CS 5263 & CS 4233 Bioinformatics

1. CS 5263 & CS 4233 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. Transcriptional Regulation of genes Transcription Factor (TF) (Protein) RNA polymerase (Protein) DNA Promoter Gene

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

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

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

13. 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

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 A S G T K T K A C

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

22. Sequence Logo 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 x1, x2, . . . , xn with the respective probabilities p1, p2, . . . , pn is defined as

24. 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

25. 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

26. Sequence Logo

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. 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

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. 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 4K patterns,we can search the -neighborhood of every word in S. α-neighborhood

38. Extended sample-driven (ESD) approaches • Naïve: N Kα3αNK # of patterns to test # of words in sequences

39. 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 • Details later

40. Probabilistic modeling approaches for motif finding

41. 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

42. 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-)

43. 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)

44. 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

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

46. 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

47. 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

48. 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

49. 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

50. Limits of Motif Finders 0 • 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 ??? gene