Lecture 20 Practical issues in motif finding Final project CS5263 Bioinformatics Lecture 20 Practical issues in motif finding Final project

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

Sequence Logo 1 2 3 4 5 6 7 8 9 A .97 .10 .02 .03 .01 .05 .85 C .40 .04 G .95 .3 T .90 .45 .6 .91 I 1.76 0.28 1.64 1.37 0.40 0.60 1.15 1.42

Finding Motifs

Phylogenetic footprinting Motif finding schemes Conservation Yes No Whole genome Genome 1 & 2 & 3 Genome 1 Gene 1A & 1B & 1C or Gene Set 1 & 2 & 3 Gene Set 1 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.

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

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) )

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.

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 )

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

WEEDER Naïve: N Kα 3α NK # of patterns to test # of words in sequences

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

WEEDER: algorithm sketch Current pattern P, |P| < K A list containing all eligible nodes: with at most α mismatches to P For each node, remember #mismatches accumulated (e), and 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 A C G T T # mismatches (e, B) Seq occ

WEEDER: algorithm sketch Current pattern P A C G T T A 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 (e, B)

WEEDER: complexity Can get all D(P, S) in time O(nN (K choose α) 3α) ~ O(nN Kα 3α). n: # sequences. Needed for Bit OR. Better than O(KN 4K) since usually α << K Kα 3α may still be expensive for large K E.g. K = 20, α = 6

WEEDER: More tricks Eligible nodes: with at most α mismatches to P Current pattern P A C G T T A 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

MULTIPROFILER W differs from W* at  positions. The consensus sequence for the words in the -neighborhood of W is similar to W. If we ignore all the chars that are similar to W, the rest may suggest the difference between W and W* W* W W*: ACGTACG W: ATGTAAG

MULTIPROFILER: alg sketch For each word P in S Find its α-neighborhood in S List of words: C For each position j from 1..K of the words in C Find the most popular char that differ from P[j] Replace α positions in P with the chars found above Call the new word P’ W* = argmin D(P’, S) W* W W*: ACGTACG W: ATGTAAG

MULTIPROFILER Complexity not discussed in the paper More efficient than WEEDER for longer patterns: N < Kα 3α How to choose α is an issue: Large α: too many noises in neighborhood Small α: few true instances in neighborhood W* W W*: ACGTACG W: ATGTAAG

Probabilistic modeling approaches for motif finding

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

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-)

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

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

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

Gibbs Sampling position probability 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 Simultaneously update predictions of all sequences

Gibbs sampling motif finders Gibbs Sampler, based on C. Larence et.al. Science, 1993 AlignACE, Nat Biotech 1998, developed in Church lab, Harvard Univ BioProspector, X. Liu et. al. PSB 2001 , an improvement of AlignACE

Limits of Motif Finders ??? gene 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 Similar issue for number of sequences

Challenging problem (k, d)-motif challenge problem d mutations n = 20 k L = 1000 (k, d)-motif challenge problem Many algorithms fail at (15, 4)-motif for n = 20 and L = 1000 Combinatorial algorithms usually work better on challenge problems However, they are usually designed to find (k, d)-motifs Performance in real data varies

(15, 4)-motif Information content: 11.7 bits ~ 6mers. Expected occurrence 1 per 7k bp

Actual Results by MEME llr = 163 E-value = 3.2e+005

(15, 4’)-motif Motif length: 15 Each instance differs at most 4 bases from consensus Information content: 14.8 Much easier problem

Actual Results by MEME sites = 20     llr = 240     E-value = 4.7e-013 sites = 5     llr = 95     E-value = 1.8e+006 sites = 2     llr = 38     E-value = 3.0e+006

Results for some real genes llr = 394     E-value = 2.0e-023 llr = 347     E-value = 9.8e-002 llr = 110     E-value = 1.4e+004

Motif finding in practice Now we’ve found some good looking motifs 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

To make sense about 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

Strategies to improve results 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 according to their similarities

Strategies to improve results Compare with known motifs in database TRANSFAC JASPAR Issues: How to determine similarity between motifs? Alignment between matrices How similar is similar? Empirically determine some threshold

Strategies to improve results Statistical test of significance Enrichment in target sequences vs background sequences Background set B Target set T 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

Statistical test for significance Background set + target set B + T P Target set T M N Appeared in n sequences Appeared in m sequences Intuitively: if n / N >> m / M P is enriched (over-represented) in T Statistical significance?

Hypergeometric distribution A box with M balls, of which N are red, and the rest are blue. If we randomly draw m balls from the box What’s the probability we’ll see n red balls? If P is very small, we are probably not drawing randomly Red ball: target sequences Blue ball: background sequences Total # of choices: (M choose m) # of choices to have n red balls: (N choose n) x (M-N choose m-n)

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? This can be interpreted as the p-value for the null hypothesis that we are randomly picking. Alternative hypothesis: our selection favors red balls. Equivalent: the target set T is enriched with motif P. Or: P is over-represented in T.

Examples Yeast genome has 6000 genes Select 50 genes believed to be co-regulated by a common TF Found a motif for these 50 genes It appeared in 20 out of these 50 genes In the whole genome, 100 genes have this motif M = 6000, N = 50, m = 100+20 = 120, n = 20 Intuition: m/M = 120/6000. In Genome, 1 out 50 genes have the motif N = 50, would expect only 1 gene in the target set to have the motif 20-fold enrichment P-value = 6 x 10-22 n = 5. 5-fold enrichment. P-value = 0.003 Normally a very low p-value is needed, e.g. 10-10

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 a sequence contains a motif, a cutoff has to be decided With different cutoffs, you get different number of genes with the motif Hyper-geometric test first assumes a cutoff It may be better to look at a range of cutoffs

ROC curve for motif significance Background set + target set B + T P Target set T M N Given a score cutoff Appeared in n sequences Appeared in m sequences 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 

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

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

Other strategies Finding motif modules Location preference 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 detect 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.

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).

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 Phylogenetic conservation is the key

Final project Write a review paper on a topic that we didn’t cover in lectures Or Implement an algorithm and do some experiments Compare several algorithms (existing implementation ok) Combine several algorithms to form a pipeline (e.g. gene expression + motif analysis) Final: 5 -10 pages report (single space, single column, 12pt) + 15 minutes presentation

Possible topics for term paper Haplotype inferencing Computational challenges associated with new microarray technologies Phylogenetic footprinting Small RNA gene / target prediction (siRNA, mRNA, …) Biomedical text mining Protein structure prediction Topology of biological networks

An example project Given a gene expression data (say cell cycle) Cluster genes using k-means Find motifs using several algorithms (Cluster and combine similar motifs) Rank motifs according to their specificity to the target sequences comparing to the other clusters Get their logos Use the sequences to search the whole genome for more genes with the motif Do they have any functional significance?