1. CS262 Lecture 17, Win07, Batzoglou Gene Regulation and Microarrays

2. CS262 Lecture 17, Win07, Batzoglou Overview A. Gene Expression and Regulation B. Measuring Gene Expression: Microarrays C. Finding Regulatory Motifs

3. CS262 Lecture 17, Win07, Batzoglou Cells respond to environment Cell responds to environment— various external messages

4. CS262 Lecture 17, Win07, Batzoglou Genome is fixed – Cells are dynamic A genome is static  Every cell in our body has a copy of same genome A cell is dynamic  Responds to external conditions  Most cells follow a cell cycle of division Cells differentiate during development Gene expression varies according to:  Cell type  Cell cycle  External conditions  Location slide credits: M. Kellis

5. CS262 Lecture 17, Win07, Batzoglou Where gene regulation takes place Opening of chromatin Transcription Translation Protein stability Protein modifications

6. CS262 Lecture 17, Win07, Batzoglou Transcriptional Regulation Efficient place to regulate: No energy wasted making intermediate products However, slowest response time After a receptor notices a change: 1.Cascade message to nucleus 2.Open chromatin & bind transcription factors 3.Recruit RNA polymerase and transcribe 4.Splice mRNA and send to cytoplasm 5.Translate into protein

7. CS262 Lecture 17, Win07, Batzoglou Transcription Factors Binding to DNA Transcription regulation: Transcription factors bind DNA Binding recognizes DNA substrings: Regulatory motifs

8. CS262 Lecture 17, Win07, Batzoglou Promoter and Enhancers Promoter necessary to start transcription Enhancers can affect transcription from afar

9. CS262 Lecture 17, Win07, Batzoglou Transcription Factor (Protein) DNA Gene Regulation with TFs Regulatory Element Gene RNA polymerase

10. CS262 Lecture 17, Win07, Batzoglou Gene RNA polymerase Transcription Factor (Protein) Regulatory Element DNA Gene Regulation with TFs

11. CS262 Lecture 17, Win07, Batzoglou DNA New protein Gene Regulation with TFs Transcription Factor (Protein) Regulatory Element Gene RNA polymerase

12. TTATATTGAATTTTCAAAAATTCTTACTTTTTTTTTGGATGGACGCAAAGAAGTTTAATAATCATATTACATGGCATTACCACCATATA CATATCCATATCTAATCTTACTTATATGTTGTGGAAATGTAAAGAGCCCCATTATCTTAGCCTAAAAAAACCTTCTCTTTGGAACTTTC AGTAATACGCTTAACTGCTCATTGCTATATTGAAGTACGGATTAGAAGCCGCCGAGCGGGCGACAGCCCTCCGACGGAAGACTCTCCTC CGTGCGTCCTCGTCTTCACCGGTCGCGTTCCTGAAACGCAGATGTGCCTCGCGCCGCACTGCTCCGAACAATAAAGATTCTACAATACT AGCTTTTATGGTTATGAAGAGGAAAAATTGGCAGTAACCTGGCCCCACAAACCTTCAAATTAACGAATCAAATTAACAACCATAGGATG ATAATGCGATTAGTTTTTTAGCCTTATTTCTGGGGTAATTAATCAGCGAAGCGATGATTTTTGATCTATTAACAGATATATAAATGGAA AAGCTGCATAACCACTTTAACTAATACTTTCAACATTTTCAGTTTGTATTACTTCTTATTCAAATGTCATAAAAGTATCAACAAAAAAT TGTTAATATACCTCTATACTTTAACGTCAAGGAGAAAAAACTATAATGACTAAATCTCATTCAGAAGAAGTGATTGTACCTGAGTTCAA TTCTAGCGCAAAGGAATTACCAAGACCATTGGCCGAAAAGTGCCCGAGCATAATTAAGAAATTTATAAGCGCTTATGATGCTAAACCGG ATTTTGTTGCTAGATCGCCTGGTAGAGTCAATCTAATTGGTGAACATATTGATTATTGTGACTTCTCGGTTTTACCTTTAGCTATTGAT TTTGATATGCTTTGCGCCGTCAAAGTTTTGAACGATGAGATTTCAAGTCTTAAAGCTATATCAGAGGGCTAAGCATGTGTATTCTGAAT CTTTAAGAGTCTTGAAGGCTGTGAAATTAATGACTACAGCGAGCTTTACTGCCGACGAAGACTTTTTCAAGCAATTTGGTGCCTTGATG AACGAGTCTCAAGCTTCTTGCGATAAACTTTACGAATGTTCTTGTCCAGAGATTGACAAAATTTGTTCCATTGCTTTGTCAAATGGATC ATATGGTTCCCGTTTGACCGGAGCTGGCTGGGGTGGTTGTACTGTTCACTTGGTTCCAGGGGGCCCAAATGGCAACATAGAAAAGGTAA AAGAAGCCCTTGCCAATGAGTTCTACAAGGTCAAGTACCCTAAGATCACTGATGCTGAGCTAGAAAATGCTATCATCGTCTCTAAACCA GCATTGGGCAGCTGTCTATATGAATTAGTCAAGTATACTTCTTTTTTTTACTTTGTTCAGAACAACTTCTCATTTTTTTCTACTCATAA CTTTAGCATCACAAAATACGCAATAATAACGAGTAGTAACACTTTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGA TAATGTTTTCAATGTAAGAGATTTCGATTATCCACAAACTTTAAAACACAGGGACAAAATTCTTGATATGCTTTCAACCGCTGCGTTTT GGATACCTATTCTTGACATGATATGACTACCATTTTGTTATTGTACGTGGGGCAGTTGACGTCTTATCATATGTCAAAG...TTGCGAA GTTCTTGGCAAGTTGCCAACTGACGAGATGCAGTAACACTTTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAA TGTTTTCAATGTAAGAGATTTCGATTATCCACAAACTTTAAAACACAGGGACAAAATTCTTGATATGCTTTCAACCGCTGCGTTTTGGA TACCTATTCTTGACATGATATGACTACCATTTTGTTATTGTACGTGGGGCAGTTGACGTCTTATCATATGTCAAAGTCATTTGCGAAGT TCTTGGCAAGTTGCCAACTGACGAGATGCAGTTTCCTACGCATAATAAGAATAGGAGGGAATATCAAGCCAGACAATCTATCATTACAT TTAAGCGGCTCTTCAAAAAGATTGAACTCTCGCCAACTTATGGAATCTTCCAATGAGACCTTTGCGCCAAATAATGTGGATTTGGAAAA AGAGTATAAGTCATCTCAGAGTAATATAACTACCGAAGTTTATGAGGCATCGAGCTTTGAAGAAAAAGTAAGCTCAGAAAAACCTCAAT ACAGCTCATTCTGGAAGAAAATCTATTATGAATATGTGGTCGTTGACAAATCAATCTTGGGTGTTTCTATTCTGGATTCATTTATGTAC AACCAGGACTTGAAGCCCGTCGAAAAAGAAAGGCGGGTTTGGTCCTGGTACAATTATTGTTACTTCTGGCTTGCTGAATGTTTCAATAT CAACACTTGGCAAATTGCAGCTACAGGTCTACAACTGGGTCTAAATTGGTGGCAGTGTTGGATAACAATTTGGATTGGGTACGGTTTCG TTGGTGCTTTTGTTGTTTTGGCCTCTAGAGTTGGATCTGCTTATCATTTGTCATTCCCTATATCATCTAGAGCATCATTCGGTATTTTC TTCTCTTTATGGCCCGTTATTAACAGAGTCGTCATGGCCATCGTTTGGTATAGTGTCCAAGCTTATATTGCGGCAACTCCCGTATCATT AATGCTGAAATCTATCTTTGGAAAAGATTTACAATGATTGTACGTGGGGCAGTTGACGTCTTATCATATGTCAAAGTCATTTGCGAAGT TCTTGGCAAGTTGCCAACTGACGAGATGCAGTAACACTTTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATG TTTTCAATGTAAGAGATTTCGATTATCCACAAACTTTAAAACACAGGGACAAAATTCTTGATATGCTTTCAACCGCTGCGTTTTGGATA CCTATTCTTGACATGATATGACTACCATTTTGTTATTGTTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATG TTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTA AGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGA TTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATA GTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATG CTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACT TAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGAT TGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAAT

13. TTATATTGAATTTTCAAAAATTCTTACTTTTTTTTTGGATGGACGCAAAGAAGTTTAATAATCATATTACATGGCATTACCACCATATA CATATCCATATCTAATCTTACTTATATGTTGTGGAAATGTAAAGAGCCCCATTATCTTAGCCTAAAAAAACCTTCTCTTTGGAACTTTC AGTAATACGCTTAACTGCTCATTGCTATATTGAAGTACGGATTAGAAGCCGCCGAGCGGGCGACAGCCCTCCGACGGAAGACTCTCCTC CGTGCGTCCTCGTCTTCACCGGTCGCGTTCCTGAAACGCAGATGTGCCTCGCGCCGCACTGCTCCGAACAATAAAGATTCTACAATACT AGCTTTTATGGTTATGAAGAGGAAAAATTGGCAGTAACCTGGCCCCACAAACCTTCAAATTAACGAATCAAATTAACAACCATAGGATG ATAATGCGATTAGTTTTTTAGCCTTATTTCTGGGGTAATTAATCAGCGAAGCGATGATTTTTGATCTATTAACAGATATATAAATGGAA AAGCTGCATAACCACTTTAACTAATACTTTCAACATTTTCAGTTTGTATTACTTCTTATTCAAATGTCATAAAAGTATCAACAAAAAAT TGTTAATATACCTCTATACTTTAACGTCAAGGAGAAAAAACTATAATGACTAAATCTCATTCAGAAGAAGTGATTGTACCTGAGTTCAA TTCTAGCGCAAAGGAATTACCAAGACCATTGGCCGAAAAGTGCCCGAGCATAATTAAGAAATTTATAAGCGCTTATGATGCTAAACCGG ATTTTGTTGCTAGATCGCCTGGTAGAGTCAATCTAATTGGTGAACATATTGATTATTGTGACTTCTCGGTTTTACCTTTAGCTATTGAT TTTGATATGCTTTGCGCCGTCAAAGTTTTGAACGATGAGATTTCAAGTCTTAAAGCTATATCAGAGGGCTAAGCATGTGTATTCTGAAT CTTTAAGAGTCTTGAAGGCTGTGAAATTAATGACTACAGCGAGCTTTACTGCCGACGAAGACTTTTTCAAGCAATTTGGTGCCTTGATG AACGAGTCTCAAGCTTCTTGCGATAAACTTTACGAATGTTCTTGTCCAGAGATTGACAAAATTTGTTCCATTGCTTTGTCAAATGGATC ATATGGTTCCCGTTTGACCGGAGCTGGCTGGGGTGGTTGTACTGTTCACTTGGTTCCAGGGGGCCCAAATGGCAACATAGAAAAGGTAA AAGAAGCCCTTGCCAATGAGTTCTACAAGGTCAAGTACCCTAAGATCACTGATGCTGAGCTAGAAAATGCTATCATCGTCTCTAAACCA GCATTGGGCAGCTGTCTATATGAATTAGTCAAGTATACTTCTTTTTTTTACTTTGTTCAGAACAACTTCTCATTTTTTTCTACTCATAA CTTTAGCATCACAAAATACGCAATAATAACGAGTAGTAACACTTTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGA TAATGTTTTCAATGTAAGAGATTTCGATTATCCACAAACTTTAAAACACAGGGACAAAATTCTTGATATGCTTTCAACCGCTGCGTTTT GGATACCTATTCTTGACATGATATGACTACCATTTTGTTATTGTACGTGGGGCAGTTGACGTCTTATCATATGTCAAAG...TTGCGAA GTTCTTGGCAAGTTGCCAACTGACGAGATGCAGTAACACTTTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAA TGTTTTCAATGTAAGAGATTTCGATTATCCACAAACTTTAAAACACAGGGACAAAATTCTTGATATGCTTTCAACCGCTGCGTTTTGGA TACCTATTCTTGACATGATATGACTACCATTTTGTTATTGTACGTGGGGCAGTTGACGTCTTATCATATGTCAAAGTCATTTGCGAAGT TCTTGGCAAGTTGCCAACTGACGAGATGCAGTTTCCTACGCATAATAAGAATAGGAGGGAATATCAAGCCAGACAATCTATCATTACAT TTAAGCGGCTCTTCAAAAAGATTGAACTCTCGCCAACTTATGGAATCTTCCAATGAGACCTTTGCGCCAAATAATGTGGATTTGGAAAA AGAGTATAAGTCATCTCAGAGTAATATAACTACCGAAGTTTATGAGGCATCGAGCTTTGAAGAAAAAGTAAGCTCAGAAAAACCTCAAT ACAGCTCATTCTGGAAGAAAATCTATTATGAATATGTGGTCGTTGACAAATCAATCTTGGGTGTTTCTATTCTGGATTCATTTATGTAC AACCAGGACTTGAAGCCCGTCGAAAAAGAAAGGCGGGTTTGGTCCTGGTACAATTATTGTTACTTCTGGCTTGCTGAATGTTTCAATAT CAACACTTGGCAAATTGCAGCTACAGGTCTACAACTGGGTCTAAATTGGTGGCAGTGTTGGATAACAATTTGGATTGGGTACGGTTTCG TTGGTGCTTTTGTTGTTTTGGCCTCTAGAGTTGGATCTGCTTATCATTTGTCATTCCCTATATCATCTAGAGCATCATTCGGTATTTTC TTCTCTTTATGGCCCGTTATTAACAGAGTCGTCATGGCCATCGTTTGGTATAGTGTCCAAGCTTATATTGCGGCAACTCCCGTATCATT AATGCTGAAATCTATCTTTGGAAAAGATTTACAATGATTGTACGTGGGGCAGTTGACGTCTTATCATATGTCAAAGTCATTTGCGAAGT TCTTGGCAAGTTGCCAACTGACGAGATGCAGTAACACTTTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATG TTTTCAATGTAAGAGATTTCGATTATCCACAAACTTTAAAACACAGGGACAAAATTCTTGATATGCTTTCAACCGCTGCGTTTTGGATA CCTATTCTTGACATGATATGACTACCATTTTGTTATTGTTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATG TTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTA AGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGA TTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATA GTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATG CTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACT TAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGAT TGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATTT Promoter motifs 3’ UTR motifsExons Introns

14. CS262 Lecture 17, Win07, Batzoglou Example: A Human heat shock protein TATA box: positioning transcription start TATA, CCAAT: constitutive transcription GRE: glucocorticoid response MRE:metal response HSE:heat shock element TATASP1 CCAAT AP2 HSE AP2CCAAT SP1 promoter of heat shock hsp70 0 --158 GENE

15. CS262 Lecture 17, Win07, Batzoglou The Cell as a Regulatory Network Genes = wires Motifs = gates 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

16. CS262 Lecture 17, Win07, Batzoglou The Cell as a Regulatory Network (2)

17. CS262 Lecture 17, Win07, Batzoglou DNA Microarrays Measuring gene transcription in a high- throughput fashion

18. CS262 Lecture 17, Win07, Batzoglou What is a microarray

19. CS262 Lecture 17, Win07, Batzoglou What is a microarray A 2D array of DNA sequences from thousands of genes Each spot has many copies of same gene Measure number of hybridizations per spot Result: Thousands of “experiments” – one per gene – in one go Perform many microarrays for different conditions:  Time during cell cycle  Temperature  Nutrient level

20. CS262 Lecture 17, Win07, Batzoglou Goal of Microarray Experiments Measure level of gene expression across many different conditions:  Expression Matrix M: {genes}  {conditions}: M ij = |gene i | in condition j Group genes into coregulated sets  Observe cells under different conditions  Find genes with similar expression profiles Potentially regulated by same TF slide credits: M. Kellis

21. CS262 Lecture 17, Win07, Batzoglou Clustering vs. Classification Clustering  Idea: Groups of genes that share similar function have similar expression patterns Hierarchical clustering k-means Bayesian approaches Projection techniques Principal Component Analysis Independent Component Analysis Classification  Idea: A cell can be in one of several states (Diseased vs. Healthy, Cancer X vs. Cancer Y vs. Normal)  Can we train an algorithm to use the gene expression patterns to determine which state a cell is in? Support Vector Machines Decision Trees Neural Networks K-Nearest Neighbors

22. CS262 Lecture 17, Win07, Batzoglou Clustering Algorithms b e d f a c h g abdefghc K-means b e d f a c h g c1 c2 c3 abghcdef Hierarchical slide credits: M. Kellis

23. CS262 Lecture 17, Win07, Batzoglou Hierarchical clustering Bottom-up algorithm:  Initialization: each point in a separate cluster At each step:  Choose the pair of closest clusters  Merge The exact behavior of the algorithm depends on how we define the distance CD(X,Y) between clusters X and Y Avoids the problem of specifying the number of clusters b e d f a c h g slide credits: M. Kellis

24. CS262 Lecture 17, Win07, Batzoglou Distance between clusters CD(X,Y)=min x  X, y  Y D(x,y) Single-link method CD(X,Y)=max x  X, y  Y D(x,y) Complete-link method CD(X,Y)=avg x  X, y  Y D(x,y) Average-link method CD(X,Y)=D( avg(X), avg(Y) ) Centroid method e d f h g e d f h g e d f h g e d f h g slide credits: M. Kellis

25. CS262 Lecture 17, Win07, Batzoglou Results of Clustering Gene Expression CLUSTER is simple and easy to use De facto standard for microarray analysis Time: O(N 2 M) N: #genes M: #conditions

26. CS262 Lecture 17, Win07, Batzoglou K-Means Clustering Algorithm Each cluster X i has a center c i Define the clustering cost criterion COST(X 1,…X k ) = ∑ Xi ∑ x  Xi |x – c i | 2 Algorithm tries to find clusters X 1 …X k and centers c 1 …c k that minimize COST K-means algorithm:  Initialize centers  Repeat: Compute best clusters for given centers → Attach each point to the closest center Compute best centers for given clusters → Choose the centroid of points in cluster  Until the changes in COST are “small” b e d f a c h g c1 c2 c3 slide credits: M. Kellis

27. CS262 Lecture 17, Win07, Batzoglou K-Means Algorithm Randomly Initialize Clusters

28. CS262 Lecture 17, Win07, Batzoglou K-Means Algorithm Assign data points to nearest clusters

29. CS262 Lecture 17, Win07, Batzoglou K-Means Algorithm Recalculate Clusters

30. CS262 Lecture 17, Win07, Batzoglou K-Means Algorithm Recalculate Clusters

31. CS262 Lecture 17, Win07, Batzoglou K-Means Algorithm Repeat

32. CS262 Lecture 17, Win07, Batzoglou K-Means Algorithm Repeat

33. CS262 Lecture 17, Win07, Batzoglou K-Means Algorithm Repeat … until convergence Time: O(KNM) per iteration N: #genes M: #conditions

34. CS262 Lecture 17, Win07, Batzoglou Mixture of Gaussians – Probabilistic K-means Data is modeled as mixture of K Gaussians  N(  1,  2 I), …, N(  K,  2 I)  Prior probabilities  1, …,  K Different  i for every Gaussian i, or even different covariance matrices are possible, but learning becomes harder  P(x) = ∑ i P(x | N(  1,  2 I))   i  Use EM to learn parameters

35. CS262 Lecture 17, Win07, Batzoglou Analysis of Clustering Data Statistical Significance of Clusters  Gene Ontologyhttp://www.geneontology.org/http://www.geneontology.org/  KEGG http://www.genome.jp/kegg/http://www.genome.jp/kegg/ Regulatory motifs responsible for common expression Regulatory Networks Experimental Verification

36. CS262 Lecture 17, Win07, Batzoglou Evaluating clusters – Hypergeometric Distribution +–N genes, p labeled +, (N-p) – +Cluster: k genes, m labeled + +P-value of single cluster containing k genes of which at least r are + +– Prob a random set of k genes has m + and k-m – genes + P-value that at least r genes are + in the cluster slide credits: M. Kellis

37. CS262 Lecture 17, Win07, Batzoglou Finding Regulatory Motifs

38. CS262 Lecture 17, Win07, Batzoglou Regulatory Motif Discovery DNA Group of co-regulated genes Common subsequence Find motifs within groups of corregulated genes slide credits: M. Kellis

39. CS262 Lecture 17, Win07, Batzoglou Characteristics of Regulatory Motifs Tiny Highly Variable ~Constant Size  Because a constant-size transcription factor binds Often repeated Low-complexity-ish

40. CS262 Lecture 17, Win07, Batzoglou Sequence Logos Height of each letter proportional to its frequency Height of all letters proportional to information content at that position

41. CS262 Lecture 17, Win07, Batzoglou Problem Definition Probabilistic Motif: M ij ; 1  i  W 1  j  4 M ij = Prob[ letter j, pos i ] Find best M, and positions p 1,…, p N in sequences Combinatorial Motif M: m 1 …m W Some of the m i ’s blank Find M that occurs in all s i with  k differences Given a collection of promoter sequences s 1,…, s N of genes with common expression

42. CS262 Lecture 17, Win07, Batzoglou Discrete Approaches to Motif Finding

43. CS262 Lecture 17, Win07, Batzoglou Discrete Formulations Given 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 any word in x i d(W, S) =  i d(W, x i )

44. CS262 Lecture 17, Win07, Batzoglou 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 |) Advantage: Finds provably “best” motif W Disadvantage: Time

45. CS262 Lecture 17, Win07, Batzoglou Exhaustive Searches 2. Sample-driven algorithm: For W = any K-long word occurring 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 ) Advantage: Time Disadvantage:If the true motif is weak and does not occur in data then a random motif may score better than any instance of true motif

46. CS262 Lecture 17, Win07, Batzoglou MULTIPROFILER Extended sample-driven approach Given a K-long word W, define: N α (W) = words W’ in S s.t. d(W,W’)  α Idea: Assume W is occurrence of true motif W * Will use N α (W) to correct “errors” in W

47. CS262 Lecture 17, Win07, Batzoglou MULTIPROFILER Assume W differs from true motif W * in at most L positions Define: A wordlet G of W is a L-long pattern with blanks, differing from W  L is smaller than the word length K Example: K = 7; L = 3 W = ACGTTGA G = --A--CG

48. CS262 Lecture 17, Win07, Batzoglou MULTIPROFILER Algorithm: For each W in S: For L = 1 to L max 1.Find the α- neighbors of W in S  N α (W) 2.Find all “strong” L-long wordlets G in N a (W) 3.For each wordlet G, 1.Modify W by the wordlet G  W’ 2.Compute d(W’, S) Report W * = argmin d(W’, S) Step 2 above: Smaller motif-finding problem; Use exhaustive search

49. CS262 Lecture 17, Win07, Batzoglou Expectation Maximization in Motif Finding

50. CS262 Lecture 17, Win07, Batzoglou All K-long words motif background Expectation Maximization Algorithm (sketch): 1.Given genomic sequences find all k-long words 2.Assume each word is motif or background 3.Find likeliest Motif Model Background Model classification of words into either Motif or Background

51. CS262 Lecture 17, Win07, Batzoglou Expectation Maximization Given sequences x 1, …, x N, Find all k-long words X 1,…, X n Define motif model: M = (M 1,…, M K ) M i = (M i1,…, M i4 ) (assume {A, C, G, T}) where M ij = Prob[ letter j occurs in motif position i ] Define background model: B = B 1, …, B 4 B i = Prob[ letter j in background sequence ] motif background ACGTACGT M1M1 MKMK M1M1 B

52. CS262 Lecture 17, Win07, Batzoglou Expectation Maximization Define Z i1 = { 1, if X i is motif; 0, otherwise } Z i2 = { 0, if X i is motif; 1, otherwise } Given a word X i = x[s]…x[s+k], P[ X i, Z i1 =1 ] = M 1x[s] …M kx[s+k] P[ X i, Z i2 =1 ] = (1 – ) B x[s] …B x[s+k] Let 1 = ; 2 = (1 – ) motif background ACGTACGT M1M1 MKMK M1M1 B 1 –

53. CS262 Lecture 17, Win07, Batzoglou Expectation Maximization Define: Parameter space  = (M, B)  1 : Motif;  2 : Background Objective: Maximize log likelihood of model: ACGTACGT M1M1 MKMK M1M1 B 1 – 

54. CS262 Lecture 17, Win07, Batzoglou Expectation Maximization Maximize expected likelihood, in iteration of two steps: Expectation: Find expected value of log likelihood: Maximization: Maximize expected value over ,

55. CS262 Lecture 17, Win07, Batzoglou Expectation: Find expected value of log likelihood: where expected values of Z can be computed as follows: Expectation Maximization: E-step

56. CS262 Lecture 17, Win07, Batzoglou Expectation Maximization: M-step Maximization: Maximize expected value over  and independently For, this has the following solution: (we won’t prove it) Effectively, NEW is the expected # of motifs per position, given our current parameters

57. CS262 Lecture 17, Win07, Batzoglou For  = (M, B), define c jk = E[ # times letter k appears in motif position j] c 0k = E[ # times letter k appears in background] c ij values are calculated easily from Z* values It then follows: to not allow any 0’s, add pseudocounts Expectation Maximization: M-step

58. CS262 Lecture 17, Win07, Batzoglou Initial Parameters Matter! Consider the following artificial example: 6-mers X 1, …, X n :(n = 2000)  990 words “AAAAAA”  990 words “CCCCCC”  20 words “ACACAC” Some local maxima: = 49.5%; B = 100/101 C, 1/101 A M = 100% AAAAAA = 1%; B = 50% C, 50% A M = 100% ACACAC

59. CS262 Lecture 17, Win07, Batzoglou Overview of EM Algorithm 1.Initialize parameters  = (M, B), :  Try different values of from N -1/2 up to 1/(2K) 2.Repeat: a.Expectation b.Maximization 3.Until change in  = (M, B), falls below  4.Report results for several “good”

60. CS262 Lecture 17, Win07, Batzoglou Gibbs Sampling in Motif Finding

61. CS262 Lecture 17, Win07, Batzoglou Gibbs Sampling Given:  x 1, …, x N,  motif length K,  background B, Find:  Model M  Locations a 1,…, a N in x 1, …, x N Maximizing log-odds likelihood ratio:

62. CS262 Lecture 17, Win07, Batzoglou Gibbs Sampling AlignACE: first statistical motif finder BioProspector: improved version of AlignACE Algorithm (sketch): 1.Initialization: a.Select random locations in sequences x 1, …, x N b.Compute an initial model M from these locations 2.Sampling Iterations: a.Remove one sequence x i b.Recalculate model c.Pick a new location of motif in x i according to probability the location is a motif occurrence

63. CS262 Lecture 17, Win07, Batzoglou Gibbs Sampling Initialization: Select random locations  1,…,  N in x 1, …, x N For these locations, compute M: where  j are pseudocounts to avoid 0s, and B =  j  j That is, M kj is the number of occurrences of letter j in motif position k, over the total

64. CS262 Lecture 17, Win07, Batzoglou Gibbs Sampling Predictive Update: Select a sequence x = x i Remove x i, recompute model: where  j are pseudocounts to avoid 0s, and B =  j  j M

65. CS262 Lecture 17, Win07, Batzoglou Gibbs Sampling Sampling: For every K-long word x j,…,x j+k-1 in x: Q j = Prob[ word | motif ] = M(1,x j )  …  M(k,x j+k-1 ) P i = Prob[ word | background ] B(x j )  …  B(x j+k-1 ) Let Sample a random new position a i according to the probabilities A 1,…, A |x|-k+1. 0|x| Prob

66. CS262 Lecture 17, Win07, Batzoglou Gibbs Sampling Running Gibbs Sampling: 1.Initialize 2.Run until convergence 3.Repeat 1,2 several times, report common motifs

67. CS262 Lecture 17, Win07, Batzoglou Advantages / Disadvantages Very similar to EM Advantages: Easier to implement Less dependent on initial parameters More versatile, easier to enhance with heuristics Disadvantages: More dependent on all sequences to exhibit the motif Less systematic search of initial parameter space

68. CS262 Lecture 17, Win07, Batzoglou Repeats, and a Better Background Model Repeat DNA can be confused as motif  Especially low-complexity CACACA… AAAAA, etc. Solution: more elaborate background 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)

69. CS262 Lecture 17, Win07, Batzoglou 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 Motif Challenge problem: Find a (15,4) motif in N sequences of length 0 gene ???

70. CS262 Lecture 17, Win07, Batzoglou Example Application: Motifs in Yeast Group: Tavazoie et al. 1999, G. Church’s lab, Harvard Data: Microarrays on 6,220 mRNAs from yeast Affymetrix chips (Cho et al.) 15 time points across two cell cycles 1.Clustering genes according to common expression K-means clustering -> 30 clusters, 50-190 genes/cluster Clusters correlate well with known function 2.AlignACE motif finding 600-long upstream regions

71. CS262 Lecture 17, Win07, Batzoglou Motifs in Periodic Clusters

72. CS262 Lecture 17, Win07, Batzoglou Motifs in Non-periodic Clusters

73. CS262 Lecture 17, Win07, Batzoglou Motifs are preferentially conserved across evolution Scer TTATATTGAATTTTCAAAAATTCTTACTTTTTTTTTGGATGGACGCAAAGAAGTTTAATAATCATATTACATGGCATTACCACCATATACA Spar CTATGTTGATCTTTTCAGAATTTTT-CACTATATTAAGATGGGTGCAAAGAAGTGTGATTATTATATTACATCGCTTTCCTATCATACACA Smik GTATATTGAATTTTTCAGTTTTTTTTCACTATCTTCAAGGTTATGTAAAAAA-TGTCAAGATAATATTACATTTCGTTACTATCATACACA Sbay TTTTTTTGATTTCTTTAGTTTTCTTTCTTTAACTTCAAAATTATAAAAGAAAGTGTAGTCACATCATGCTATCT-GTCACTATCACATATA * * **** * * * ** ** * * ** ** ** * * * ** ** * * * ** * * * Scer TATCCATATCTAATCTTACTTATATGTTGT-GGAAAT-GTAAAGAGCCCCATTATCTTAGCCTAAAAAAACC--TTCTCTTTGGAACTTTCAGTAATACG Spar TATCCATATCTAGTCTTACTTATATGTTGT-GAGAGT-GTTGATAACCCCAGTATCTTAACCCAAGAAAGCC--TT-TCTATGAAACTTGAACTG-TACG Smik TACCGATGTCTAGTCTTACTTATATGTTAC-GGGAATTGTTGGTAATCCCAGTCTCCCAGATCAAAAAAGGT--CTTTCTATGGAGCTTTG-CTA-TATG Sbay TAGATATTTCTGATCTTTCTTATATATTATAGAGAGATGCCAATAAACGTGCTACCTCGAACAAAAGAAGGGGATTTTCTGTAGGGCTTTCCCTATTTTG ** ** *** **** ******* ** * * * * * * * ** ** * *** * *** * * * Scer CTTAACTGCTCATTGC-----TATATTGAAGTACGGATTAGAAGCCGCCGAGCGGGCGACAGCCCTCCGACGGAAGACTCTCCTCCGTGCGTCCTCGTCT Spar CTAAACTGCTCATTGC-----AATATTGAAGTACGGATCAGAAGCCGCCGAGCGGACGACAGCCCTCCGACGGAATATTCCCCTCCGTGCGTCGCCGTCT Smik TTTAGCTGTTCAAG--------ATATTGAAATACGGATGAGAAGCCGCCGAACGGACGACAATTCCCCGACGGAACATTCTCCTCCGCGCGGCGTCCTCT Sbay TCTTATTGTCCATTACTTCGCAATGTTGAAATACGGATCAGAAGCTGCCGACCGGATGACAGTACTCCGGCGGAAAACTGTCCTCCGTGCGAAGTCGTCT ** ** ** ***** ******* ****** ***** *** **** * *** ***** * * ****** *** * *** Scer TCACCGG-TCGCGTTCCTGAAACGCAGATGTGCCTCGCGCCGCACTGCTCCGAACAATAAAGATTCTACAA-----TACTAGCTTTT--ATGGTTATGAA Spar TCGTCGGGTTGTGTCCCTTAA-CATCGATGTACCTCGCGCCGCCCTGCTCCGAACAATAAGGATTCTACAAGAAA-TACTTGTTTTTTTATGGTTATGAC Smik ACGTTGG-TCGCGTCCCTGAA-CATAGGTACGGCTCGCACCACCGTGGTCCGAACTATAATACTGGCATAAAGAGGTACTAATTTCT--ACGGTGATGCC Sbay GTG-CGGATCACGTCCCTGAT-TACTGAAGCGTCTCGCCCCGCCATACCCCGAACAATGCAAATGCAAGAACAAA-TGCCTGTAGTG--GCAGTTATGGT ** * ** *** * * ***** ** * * ****** ** * * ** * * ** *** Scer GAGGA-AAAATTGGCAGTAA----CCTGGCCCCACAAACCTT-CAAATTAACGAATCAAATTAACAACCATA-GGATGATAATGCGA------TTAG--T Spar AGGAACAAAATAAGCAGCCC----ACTGACCCCATATACCTTTCAAACTATTGAATCAAATTGGCCAGCATA-TGGTAATAGTACAG------TTAG--G Smik CAACGCAAAATAAACAGTCC----CCCGGCCCCACATACCTT-CAAATCGATGCGTAAAACTGGCTAGCATA-GAATTTTGGTAGCAA-AATATTAG--G Sbay GAACGTGAAATGACAATTCCTTGCCCCT-CCCCAATATACTTTGTTCCGTGTACAGCACACTGGATAGAACAATGATGGGGTTGCGGTCAAGCCTACTCG **** * * ***** *** * * * * * * * * ** Scer TTTTTAGCCTTATTTCTGGGGTAATTAATCAGCGAAGCG--ATGATTTTT-GATCTATTAACAGATATATAAATGGAAAAGCTGCATAACCAC-----TT Spar GTTTT--TCTTATTCCTGAGACAATTCATCCGCAAAAAATAATGGTTTTT-GGTCTATTAGCAAACATATAAATGCAAAAGTTGCATAGCCAC-----TT Smik TTCTCA--CCTTTCTCTGTGATAATTCATCACCGAAATG--ATGGTTTA--GGACTATTAGCAAACATATAAATGCAAAAGTCGCAGAGATCA-----AT Sbay TTTTCCGTTTTACTTCTGTAGTGGCTCAT--GCAGAAAGTAATGGTTTTCTGTTCCTTTTGCAAACATATAAATATGAAAGTAAGATCGCCTCAATTGTA * * * *** * ** * * *** *** * * ** ** * ******** **** * Scer TAACTAATACTTTCAACATTTTCAGT--TTGTATTACTT-CTTATTCAAAT----GTCATAAAAGTATCAACA-AAAAATTGTTAATATACCTCTATACT Spar TAAATAC-ATTTGCTCCTCCAAGATT--TTTAATTTCGT-TTTGTTTTATT----GTCATGGAAATATTAACA-ACAAGTAGTTAATATACATCTATACT Smik TCATTCC-ATTCGAACCTTTGAGACTAATTATATTTAGTACTAGTTTTCTTTGGAGTTATAGAAATACCAAAA-AAAAATAGTCAGTATCTATACATACA Sbay TAGTTTTTCTTTATTCCGTTTGTACTTCTTAGATTTGTTATTTCCGGTTTTACTTTGTCTCCAATTATCAAAACATCAATAACAAGTATTCAACATTTGT * * * * * * ** *** * * * * ** ** ** * * * * * *** * Scer TTAA-CGTCAAGGA---GAAAAAACTATA Spar TTAT-CGTCAAGGAAA-GAACAAACTATA Smik TCGTTCATCAAGAA----AAAAAACTA.. Sbay TTATCCCAAAAAAACAACAACAACATATA * * ** * ** ** ** Gal10Gal1 Gal4 GAL10 GAL1 TBP GAL4 MIG1 TBP MIG1 Factor footprint Conservation island slide credits: M. Kellis Is this enough to discover motifs? No.

74. CS262 Lecture 17, Win07, Batzoglou Comparison-based Regulatory Motif Discovery Study known motifs Derive conservation rules Discover novel motifs slide credits: M. Kellis

75. CS262 Lecture 17, Win07, Batzoglou Known motifs are frequently conserved Across the human promoter regions, the Err  motif:  appears 434 times  is conserved 162 times Human Dog Mouse Rat Err  Conservation rate: 37% Compare to random control motifs –Conservation rate of control motifs: 6.8% –Err  enrichment: 5.4-fold –Err  p-value < 10 -50 (25 standard deviations under binomial) Motif Conservation Score (MCS) slide credits: M. Kellis

76. CS262 Lecture 17, Win07, Batzoglou Finding conserved motifs in whole genomes M. Kellis PhD Thesis on yeasts, X. Xie & M. Kellis on mammals 1.Define seed “mini-motifs” 2.Filter and isolate mini-motifs that are more conserved than average 3.Extend mini-motifs to full motifs 4.Validate against known databases of motifs & annotations 5.Report novel motifs CTACGA N slide credits: M. Kellis

77. CS262 Lecture 17, Win07, Batzoglou Test 1: Intergenic conservation Total count Conserved count CGG-11-CCG slide credits: M. Kellis

78. CS262 Lecture 17, Win07, Batzoglou Test 2: Intergenic vs. Coding Coding Conservation Intergenic Conservation CGG-11-CCG Higher Conservation in Genes slide credits: M. Kellis

79. CS262 Lecture 17, Win07, Batzoglou Test 3: Upstream vs. Downstream CGG-11-CCG Downstream motifs? Most Patterns Downstream Conservation Upstream Conservation slide credits: M. Kellis

80. CS262 Lecture 17, Win07, Batzoglou Extend Collapse Full Motifs Constructing full motifs 2,000 Mini-motifs 72 Full motifs 6 CTA CGA R R CTGRC CGAA ACCTGCGAACTGRCCGAACTRAY CGAA Y 5 Extend Collapse Merge Test 1Test 2Test 3 slide credits: M. Kellis

81. CS262 Lecture 17, Win07, Batzoglou Summary for promoter motifs RankDiscovered Motif Known TF motif Tissue Enrichment Distance bias 1RCGCAnGCGYNRF-1Yes 2CACGTGMYCYes 3SCGGAAGYELK-1Yes 4ACTAYRnnnCCCRYes 5GATTGGYNF-YYes 6GGGCGGRSP1Yes 7TGAnTCAAP-1Yes 8TMTCGCGAnRYes 9TGAYRTCAATF3Yes 10GCCATnTTGYY1Yes 11MGGAAGTGGABPYes 12CAGGTGE12Yes 13CTTTGTLEF1Yes 14TGACGTCAATF3Yes 15CAGCTGAP-4Yes 16RYTTCCTGC-ETS-2Yes 17AACTTTIRF1(*)Yes 18TCAnnTGAYSREBP-1Yes 19GKCGCn(7)TGAYGYes 20GTGACGYE4F1Yes 21GGAAnCGGAAnYYes 22TGCGCAnKYes 23TAATTACHX10Yes 24GGGAGGRRMAZYes 25TGACCTYERRAYes 174 promoter motifs 70 match known TF motifs 115 expression enrichment 60 show positional bias  75% have evidence Control sequences < 2% match known TF motifs < 5% expression enrichment < 3% show positional bias  < 7% false positives Most discovered motifs are likely to be functional New slide credits: M. Kellis