CS 6243 Machine Learning

1. CS 6243 Machine Learning Advanced topic: pattern recognition (DNA motif finding)

2. Final Project • Draft description available on course website • More details will be posted soon • Group size 2 to 4 acceptable, with higher expectation for larger teams • Predict Protein-DNA binding

3. Biological background for TF-DNA binding

4. 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

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

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

7. Transcriptional Regulation of genes Transcription Factor (TF) (Protein) RNA polymerase (Protein) DNA Promoter Gene

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

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

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

11. The Cell as a Regulatory Network If C then D gene D A B C Make D If B then NOT D D If A and B then D gene B D C Make B If D then B

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

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

14. Protein Binding Microarray

15. 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 . . .

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

17. 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

18. 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)

19. Position-Specific Weight Matrix A S G T K T K A C

20. Sequence Logo frequency http://weblogo.berkeley.edu/ http://biodev.hgen.pitt.edu/cgi-bin/enologos/enologos.cgi

21. Sequence Logo http://weblogo.berkeley.edu/ http://biodev.hgen.pitt.edu/cgi-bin/enologos/enologos.cgi

22. Entropy and information content • Entropy: a measure of uncertainty • The entropy of a random variable X that can assume the n different values x1, x2, . . . , xn with the respective probabilities p1, p2, . . . , pn is defined as

23. Entropy and information content • Example: A,C,G,T with equal probability • H = 4 * (-0.25 log2 0.25) = log2 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 log2 0.5) = log2 2 = 1 bit • 100% A • H = 1 * (-1 log2 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

24. Entropy and information content Expected occurrence in random DNA: 1 / 210.4 = 1 / 1340 Expected occurrence of an exact 5-mer: 1 / 210 = 1 / 1024

25. Sequence Logo

26. 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

27. Finding Motifs

28. 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

29. 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

30. Combinatorial motif finding Given a set of sequences S = {x1, …, xn} • A motif W is a consensus string w1…wK • Find motif W* with “best” match to x1, …, xn Definition of “best”: d(W, xi) = min hamming dist. between W and a word in xi d(W, S) = i d(W, xi) W* = argmin( d(W, S) )

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

32. Exhaustive searches 2. Sample-driven algorithm: For W = a K-char word in some xi Find d( W, S ) Report W* = argmin( d( W, S ) ) OR Report a local improvement of W* Running time: O( K N2 )

33. 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

34. 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

35. 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

36. 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

37. Probabilistic modeling approaches for motif finding

38. Probabilistic modeling approaches • A motif model • Usually a PWM • M = (Pij), 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 = (bi), i = 1..4 • A word can be generated by M or B

39. Expectation-Maximization • For any word W, • P(W | M) = PW[1] 1 PW[2] 2…PW[K] K • P(W | B) = bW[1] bW[2] …bW[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-)

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

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

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

43. 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

44. Gibbs Sampling Initialize: Randomly assign each word to M or B • Let Zxy = 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 Zx*y for X* • Sample a y* from Zx*y. • Let Zx*y = 1 for y = y* and 0 otherwise

45. 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 position probability Sampling Simultaneously update predictions of all sequences

46. 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 0th order: B = { pA, pC, pG, pT } 1st order: B = { P(A|A), P(A|C), …, P(T|T) } … Kth order: B = { P(X | b1…bK); X, bi{A,C,G,T} } Has been applied to EM and Gibbs (up to 3rd order)

47. Gibbs sampling motif finders • Gibbs Sampler • First appeared as: Larence et.al. Science 262(5131):208-214. • Continually developed and updated. webpage • 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. • 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. • Allow two-block motifs • Consider higher-order markov models