CS 5263 Bioinformatics Lecture 11 Motif finding HW

CS 5263 Bioinformatics Lecture 11 Motif finding

HW 2 2(C) Click to find out K and lambda

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

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

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

Biological background for motif finding

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

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

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

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

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

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

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

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

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

Experimental methods • DNase footprinting – Tedious – Time-consuming • High-throughput techniques: Ch. IP-chip, Ch. IPseq – Expensive – Other limitations

Computational methods for finding 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

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

Characteristics of Regulatory Motifs • Tiny (6 -12 bp) • Intergenic regions are very long • Highly Variable • ~Constant Size – Because a constant-size transcription factor binds • Often repeated • Often conserved

Motif representation • Collection of exact words – {ACGTTAC, ACGCTAC, AGGTGAC, …} • Consensus sequence (with wild cards) – {Ac. GTg. Tt. AC} – {ASGTKTKAC} S=C/G, K=G/T (IUPAC code) • Position-specific weight matrices (PWM)

Position-Specific Weight Matrix 1 2 3 4 5 6 7 8 9 A . 97 . 10 . 02 . 03 . 10 . 01 . 05 . 85 . 03 C . 01 . 40 . 01 . 04 . 05 . 01 . 05 . 03 G . 01 . 40 . 95 . 03 . 40 . 01 . 3 . 05 . 03 T . 01 . 10 . 02 . 90 . 45 . 97 . 6 . 05 . 91 S G T K A A C

frequency Sequence Logo 1 2 3 4 5 6 7 8 9 A . 97 . 10 . 02 . 03 . 10 . 01 . 05 . 85 . 03 C . 01 . 40 . 01 . 04 . 05 . 01 . 05 . 03 G . 01 . 40 . 95 . 03 . 40 . 01 . 3 . 05 . 03 T . 01 . 10 . 02 . 90 . 45 . 97 . 6 . 05 . 91 http: //weblogo. berkeley. edu/ http: //biodev. hgen. pitt. edu/cgi-bin/enologos. cgi

Sequence Logo 1 2 3 4 5 6 7 8 9 A . 97 . 10 . 02 . 03 . 10 . 01 . 05 . 85 . 03 C . 01 . 40 . 01 . 04 . 05 . 01 . 05 . 03 G . 01 . 40 . 95 . 03 . 40 . 01 . 3 . 05 . 03 T . 01 . 10 . 02 . 90 . 45 . 97 . 6 . 05 . 91 http: //weblogo. berkeley. edu/ http: //biodev. hgen. pitt. edu/cgi-bin/enologos. cgi

Entropy and information content • Entropy: a measure of uncertainty • The entropy of a random variable X that can assume the n different values x 1, x 2, . . . , xn with the respective probabilities p 1, p 2, . . . , pn is defined as

Entropy and information content • Example: A, C, G, T with equal probability § H = 4 * (-0. 25 log 2 0. 25) = log 2 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 log 2 0. 5) = log 2 2 = 1 bit • 100% A § H = 1 * (-1 log 2 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

Entropy and information content A C G 1. 97. 01 2. 10. 40 3. 02. 01. 95 4. 03. 04. 03 5. 10. 05. 40 6. 01. 01 7. 05. 3 T H I 8. 85. 05 9. 03. 03 . 01. 10. 02. 90. 45. 97. 6. 05. 91. 24 1. 72. 36. 63 1. 60 0. 24 1. 40 0. 85 0. 58 1. 76 0. 28 1. 64 1. 37 0. 40 1. 76 0. 60 1. 15 1. 42 Mean 1. 15 Total 10. 4 Expected occurrence in random DNA: 1 / 210. 4 = 1 / 1340 Expected occurrence of an exact 5 -mer: 1 / 210 = 1 / 1024

Sequence Logo 1 2 3 4 5 6 7 8 9 A C G . 97 . 10 . 02 . 03 . 10 . 01 . 05 . 85 . 03 . 01 . 40 . 01 . 04 . 05 . 01 . 05 . 03 . 01 . 40 . 95 . 03 . 40 . 01 . 3 . 05 . 03 T I . 01 . 10 . 02 . 90 . 45 . 97 . 6 . 05 . 91 1. 76 0. 28 1. 64 1. 37 0. 40 1. 76 0. 60 1. 15 1. 42

Real example • E. coli. Promoter • “TATA-Box” ~ 10 bp upstream of transcription start • TACGAT • TAAAAT • TATACT Consensus: TATAAT • GATAAT • TATGAT Note: none of the instances • TATGTT matches the consensus perfectly

Finding Motifs

Motif finding schemes Conservation Yes No Whole Yes Genome 1 & 2 & 3 Genome 1 Dictionary building genome Phylogenetic footprinting No Gene 1 A & 1 B & 1 C or “Motif finding” Gene Set 1 & 2 & 3 1 A 1 B 1 C Gene set 1 Gene set 2 Gene set 3 Genome 2 Genome 3 Genome 1 Ideally, all information should be used, at some stage. i. e. , inside algorithm vs pre- or post-processing.

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 – Will discuss in later lectures

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

Combinatorial motif finding Given a set of sequences S = {x 1, …, xn} • A motif W is a consensus string w 1…w. K • Find motif W* with “best” match to x 1, …, 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 (4 K possibilities) Find d( W, S ) Report W* = argmin( d(W, S) ) Running time: O( K N 4 K ) (where N = i |xi|) Guaranteed to find the optimal solution.

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 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” ~ 10 bp upstream of transcription start • TACGAT • TAAAAT • TATACT Consensus: TATAAT • GATAAT Each instance differs at most 2 • TATGAT bases from the consensus • TATGTT None of the instances matches the consensus perfectly

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

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

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, …, AC 1 ACGGTTG , ACGCCTG , CGAACTT , AGAACTA , GGGCTCT … GGGGTGT …

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

• C 1, …, Cn are user-defined heuristic constants Running time: O(k. N 2) + O(k. N C 1) + O(k. N C 2) + … + O(k. N Cn) = O(k. N 2 + k. NCtotal) Where Ctotal = i Ci, typically O(n. C), where C is a big constant

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 α-neighborhood 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.

Extended sample-driven (ESD) approaches • 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 # mismatches (e, B) Seq occ A C G T T • 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

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

WEEDER: complexity • Can get all patterns in time O(Nn(K choose α) 3α) ~ O(N n. Kα 3α). n: # sequences. Needed for Bit OR. • Better than O(KN 4 K) and O(N Kα 3α NK) since usually α << K • Kα 3α may still be expensive for large K – E. g. K = 20, α = 6

WEEDER: More tricks 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* W*: ACGTACG W: ATGTAAG W 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*

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

MULTIPROFILER W* W*: ACGTACG W: ATGTAAG W • No complexity provided 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

Challenging 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 problem – However, they are usually designed to find (k, d)-motifs – Performance in real data varies

Probabilistic modeling approaches for motif finding Will be covered later