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CS5263 Bioinformatics. Lecture 18 Motif finding. 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
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CS5263 Bioinformatics Lecture 18 Motif finding
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 • Distinguish functional vs non-functional motifs • Search for instances of given motifs • Interpretation of motifs
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
Cells respond to environment Various external messages Heat Responds to environmental conditions Food Supply
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
Gene regulation • … is responsible for the dynamic cell • Gene expression (production of protein) varies according to: • Cell type • Cell cycle • External conditions • Location
Where gene regulation takes place • Opening of chromatin • Transcription • Translation • Protein stability • Protein modifications
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
Transcription Factors Binding to DNA Transcriptional regulation: • Certain transcription factors bind to DNA Binding recognizes DNA substrings: • Regulatory motifs
Regulation of Genes Transcription Factor (TF) (Protein) RNA polymerase (Protein) DNA Promoter Gene
Regulation of Genes Transcription Factor (TF) (Protein) RNA polymerase (Protein) DNA Gene Regulatory Element, TF binding site, TF binding motif, cis-regulatory motif (element)
Regulation of Genes Transcription Factor (Protein) RNA polymerase DNA Regulatory Element Gene
Regulation of Genes New protein RNA polymerase Transcription Factor DNA Regulatory Element Gene
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
Code for protein-DNA binding? Some knowledge exists
Experimental methods • DNase footprinting
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
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 . . .
Essentially a Multiple Local Alignment • Find “best” multiple local alignment . . .
Then why don’t we just use multiple sequence alignment algorithms like the Multidimensional Dynamic Programming?
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 • 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 S G T K T K A C
Sequence Logo frequency
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
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
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
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
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
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
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
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
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
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.
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 • 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 = {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 )
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