1. CS 5263 Bioinformatics Motif finding

2. What is a (biological) motif? A motif is a recurring fragment, theme or pattern Sequence motif: a sequence pattern of nucleotides in a DNA sequence or amino acids in a protein Structural motif: a pattern in a protein structure formed by the spatial arrangement of amino acids. Network motif: patterns that occur in different parts of a network at frequencies much higher than those found in randomized network Commonality: –higher frequency than would be expected by chance –Has, or is conjectured to have, a biological significance

3. Sequence motif finding Given: a set of sequences Goal: find sequence motifs that appear in all or the majority of the sequences, and are likely associated with some functions –In DNA: regulatory sequences Other names: transcription factor binding sites, transcription factor binding motifs, cis-regulatory elements, cis-regulatory motifs, DNA motifs, etc. –In protein: functional/structural domains

4. Roadmap Biological background Representation of motifs Algorithms for finding motifs Other issues –Search for instances of given motifs –Distinguish functional vs non-functional motifs

5. Biological background for motif finding

6. Genome is fixed – Cells are dynamic A genome is static –(almost) Every cell in our body has a copy of the same genome A cell is dynamic –Responds to internal/external conditions –Most cells follow a cell cycle of division –Cells differentiate during development

7. Gene regulation … is responsible for the dynamic cell Gene expression (production of protein) varies according to: –Cell type –Cell cycle –External conditions –Location –Etc.

8. Where gene regulation takes place Opening of chromatin Transcription Translation Protein stability Protein modifications

9. GenePromoter RNA polymerase (Protein) Transcription Factor (TF) (Protein) DNA Transcriptional Regulation of genes

10. Gene TF binding site, cis-regulatory element RNA polymerase (Protein) Transcription Factor (TF) (Protein) DNA Transcriptional Regulation of genes

11. Gene RNA polymerase Transcription Factor (Protein) DNA TF binding site, cis-regulatory element

12. Gene RNA polymerase Transcription Factor DNA New protein Transcriptional Regulation of genes TF binding site, cis-regulatory element

13. The Cell as a Regulatory Network ABMake DC If C then D If B then NOT D If A and B then D D Make BD If D then B C gene D gene B

14. Transcription Factors Binding to DNA Transcriptional regulation: Transcription factors bind to DNA Binding recognizes specific DNA substrings: Regulatory motifs

15. Experimental methods DNase footprinting –Tedious –Time-consuming High-throughput techniques: ChIP-chip, ChIP- seq –Expensive –Other limitations

16. Computational methods for finding cis-regulatory motifs Given a collection of genes that are believed to be regulated by the same/similar protein –Co-expressed genes –Evolutionarily conserved genes Find the common TF-binding motif from promoters......

17. Essentially a Multiple Local Alignment Find “best” multiple local alignment Multidimensional Dynamic Programming? –Heuristics must be used...... instance

18. Characteristics of cis-Regulatory Motifs Tiny (6-12bp) Intergenic regions are very long Highly Variable ~Constant Size –Because a constant-size transcription factor binds Often repeated Often conserved

19. Motif representation Collection of exact words –{ACGTTAC, ACGCTAC, AGGTGAC, …} Consensus sequence (with wild cards) –{AcGTgTtAC} –{ASGTKTKAC} S=C/G, K=G/T (IUPAC code) Position-specific weight matrices (PWM)

20. Position-Specific Weight Matrix 123456789 A.97.10.02.03.10.01.05.85.03 C.01.40.01.04.05.01.05.03 G.01.40.95.03.40.01.3.05.03 T.01.10.02.90.45.97.6.05.91 ASGTKTKA C

21. Sequence Logo frequency 123456789 A.97.10.02.03.10.01.05.85.03 C.01.40.01.04.05.01.05.03 G.01.40.95.03.40.01.3.05.03 T.01.10.02.90.45.97.6.05.91 http://weblogo.berkeley.edu/ http://biodev.hgen.pitt.edu/cgi-bin/enologos/enologos.cgi

22. Sequence Logo 123456789 A.97.10.02.03.10.01.05.85.03 C.01.40.01.04.05.01.05.03 G.01.40.95.03.40.01.3.05.03 T.01.10.02.90.45.97.6.05.91 http://weblogo.berkeley.edu/ http://biodev.hgen.pitt.edu/cgi-bin/enologos/enologos.cgi

23. Entropy and information content Entropy: a measure of uncertainty The entropy of a random variable X that can assume the n different values x 1, x 2,..., x n with the respective probabilities p 1, p 2,..., p n is defined as

24. Entropy and information content Example: A,C,G,T with equal probability  H = 4 * (-0.25 log 2 0.25) = log 2 4 = 2 bits  Need 2 bits to encode (e.g. 00 = A, 01 = C, 10 = G, 11 = T)  Maximum uncertainty 50% A and 50% C:  H = 2 * (-0. 5 log 2 0.5) = log 2 2 = 1 bit 100% A  H = 1 * (-1 log 2 1) = 0 bit  Minimum uncertainty Information: the opposite of uncertainty  I = maximum uncertainty – entropy  The above examples provide 0, 1, and 2 bits of information, respectively

25. Entropy and information content 123456789 A.97.10.02.03.10.01.05.85.03 C.01.40.01.04.05.01.05.03 G.01.40.95.03.40.01.3.05.03 T.01.10.02.90.45.97.6.05.91 H.241.72.36.631.600.241.400.850.58 I1.760.281.641.370.401.760.601.151.42 Mean 1.15 Total 10.4 Expected occurrence in random DNA: 1 / 2 10.4 = 1 / 1340 Expected occurrence of an exact 5-mer: 1 / 2 10 = 1 / 1024

26. Sequence Logo 123456789 A.97.10.02.03.10.01.05.85.03 C.01.40.01.04.05.01.05.03 G.01.40.95.03.40.01.3.05.03 T.01.10.02.90.45.97.6.05.91 I 1.760.281.641.370.401.760.601.151.42

27. Real example E. coli. Promoter “TATA-Box” ~ 10bp upstream of transcription start TACGAT TAAAAT TATACT GATAAT TATGAT TATGTT Consensus: TATAAT Note: none of the instances matches the consensus perfectly

28. Finding Motifs

29. Motif finding schemes Genome 1Genome 2 Gene set 1Gene set 2 Conservation YesNo Whole genome YesGenome 1 & 2 & 3Genome 1 NoGene 1A & 1B & 1C or Gene Set 1 & 2 & 3 Gene Set 1 Genome 3 Gene set 3 1A1B1C Phylogenetic footprinting Dictionary building “Motif finding” Ideally, all information should be used, at some stage. i.e., inside algorithm vs pre- or post-processing.

30. Classification of approaches Combinatorial algorithms –Based on enumeration of words and computing word similarities Probabilistic algorithms –Construct probabilistic models to distinguish motifs vs non-motifs

31. Combinatorial motif finding Idea 1: find all k-mers that appeared at least m times –m may be chosen such that # occurrence is statistically significant –Problem: most motifs have divergence. Each variation may only appear once. Idea 2: find all k-mers, considering IUPAC nucleic acid codes –e.g. ASGTKTKAC, S = C/G, K = G/T –Still inflexible Idea 3: find k-mers that approximately appeared at least m times –i.e. allow some mismatches

32. Combinatorial motif finding Given a set of sequences S = {x 1, …, x n } A motif W is a consensus string w 1 …w K Find motif W * with “best” match to x 1, …, x n Definition of “best”: d(W, x i ) = min hamming dist. between W and a word in x i d(W, S) =  i d(W, x i ) W* = argmin( d(W, S) )

33. Exhaustive searches 1. Pattern-driven algorithm: For W = AA…A to TT…T (4 K possibilities) Find d( W, S ) Report W* = argmin( d(W, S) ) Running time: O( K N 4 K ) (where N =  i |x i |) Guaranteed to find the optimal solution.

34. Exhaustive searches 2. Sample-driven algorithm: For W = a K-char word in some x i Find d( W, S ) Report W* = argmin( d( W, S ) ) OR Report a local improvement of W * Running time: O( K N 2 )

35. Exhaustive searches Problem with sample-driven approach: If: –True motif does not occur in data, and –True motif is “weak” Then, –random strings may score better than any instance of true motif

36. Example E. coli. Promoter “TATA-Box” ~ 10bp upstream of transcription start TACGAT TAAAAT TATACT GATAAT TATGAT TATGTT Consensus: TATAAT Each instance differs at most 2 bases from the consensus None of the instances matches the consensus perfectly

37. Heuristic methods Cannot afford exhaustive search on all patterns Sample-driven approaches may miss real patterns However, a real pattern should not differ too much from its instances in S Start from the space of all words in S, extend to the space with real patterns

38. Some of the popular tools Consensus (Hertz & Stormo, 1999) WINNOWER (Pevzner & Sze, 2000) MULTIPROFILER (Keich & Pevzner, 2002) PROJECTION (Buhler & Tompa, 2001) WEEDER (Pavesi et. al. 2001) And dozens of others

39. Consensus Algorithm: Cycle 1: For each word W in S For each word W’ in S Create alignment (gap free) of W, W’ Keep the C 1 best alignments, A 1, …, A C1 ACGGTTG,CGAACTT,GGGCTCT … ACGCCTG,AGAACTA,GGGGTGT …

40. Algorithm (cont’d): Cycle i: For each word W in S For each alignment A j from cycle i-1 Create alignment (gap free) of W, A j Keep the C i best alignments A 1, …, A Ci

41. C 1, …, C n are user-defined heuristic constants Running time: O(kN 2 ) + O(kN C 1 ) + O(kN C 2 ) + … + O(kN C n ) = O(kN 2 + kNC total ) Where C total =  i C i, typically O(nC), where C is a big constant

42. Extended sample-driven (ESD) approaches Hybrid between pattern-driven and sample-driven Assume each instance does not differ by more than α bases to the motif (  usually depends on k) motif instance  The real motif will reside in the  - neighborhood of some words in S. Instead of searching all 4 K patterns, we can search the  -neighborhood of every word in S. α-neighborhood

43. Extended sample-driven (ESD) approaches Naïve: N K α 3 α NK # of patterns to test# of words in sequences

44. Better idea Using a joint suffix tree, find all patterns that: –Have length K –Appeared in at least m sequences with at most α mismatches Post-processing

45. WEEDER: algorithm sketch A list containing all eligible nodes: with at most α mismatches to P For each node, remember #mismatches accumulated (e  α ), and a bit vector (B) for seq occ, e.g. [011100010] Bit OR all B’s to get seq occurrence for P Suppose #occ >= m –Pattern still valid Now add a letter ACGTTACGTT Current pattern P, |P| < K (e, B) # mismatches Seq occ

46. WEEDER: algorithm sketch Simple extension: no branches. –No change to B –e may increase by 1 or no change –Drop node if e > α Branches: replace a node with its child nodes –Drop if e > α –B may change Re-do Bit OR using all B’s Try a different char if #occ < m Report P when |P| = K ACGTTAACGTTA Current pattern P (e, B)

47. WEEDER: complexity Can get all patterns in time O(Nn(K choose α) 3 α ) ~ O(N nK α 3 α ). n: # sequences. Needed for Bit OR. Better than O(KN 4 K ) and O(N K α 3 α NK) since usually α << K K α 3 α may still be expensive for large K –E.g. K = 20, α = 6

48. WEEDER: More tricks Eligible nodes: with at most α mismatches to P Eligible nodes: with at most min(  L, α) mismatches to P –L: current pattern length –  : error ratio –Require that mismatches to be somewhat evenly distributed among positions Prune tree at length K ACGTTAACGTTA Current pattern P

49. Probabilistic modeling approaches for motif finding

50. Probabilistic modeling approaches A motif model –Usually a PWM –M = (P ij ), i = 1..4, j = 1..k, k: motif length A background model –Usually the distribution of base frequencies in the genome (or other selected subsets of sequences) –B = (b i ), i = 1..4 A word can be generated by M or B

51. Expectation-Maximization For any word W,  P(W | M) = P W[1] 1 P W[2] 2 …P W[K] K  P(W | B) = b W[1] b W[2] …b W[K] Let = P(M), i.e., the probability for any word to be generated by M. Then P(B) = 1 - Can compute the posterior probability P(M|W) and P(B|W)  P(M|W) ~ P(W|M) *  P(B|W) ~ P(W|B) * (1- )

52. Expectation-Maximization Initialize: Randomly assign each word to M or B Let Z xy = 1 if position y in sequence x is a motif, and 0 otherwise Estimate parameters M,, B Iterate until converge: E-step: Z xy = P(M | X[y..y+k-1]) for all x and y M-step: re-estimate M, given Z (B usually fixed)

53. Expectation-Maximization E-step: Z xy = P(M | X[y..y+k-1]) for all x and y M-step: re-estimate M, given Z Initialize E-step M-step probability position 1 9 5 1 9 5

54. MEME Multiple EM for Motif Elicitation Bailey and Elkan, UCSD http://meme.sdsc.edu/ Multiple starting points Multiple modes: ZOOPS, OOPS, TCM

55. Gibbs Sampling Another very useful technique for estimating missing parameters EM is deterministic –Often trapped by local optima Gibbs sampling: stochastic behavior to avoid local optima

56. Gibbs Sampling Initialize: Randomly assign each word to M or B Let Z xy = 1 if position y in sequence x is a motif, and 0 otherwise Estimate parameters M, B, Iterate: Randomly remove a sequence X* from S Recalculate model parameters using S \ X* Compute Z x*y for X* Sample a y* from Z x*y. Let Z x*y = 1 for y = y* and 0 otherwise

57. Gibbs Sampling Gibbs sampling: sample one position according to probability –Update prediction of one training sequence at a time Viterbi: always take the highest EM: take weighted average Sampling Simultaneously update predictions of all sequences position probability

58. Better background model Repeat DNA can be confused as motif –Especially low-complexity CACACA… AAAAA, etc. Solution: more elaborate background model –Higher-order Markov model 0 th order: B = { p A, p C, p G, p T } 1 st order: B = { P(A|A), P(A|C), …, P(T|T) } … K th order: B = { P(X | b 1 …b K ); X, b i  {A,C,G,T} } Has been applied to EM and Gibbs (up to 3 rd order)

59. Gibbs sampling motif finders Gibbs Sampler –First appeared as: Larence et.al. Science 262(5131):208-214. –Continually developed and updated. webpagewebpage –The newest version: Thompson et. al. Nucleic Acids Res. 35 (s2):W232- W237 AlignACE –Hughes et al., J. of Mol Bio, 2000 10;296(5):1205-14.Hughes et al., J. of Mol Bio, 2000 10;296(5):1205-14. –Allow don’t care positions –Additional tools to scan motifs on new seqs, and to compare and group motifs BioProspector, X. Liu et. al. PSB 2001, an improvement of AlignACE –Liu, Brutlag and Liu. Pac Symp Biocomput. 2001;:127-38.Liu, Brutlag and Liu. Pac Symp Biocomput. 2001;:127-38 –Allow two-block motifs –Consider higher-order markov models

60. Limits of Motif Finders Given upstream regions of coregulated genes: –Increasing length makes motif finding harder – random motifs clutter the true ones –Decreasing length makes motif finding harder – true motif missing in some sequences 0 gene ???

61. Challenging problem (k, d)-motif challenge problem Many algorithms fail at (15, 4)-motif for n = 20 and L = 600 Combinatorial algorithms usually work better on challenge problem –However, they are usually designed to find (k, d)-motifs –Performance in real data varies k d mutations n = 20 L = 600

62. (15, 4)-motif Information content: 11.7 bits ~ 6mers. Expected occurrence 1 per 3k bp

63. Actual Results by MEME llr = 163 E-value = 3.2e+005 llr = 177 E-value = 1.5e+006 llr = 88 E-value = 2.5e+005

64. Motif finding in practice Where the input come from? Possibility 1: microarray studies (later) Possibility 2: phylogenetic analysis (not covered) Possibility 3: ChIP-chip Possibility 4: ChIP-seq

65. Chromatin Immunoprecipitation (ChIP) ChIP is a method to investigate protein-DNA interaction in vivo. The output of ChIP is enriched fragments of DNA that were bound by a particular protein. The identity of DNA fragments need to be further determined by a second method.

66. ChIPSeq Workflow ChIP Size Selection Sequencing Mapping onto Genome

67. ChIP-chip Array of intergenic sequences from the whole genome ChIP

68. How to make sense of the motifs? Each program usually reports a number of motifs (tens to hundreds) –Many motifs are variations of each other –Each program also report some different ones Each program has its own way of scoring motifs –Best scored motifs often not interesting –AAAAAAAA –ACACACAC –TATATATAT

69. How to make sense of the motifs? Now we’ve found some pretty-looking motifs –This is probably the easiest step What to do next? –Are they real? –How do we find more instances in the rest of the genome? –What are their functional meaning? Motifs => regulatory networks

70. How to make sense of the motifs? Combine results from different algorithms usually helpful –Ones that appeared multiple times are probably more interesting Except simple repeats like AAAAA or ATATATATA –Cluster motifs into groups. Compare with known motifs in database –TRANSFAC –JASPAR –YPD (yeast promoter database)

71. Strategies to improve results How to tell real motifs (functional) from noises? Statistical test of significance. –Enrichment in target sequences vs background sequences Target set T Background set B Assumed to contain a common motif, P Assumed to not contain P, or with very low frequency Ideal case: every sequence in T has P, no sequence in B has P

72. Statistical test for significance If n / N >> m / M –P is enriched (over-represented) in T –Statistical significance? If we randomly draw N sequences from (B+T), how likely we will see at least n sequences having P? Target set T Background set + target set B + T N M P P appeared in n sequences P appeared in m sequences

73. Hypergeometric distribution A box with M balls (seqs), of which m are red (with motifs), and the rest are blue (without motifs). –Red ball: sequences with motifs –Blue ball: sequences without motifs We randomly draw N balls (seqs) from the box What’s the probability we’ll see n red balls? # of choices to have n red balls Total # of choices to draw N balls

74. Cumulative hypergeometric test for motif significance We are interested in: if we randomly pick m balls, how likely that we’ll see at least n red balls? Null hypothesis: our selection is random. Alternative hypothesis: our selection favored red balls. When prob is small, we reject the null hypothesis. Equivalent: we accept the alternative hypothesis (The number of red balls is larger than expected).

75. Example Yeast genome has 6000 genes Select 50 genes believed to be co-regulated by a common TF Found a motif from the promoter seqs of these 50 genes The motif appears in 20 of these 50 genes In the rest of the genome, 100 genes have this motif M = 6000, N = 50, m = 100+20 = 120, n = 20 Intuitively: –m/M = 120/6000=1/50. (1 out 50 genes has the motif) –N = 50, would expect only 1 gene in the target set to have the motif –20-fold enrichment P-value = cHyperGeom(20; 6000, 50, 120) = 6 x 10 -22 This motif is significantly enriched in the set of genes

76. ROC curve for motif significance Motif is usually a PWM Any word will have a score –Typical scoring function: Log (P(W | M) / P(W | B)) –W: a word. –M: a PWM. –B: background model To determine whether motif M occurred in a sequence, a cutoff has to be decided –Different cutoffs give different # of occurrences –Stringent cutoff: low occurrence in both + and - sequences –Loose cutoff: high occurrence in both + and - sequences –It may be better to look at a range of cutoffs

77. ROC curve for motif significance With different score cutoff, will have different m and n Assume you want to use P to classify T and B Sensitivity: n / N Specificity: (M-N-m+n) / (M-N) False Positive Rate = 1 – specificity: (m – n) / (M-N) With decreasing cutoff, sensitivity , FPR  Target set T Background set + target set B + T N M P Appeared in n sequences Appeared in m sequences Given a score cutoff

78. ROC curve for motif significance ROC-AUC: area under curve. 1: the best. 0.5: random. Motif 1 is more enriched in motif 2. 1-specificity sensitivity Motif 1 Motif 2 Random A good cutoff Highest cutoff. No motif can pass the cutoff. Sensitivity = 0. specificity = 1. Lowest cutoff. Every sequence has the motif. Sensitivity = 1. specificity = 0. 0 1 10

79. Other strategies Cross-validation –Randomly divide sequences into 10 sets, hold 1 set for test. –Do motif finding on 9 sets. Does the motif also appear in the testing set? Phylogenetic conservation information –Does a motif also appears in the homologous genes of another species? –Strongest evidence –However, will not be able to find species-specific ones

80. Other strategies Finding motif modules –Will two motifs always appear in the same gene? Location preference –Some motifs appear to be in certain location E.g., within 50-150bp upstream to transcription start –If a detected motif has strong positional bias, may be a sign of its function Evidence from other types of data sources –Do the genes having the motif always have similar activities (gene expression levels) across different conditions? –Interact with the same set of proteins? –Similar functions? –etc.

81. To search for new instances Usually many false positives Score cutoff is critical Can estimate a score cutoff from the “true” binding sites Motif finding Scoring function A set of scores for the “true” sites. Take mean - std as a cutoff. (or a cutoff such that the majority of “true” sites can be predicted). Log (P(W | M) / P(W | B))

82. To search for new instances Use other information, such as positional biases of motifs to restrict the regions that a motif may appear Use gene expression data to help: the genes having the true motif should have similar activities –Risk of circular reasoning: most likely this is how you get the initial sequences to do motif finding Phylogenetic conservation is the key

83. References D’haeseleer P (2006) What are DNA sequence motifs? NATURE BIOTECHNOLOGY, 24 (4):423-425 D’haeseleer P (2006) How does DNA sequence motif discovery work? NATURE BIOTECHNOLOGY, 24 (8):959-961 MacIsaac KD, Fraenkel E (2006) Practical strategies for discovering regulatory DNA sequence motifs. PLoS Comput Biol 2(4): e36 Lawrence CE et. al. (1993) Detecting Subtle Sequence Signals: A Gibbs Sampling Strategy for Multiple Alignment, Science, 262(5131):208-214