2 1 0 3 2 0 1 total distance = 12 12 Try each possible L-mer Score is equal to the sum of the mismatches at the locations with fewest mismatches on each string. The L-mer with the lowest such score is the optimal answer.

  15. Generating all L-mers • Systematic enumeration of all DNA strings of length L. • DNA has an “alphabet” of 4 letters: { a, c, g, t } • Proteins have an alphabet of 20 letters: • one for each of 20 possible amino acids. • {A,B,C,D,E,F,G,H,I,K,L,M,N,P,Q,R,S,T,V,W} • Solve problem for any size alphabet (k) and any size L-mer (L).

  16. Definitions • k = size of alphabet • L = length of strings to be generated • a = vector containing a partial or complete L-mer. • i = number of entries in a already filled in. • Example: k = 4, L = 5, i = 2, a = (2, 4, *, * , * )

  17. ExampleAlphabet = {1, 2}k = 2, L=4 (2222) (1111) i = Depth of the Tree

  18. NEXT VERTEX i = 3 a = 1 3 2 NEXTVERTEX(a, i, L, k) if i < L a(i+1) = 1 return (a, i+1) else for j = L to j = 1 if a(j) < k then a(j) = a(j) +1 return(a, j) return (a,0) 1 i = 4 a = 1 3 2 1 i = L a = 2 3 2 1 2 2 i = L a = 2 3 2 1 2 3 j = 1 j = L

  19. Example: L = 6 k = 3 alhpabet = {1, 2, 3} When i = L (leaf node) ..... i = 6 2 3 2 1 23 i = 5 2 3 2 1 3 i = 6 2 3 2 1 3 1 i = 6 2 3 2 1 3 2 i = 6 2 3 2 1 3 3 i = 4 2 3 2 2 i = 5 2 3 2 2 1 i = 6 2 3 2 2 1 1 i = 6 2 3 2 2 1 2 i = 6 2 3 2 2 1 3 ..... 3 1 2 i = L-1 a = 2 3 2 1 3 3 1 1 2 i = L a = 2 3 2 1 3 1 i = L a = 2 3 2 1 23 j = 1 j = L

  20. Brute Force • Use NEXTVERTEX to generate nodes in the tree. • Translate each numeric value into the corresponding L-mer • (e.g.: 1=a, 2=c, 3=g, 4=t). • Score each L-mer (Hamming distance). • keep the best L-mer (and where it matched in each dna sample).

  21. Branch and Bound • Use same structure as the Brute Force method. • Looks for ways to reduce the computation. • Prune branches of the tree that cannot produce anything better than what we have so far.

  22. BYPASS • BYPASS (a, i, L, k) • for j = i to j = 1 • if a(j) < k • a(j) = a(j) + 1 • return (a, j) • return (a, 0)

  23. BRANCHANDBOUND • a = (1, 1, ..., 1) • bestDistance = infinity • i = L • while (i > 0) • if i < L • prefix = translate(a1, a2, ..., ai) • optimisticDistance = TotalDistance(prefix) • if optimisticDistance > bestDistance • (a, i) = BYPASS(a, i) • else • (a, i) = NEXTVERTEX( a, i ) • else • word = translate (a1, a2, ....., aL) • if TotalDistance( word, DNA ) < bestDistance • bestDistance = TotalDistance(word, DNA) • bestWord = word • (a, i) = NEXTVERTEX( a, i) • return bestWord

  24. Greedy Method • Picks a “good” solution. • Avoids backtracking. • Can give good results. • Generally, not the best possible solution. • But: FAST.

  25. Greedy Method • Given t dna samples (each n-long). • Find the optimal motif for the first two samples. • Lock that choice in place. • For the remainder of the samples: • for each dna sample in turn • find the L-mer that best fits with the prior choices. • never backtrack.

  26. t = 8 DNA samples Step 1: Grab the first two samples and find the optimal alignment (consider all starting points s1 and s2, and keep the largest score). Step 2: Go through each remaining sample, successively finding the starting positions (s3, s4, ...., st) that give the best consensus score for all the choices made so far.

  27. Alignment a t g c Profile a g g c a a c t Consensus 3 3 4 3 5 3 5 4 Scoring

  28. Motif Finding Example n=32 t=16 L=5 atgtgaaaaggcccaggctttgttgttctgat aatcagtttgtggctctctactatgtgcgctg catggcgtaagagcaggtgtacaccgatgctg taaatacacagattccttccgactttctgcat caagccttagctttagatctttgtctcccttt gagccatggactgtccgccagtatcttcctag cgccaactgcccgtttcgcagtgccatgttga agttcccagtcccgatcataggaatttgagca tagggatcgaatgagttgtcctagtcaatcct gtagctcctcaagggatacccacctatcgacg agccgcagcgacaacttgctcgctatctaact ccactccctaagcgctgaacaccggagttctg gaagtcttcttgctgacacattacttgctcgc gaatcgtcgtatgttttcgaccttggtggcat tctcaacatgccttcccctccccaggctatgc tgtgtctatcatcccgttagctacctaaatcg 5 16 32

  29. Branch and Bound Greedy atgtgaaaaggcccaggctttgttgttctgat ***** aatcagtttgtggctctctactatgtgcgctg ***** catggcgtaagagcaggtgtacaccgatgctg ***** taaatacacagattccttccgactttctgcat ***** caagccttagctttagatctttgtctcccttt ***** gagccatggactgtccgccagtatcttcctag ***** cgccaactgcccgtttcgcagtgccatgttga ***** agttcccagtcccgatcataggaatttgagca ***** tagggatcgaatgagttgtcctagtcaatcct ***** gtagctcctcaagggatacccacctatcgacg ***** agccgcagcgacaacttgctcgctatctaact ***** ccactccctaagcgctgaacaccggagttctg ***** gaagtcttcttgctgacacattacttgctcgc ***** gaatcgtcgtatgttttcgaccttggtggcat ***** tctcaacatgccttcccctccccaggctatgc ***** tgtgtctatcatcccgttagctacctaaatcg ***** atgtgaaaaggcccaggctttgttgttctgat ***** aatcagtttgtggctctctactatgtgcgctg ***** catggcgtaagagcaggtgtacaccgatgctg ***** taaatacacagattccttccgactttctgcat ***** caagccttagctttagatctttgtctcccttt ***** gagccatggactgtccgccagtatcttcctag ***** cgccaactgcccgtttcgcagtgccatgttga ***** agttcccagtcccgatcataggaatttgagca ***** tagggatcgaatgagttgtcctagtcaatcct ***** gtagctcctcaagggatacccacctatcgacg ***** agccgcagcgacaacttgctcgctatctaact ***** ccactccctaagcgctgaacaccggagttctg ***** gaagtcttcttgctgacacattacttgctcgc ***** gaatcgtcgtatgttttcgaccttggtggcat ***** tctcaacatgccttcccctccccaggctatgc ***** tgtgtctatcatcccgttagctacctaaatcg ***** consensus_string = ctccc consensus_count = 12 13 12 13 13 final percent score = 78.75 consensus_string = atgtg consensus_count = 14 10 11 12 10 final percent score = 71.25

  30. Branch and Bound Greedy ggccc ctctc caccg cttcc ctccc cttcc ctgcc ttccc gtcct ctcct ctcgc ctccc ctcgc cgacc ctccc atccc consensus_string = ctccc count = 12 13 12 13 13 final percent score = 78.75 atgtg atgtg aggtg ttctg atctt atgga atgtt atttg atgag aaggg acttg aagcg aagtc atgtt acatg gtgtc consensus_string = atgtg count = 14 10 11 12 10 final percent score = 71.25

  31. Example 2 n = 64 t = 16 L = 8 gattacttctcgcccccccgctaagtgtatttctctcgctacctactccgctatgcctacaaca tctaccggcattatctatcggcaatgggagcggtggtgatgcacctagcctactcctttgacta tggtccttactggcatcacgcaccgttcttggcggcctgtgcaatatcttgtccctaaataaat aactacggtcattagtgcgtaatcagcacagccgagccggataagcgacttgtaaccatcttcg gagcaagcatgcagtaggtaacgccaagagcggggctttagggagccgcaatcgggacagatct aaaggttctctggatctatagctcacaaatttgcaggggtacgacagagttatagagtgtacca ggcgctttcctcccgagcagagggaacgaacgaccataatgtaagagaatctttatgtccaagc cgtcctgtccatacgtatgttttcaaaactgcgtctagattagtgaggaacagatttaagattc atccagcaacttgtgcattcgtagggagcggacacaaaggacatgatcagacgaaacctatttt cctcaattgaggcccccccccagttgtccgaccgcacgaaccgcttcgcaaaagtgttgcccgc aaccacaccaagtattgctaatgcaccattcttatgtttttgagcagcaaagcgactacgctgt atataggaaaaatcttagtgcaccaagatttaacctgcactttgctttgaaatacaactgtcgg ctttcaataaatgttaattgcgttccctcacttgctcggtcgagtcgtatcgtattcgatcagg tagcgggcacgctcgctcgacgttcatccactcgatagagccggtcatttttcggaactagtaa ggaggaatgagtctacgtcgcgttaagacgaactttacgtgtgtgcaggcttattttcgtccac cctccgggggacgtagactgttcttccacagttctaggcggcgcggtcttggcttgaacaatga

  32. Branch and Bound Greedy gattacttctcgcccccccgctaagtgtatttctctcgctacctactccgctatgcctacaaca ******** tctaccggcattatctatcggcaatgggagcggtggtgatgcacctagcctactcctttgacta ******** tggtccttactggcatcacgcaccgttcttggcggcctgtgcaatatcttgtccctaaataaat ******** aactacggtcattagtgcgtaatcagcacagccgagccggataagcgacttgtaaccatcttcg ******** gagcaagcatgcagtaggtaacgccaagagcggggctttagggagccgcaatcgggacagatct ******** aaaggttctctggatctatagctcacaaatttgcaggggtacgacagagttatagagtgtacca ******** ggcgctttcctcccgagcagagggaacgaacgaccataatgtaagagaatctttatgtccaagc ******** cgtcctgtccatacgtatgttttcaaaactgcgtctagattagtgaggaacagatttaagattc ******** atccagcaacttgtgcattcgtagggagcggacacaaaggacatgatcagacgaaacctatttt ******** cctcaattgaggcccccccccagttgtccgaccgcacgaaccgcttcgcaaaagtgttgcccgc ******** aaccacaccaagtattgctaatgcaccattcttatgtttttgagcagcaaagcgactacgctgt ******** atataggaaaaatcttagtgcaccaagatttaacctgcactttgctttgaaatacaactgtcgg ******** ctttcaataaatgttaattgcgttccctcacttgctcggtcgagtcgtatcgtattcgatcagg ******** tagcgggcacgctcgctcgacgttcatccactcgatagagccggtcatttttcggaactagtaa ******** ggaggaatgagtctacgtcgcgttaagacgaactttacgtgtgtgcaggcttattttcgtccac ******** cctccgggggacgtagactgttcttccacagttctaggcggcgcggtcttggcttgaacaatga ******** gattacttctcgcccccccgctaagtgtatttctctcgctacctactccgctatgcctacaaca ******** tctaccggcattatctatcggcaatgggagcggtggtgatgcacctagcctactcctttgacta ******** tggtccttactggcatcacgcaccgttcttggcggcctgtgcaatatcttgtccctaaataaat ******** aactacggtcattagtgcgtaatcagcacagccgagccggataagcgacttgtaaccatcttcg ******** gagcaagcatgcagtaggtaacgccaagagcggggctttagggagccgcaatcgggacagatct ******** aaaggttctctggatctatagctcacaaatttgcaggggtacgacagagttatagagtgtacca ******** ggcgctttcctcccgagcagagggaacgaacgaccataatgtaagagaatctttatgtccaagc ******** cgtcctgtccatacgtatgttttcaaaactgcgtctagattagtgaggaacagatttaagattc ******** atccagcaacttgtgcattcgtagggagcggacacaaaggacatgatcagacgaaacctatttt ******** cctcaattgaggcccccccccagttgtccgaccgcacgaaccgcttcgcaaaagtgttgcccgc ******** aaccacaccaagtattgctaatgcaccattcttatgtttttgagcagcaaagcgactacgctgt ******** atataggaaaaatcttagtgcaccaagatttaacctgcactttgctttgaaatacaactgtcgg ******** ctttcaataaatgttaattgcgttccctcacttgctcggtcgagtcgtatcgtattcgatcagg ******** tagcgggcacgctcgctcgacgttcatccactcgatagagccggtcatttttcggaactagtaa ******** ggaggaatgagtctacgtcgcgttaagacgaactttacgtgtgtgcaggcttattttcgtccac ******** cctccgggggacgtagactgttcttccacagttctaggcggcgcggtcttggcttgaacaatga ******** consensus_string = ccatattt count = 10 11 11 11 13 10 11 14 final percent score = 71.09375 consensus_string = cgtactcc count = 11 10 13 11 10 12 10 8 final percent score = 66.40625

  33. Summary • Introduce the Motif Finding Problem • Explain its significance in bioinformatics • Develop a simple model of the problem • Design algorithmic solutions: • Brute Force • Branch and Bound • Greedy • Compare results of each method.

  34. Teaching and Learning

  35. Neural Networks for Optimization Bill Wolfe California State University Channel Islands Reference A Fuzzy Hopfield-Tank TSP Model Wolfe, W. J. INFORMS Journal on Computing, Vol. 11, No. 4, Fall 1999 pp. 329-344

  36. Neural Models • Simple processing units • Lots of them • Highly interconnected • Exchange excitatory and inhibitory signals • Variety of connection architectures/strengths • “Learning”: changes in connection strengths • “Knowledge”: connection architecture • No central processor: distributed processing

  37. Simple Neural Model • aiActivation • ei External input • wij Connection Strength Assume: wij = wji (“symmetric” network) W = (wij) is a symmetric matrix

  38. Net Input Vector Format:

  39. Dynamics • Basic idea:

  40. Energy

  41. Lower Energy • da/dt = net = -grad(E)  seeks lower energy

  42. Problem: Divergence

  43. A Fix: Saturation

  44. Keeps the activation vector inside the hypercube boundaries Encourages convergence to corners

  45. A Neural Model aiActivation eiExternal Input wijConnection Strength W (wij = wji) Symmetric

  46. Example: Inhibitory Networks • Completely inhibitory • wij = -1 for all i,j • winner take all • Inhibitory Grid • neighborhood inhibition • on-center, off-surround

More Related