CS5263 Bioinformatics

1. CS5263 Bioinformatics Lecture 18 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 • In protein: functional/structural domains

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

5. In motif finding, understanding the motivations, significance of the problems, difficulties, and ideas that have been explored are more important than knowing the details of the existing algorithms! • Most algorithms often perform poorly in real challenges! • Not necessarily a fault of algorithm designers • Algorithms will be improved

6. Biological background for motif finding

7. Cells respond to environment Various external messages Heat Responds to environmental conditions Food Supply

8. 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

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

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

11. Transcriptional Regulation • Strongest regulation happens during transcription • Best place to regulate: No energy wasted making intermediate products • However, slowest response time After a receptor notices a change: • Cascade message to nucleus • Open chromatin & bind transcription factors • Recruit RNA polymerase and transcribe • Splice mRNA and send to cytoplasm • Translate into protein

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

13. Regulation of Genes Transcription Factor (TF) (Protein) RNA polymerase (Protein) DNA Promoter Gene

14. Regulation of Genes Transcription Factor (TF) (Protein) RNA polymerase (Protein) DNA Gene Regulatory Element, TF binding site, TF binding motif, cis-regulatory motif (element)

15. Regulation of Genes Transcription Factor (Protein) RNA polymerase DNA Regulatory Element Gene

16. Regulation of Genes New protein RNA polymerase Transcription Factor DNA Regulatory Element Gene

17. 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

18. Code for protein-DNA binding? Some knowledge exists

19. However, overall code still missing

20. Experimental methods • DNase footprinting

21. Experimental methods • To determine protein-DNA binding site is tedious and time-consuming • To determine the binding specificity is even harder • Involves mutating different combinations of nucleic acids in promoter region and observe the biological effects • Computational methods can help

22. Finding Regulatory Motifs Given a collection of genes that are believed to be regulated by the same protein, Find the common TF-binding motif from promoters . . .

23. Essentially a Multiple Local Alignment • Find “best” multiple local alignment . . .

24. Then why don’t we just use multiple sequence alignment algorithms like the Multidimensional Dynamic Programming?

25. Characteristics of 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

26. Motif Representation

27. 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

28. Position Specific Weight Matrix A S G T K T K A C

29. Sequence Logo frequency

30. Sequence Logo

31. 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

32. 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

33. 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

34. Sequence Logo

35. Background-normalized Seq Logo • Many genomes have skewed base distribution • In a thermophilic bacteria (i.e. living in a hot spring), GC content can be as high as 70%. • Thus a motif ATAT in the genome of a thermophilic bacteria would contain more information than a motif GCGC

36. Relative Entropy • Definition 6.1. Let P and Q be two probability measures on the same alphabet X. Then the relative entropy (information divergence, Kullback-Leibler distance, discrimination) from P to Q is defined as • Easy to prove that if Q is a uniform distribution, D(P || Q) is equal to the Information content of P

37. Relative Entropy • Background: pA = pT = 0.2, pC = pG = 0.3 • Distribution on some column of a PWM: Case 1: pA = 0.85, pC = pG = pT = 0.05 Case 2: pG = 0.85 pC = pA = pT = 0.05 • Assuming uniform background distribution: I1 = I2 = 1.15 • With the non-uniform background distribution: • D1 = 1.42 • D2 = 0.95

38. Background-normalized Seq Logo

39. Physical interpretation • Information content is reversely proportional to the binding energy • High information content => lower energy => high affinity of binding • Relative entropy represents the specificity of the binding sites compared to random DNA sequences

40. 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

41. Finding Motifs

42. Definitions of terms • Motif: a consensus sequence or a PWM • Pattern: alias for motif (used in combinatorial motif finding) • Instance of a motif: a substring of a sequence that “matches” to the motif • How to define “match” will be shown later

43. Motif finding schemes Phylogenetic footprinting Dictionary building “Motif finding” 1A 1B 1C Gene set 1 Gene set 2 Gene set 3 Genome 1 Genome 2 Genome 3 Ideally, all information should be used, at some stage. i.e., inside algorithm vs pre- or post-processing.

44. Classification of approaches • Combinatorial search • Based on enumeration of words and computing word similarities • Analogy to DP for sequence alignment • Probabilistic modeling • Construct models to distinguish motifs vs non-motifs • Analogy to HMM for sequence alignment

45. Combinatorial motif finding • Idea 1: find all k-mers that appeared at least m times • Idea 2: find all k-mers that are statistically significant • Problem: most motifs allow divergence. Each variation may only appear once. • Idea 3: find all k-mers, considering IUPAC code • e.g. ASGTKTKAC, S = C/G, K = G/T • Still inflexible • Idea 4: find k-mers that approximately appeared at least m times • i.e. allow some mismatches

46. 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) )

47. 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.

48. Exhaustive searches 2. Sample-driven algorithm: For W = a K-long 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 )

49. 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

50. 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