CS5263 Bioinformatics Lecture 19 Motif finding

(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

Biological background for motif finding

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

The Cell as a Regulatory Network 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

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

Motif Representation

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

Position Specific Weight Matrix A C G T ASGTKTKA C

Sequence Logo frequency A C G T

Sequence Logo A C G T I

Background-normalized Seq Logo A C G T I I’

Finding Motifs

Motif finding schemes Genome 1Genome 2 Gene set 1Gene set 2 Conservation YesNo Whole genome YesGenome 1 & 2 & 3Genome 1 NoGene 1A & 1B & 1C or Gene Set 1 & 2 & 3 Gene Set 1 Genome 3 Gene set 3 1A1B1C Phylogenetic footprinting Dictionary building “Motif finding” 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 = {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 a word in x i d(W, S) =  i d(W, x i ) W* = argmin( d(W, S) )

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 |) Guaranteed to find the optimal solution.

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

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

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

Consensus Algorithm: Cycle 1: For each word W in S For each word W’ in S Create alignment (gap free) of W, W’ Keep the C 1 best alignments, A 1, …, A C1 ACGGTTG,CGAACTT,GGGCTCT … ACGCCTG,AGAACTA,GGGGTGT …

Algorithm (cont’d): Cycle i: For each word W in S For each alignment A j from cycle i-1 Create alignment (gap free) of W, A j Keep the C i best alignments A 1, …, A Ci

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

WEEDER Naïve: N K α 3 α 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 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. [ ] Bit OR all B’s to get seq occurrence for P Suppose #occ >= m –Pattern still valid Now add a letter ACGTTACGTT Current pattern P, |P| < K (e, B) # mismatches Seq occ

WEEDER: algorithm sketch 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 ACGTTAACGTTA Current pattern P (e, B)

WEEDER: complexity Can get all D(P, S) in time O(nN (K choose α) 3 α ) ~ O(nN K α 3 α ). n: # sequences. Needed for Bit OR. Better than O(KN 4 K ) since usually α << K K α 3 α 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 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 ACGTTAACGTTA Current pattern P

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 < K α 3 α 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 = (P ij ), 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 = (b i ), i = 1..4 A word can be generated by M or B

Expectation-Maximization For any word W,  P(W | M) = P W[1] 1 P W[2] 2 …P W[K] K  P(W | B) = b W[1] b W[2] …b W[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 Initialize: Randomly assign each word to M or B Let Z xy = 1 if position y in sequence x is a motif, and 0 otherwise Estimate parameters M,, B Iterate until converge: E-step: Z xy = P(M | X[y..y+k-1]) for all x and y M-step: re-estimate M, given Z (B usually fixed)

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

MEME Multiple EM for Motif Elicitation Bailey and Elkan, UCSD 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 Initialize: Randomly assign each word to M or B Let Z xy = 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 Z x*y for X* Sample a y* from Z x*y. Let Z x*y = 1 for y = y*, and 0 elsewhere

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 Sampling Simultaneously update predictions of all sequences position probability

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

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 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)

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 0 gene ???

Challenging problem (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 k d mutations n = 20 L = 1000

Information content: 13.8 bits ~ 7mers. Expected occurrence 1 per 16k bp

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. Issues: Measure similarities between two motifs (PWMs) # of clusters

Strategies to improve results Compare with known motifs in database –TRANSFAC –JASPAR Issues: –Compute similarities among motifs –How similar is similar?

Strategies to improve results Statistical test of significance –Enrichment in target sequences vs background sequences Target set T Background set B 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 If n / N >> m / M –P is enriched (over-represented) in T –Statistical significance? Target set T Background set + target set B + T N M P Appeared in n sequences Appeared in m sequences

Hypergeometric distribution A box with M balls, of which N are red, and the rest are blue. We randomly draw m balls from the box What’s the probability we’ll see n red balls? 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 = = 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 n = 5. 5-fold enrichment. P-value = Normally a very low p-value is needed, e.g

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

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

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 –Will two motifs always appear in the same gene? Location preference –Some motifs appear to be in certain location E.g., within bp 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 Usually 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