Ana Teresa Freitas 2016/2017

Transcription

1 Finding Regulatory Motifs in DNA Sequences Ana Teresa Freitas 2016/2017

2 Combinatorial Gene Regulation A recent microarray experiment showed that when gene X is knocked out, 20 other genes are not expressed How can one gene have such drastic effects?

3 Regulatory Proteins Gene X encodes regulatory protein, a.k.a. a transcription factor (TF) The 20 unexpressed genes rely on gene X s TF to induce transcription A single TF may regulate multiple genes TFs influence gene expression by binding to a specific location in the respective gene s regulatory region

4 Regulatory Regions Every gene contains a regulatory region (RR) typically stretching bp upstream of the transcriptional start site Located within the RR are the Transcription Factor Binding Sites (TFBS), also known as motifs, specific for a given transcription factor

5 Transcription Factor Binding Sites A TFBS can be located anywhere within the Regulatory Region (RR). For a single TF to regulate multiple genes, those genes RRs must contain corresponding TFBS TFBS may vary slightly across different regulatory regions since non-essential bases could mutate

6 Motif Logo Motifs can mutate on non important bases The five motifs at top right have mutations in position 3 and 5 Representations called motif logos illustrate the conserved regions of a motif TGGGGGA TGAGAGA TGGGGGA TGAGAGA TGAGGGA

7 Motif Logos: An Example (

8 Motifs and Transcriptional Start Sites ATCCCG TTCCGG ATCCCG gene gene gene ATGCCG gene ATGCCC gene

9 Identifying Motifs Genes are turned on or off by regulatory proteins These proteins bind to upstream regulatory regions of genes to either attract or block an RNA polymerase Regulatory protein X binds to a short DNA sequence called a motif So finding the same motif in multiple genes regulatory regions suggests a regulatory relationship amongst those genes

10 Identifying Motifs: Complications We do not know the motif sequence We do not know where it is located relative to the genes start Motifs can differ slightly from one gene to the next How to discern it from random motifs?

11 The Motif Finding Problem Given a random sample of DNA sequences: cctgatagacgctatctggctatccacgtacgtaggtcctctgtgcgaatctatgcgtttccaaccat agtactggtgtacatttgatacgtacgtacaccggcaacctgaaacaaacgctcagaaccagaagtgc aaacgtacgtgcaccctctttcttcgtggctctggccaacgagggctgatgtataagacgaaaatttt agcctccgatgtaagtcatagctgtaactattacctgccacccctattacatcttacgtacgtataca ctgttatacaacgcgtcatggcggggtatgcgttttggtcgtcgtacgctcgatcgttaacgtacgtc Find the pattern that is implanted in each of the individual arrays, namely, the motif

12 The Motif Finding Problem (cont d) Additional information: The hidden sequence is of length 8 The pattern is not exactly the same in each array because random point mutations may occur in the sequences

13 The Motif Finding Problem (cont d) The patterns revealed with no mutations: cctgatagacgctatctggctatccacgtacgtaggtcctctgtgcgaatctatgcgtttccaaccat agtactggtgtacatttgatacgtacgtacaccggcaacctgaaacaaacgctcagaaccagaagtgc aaacgtacgtgcaccctctttcttcgtggctctggccaacgagggctgatgtataagacgaaaatttt agcctccgatgtaagtcatagctgtaactattacctgccacccctattacatcttacgtacgtataca ctgttatacaacgcgtcatggcggggtatgcgttttggtcgtcgtacgctcgatcgttaacgtacgtc acgtacgt Consensus String

14 The Motif Finding Problem (cont d) The patterns with 2 point mutations: cctgatagacgctatctggctatccaggtacttaggtcctctgtgcgaatctatgcgtttccaaccat agtactggtgtacatttgatccatacgtacaccggcaacctgaaacaaacgctcagaaccagaagtgc aaacgttagtgcaccctctttcttcgtggctctggccaacgagggctgatgtataagacgaaaatttt agcctccgatgtaagtcatagctgtaactattacctgccacccctattacatcttacgtccatataca ctgttatacaacgcgtcatggcggggtatgcgttttggtcgtcgtacgctcgatcgttaccgtacggc

15 The Motif Finding Problem (cont d) The problem: Can we still find the motif, now that we have 2 mutations? What is the consensus sequence?

16 Defining Motifs To define a motif, lets say we know where the motif starts in the sequence The motif start positions in their sequences can be represented as s = (s 1,s 2,s 3,,s t )

17 Motifs: Profiles and Consensus Alignment a G g t a c T t C c A t a c g t a c g t T A g t a c g t C c A t C c g t a c g G A Profile C G T Line up the patterns by their start indexes s = (s 1, s 2,, s t ) Construct matrix profile with frequencies of each nucleotide in columns Consensus A C G T A C G T Consensus nucleotide in each position has the highest score in column

18 Consensus Consensus sequences help in finding motifs Think of consensus as an ancestor motif, from which mutated motifs emerged The distance between a real motif and the consensus sequence is generally less than that for two real motifs

19 Consensus (cont d)

20 Positional weight matrix (PWM) Motifs can be summarized in a sequence probability matrix PWM, Position specific scoring matrix (PSSM), or motif For example, a 7-mer binding site: Pos A C G T

21 Log-likelihood matrix PWM can be transformed into a log-likelihood matrix by dividing each entry by the background probability of the corresponding base and taking log of it. For instance, if the background probability of T is 0.3 then PWM(T,1) = ln(0.35/0.3).

22 Motif Logos Information and entropy Conserved amino acid regions contain high degree of information (high order == low entropy) Variable amino acid regions contain low degree of information (low order == high entropy) Shannon Entropy (DNA) D(i) = 2 + Σ k={a,c,g,t} P k (i)log 2 P k (i) The 2 is from log 2 ( A ); A is the number of elements in A (Alphabet), (A=4 for DNA) P k (i) is the probability of observing base k in position i

23 Motif Logos For a position with nucleotide probabilities P = 1/4, the information content is zero D(i) = 2 + 1/4 log2(1/4) + 1/4 log2(1/4) + 1/4 log2(1/4) + 1/4 log2(1/4) = 0 The size of each base printed in the logo is determined by multiplying the frequency of that base by the total information at that position Height of base k at position l = P k (l) D(l)

24 Vizualization Bases are stacked on top of each other in increasing order of their frequencies

25 Evaluating Motifs We have a guess about the consensus sequence, but how good is this consensus? Need to introduce a scoring function to compare different guesses and choose the best one.

26 Defining Some Terms t - number of sample DNA sequences n - length of each DNA sequence DNA - sample of DNA sequences (t x n array) l - length of the motif (l-mer) s i - starting position of an l-mer in sequence i s=(s 1, s 2, s t ) - array of motif s starting positions

27 Parameters In our sample sequence: l = 8 DNA cctgatagacgctatctggctatccaggtacttaggtcctctgtgcgaatctatgcgtttccaaccat agtactggtgtacatttgatccatacgtacaccggcaacctgaaacaaacgctcagaaccagaagtgc t=5 aaacgttagtgcaccctctttcttcgtggctctggccaacgagggctgatgtataagacgaaaatttt agcctccgatgtaagtcatagctgtaactattacctgccacccctattacatcttacgtccatataca ctgttatacaacgcgtcatggcggggtatgcgttttggtcgtcgtacgctcgatcgttaccgtacggc n = 69 s s 1 = 26 s 2 = 21 s 3 = 3 s 4 = 56 s 5 = 60

28 Scoring Function Given s = (s 1, s t ) and DNA: Score(s,DNA) = l max i= 1 k { A, T, C, G} count( k, i) a G g t a c T t C c A t a c g t a c g t T A g t a c g t C c A t C c g t a c g G A C G T l t Consensus a c g t a c g t Score =30

29 The Motif Finding Problem If starting positions s=(s 1, s 2, s t ) are given, the problem is easy even with mutations in the sequences because we can simply construct the profile to find the motif (consensus) But the starting positions s are usually not given. How can we align the patterns and compute the best profile matrix?

30 The Motif Finding Problem: Formulation The Motif Finding Problem: Given a set of DNA sequences, find a set of l-mers, one from each sequence, that maximizes the consensus score Input: A t x n matrix of DNA, and l, the length of the pattern to find Output: An array of t starting positions s = (s 1, s 2, s t ) maximizing Score(s,DNA)

31 The Motif Finding Problem: Brute Force Solution Compute the scores for each possible combination of starting positions s The best score will determine the best profile and the consensus pattern in DNA The goal is to maximize Score(s,DNA) by varying the starting positions s i, where: s i = [1,, n-l+1] i = [1,, t]

32 Brute Force Approach: Running Time Varying (n - l + 1) positions in each of t sequences, we re looking at (n - l + 1) t sets of starting positions For each set of starting positions, the scoring function makes l operations, so complexity is l (n l + 1) t = O(l n t )

33 Pseudocode for Brute Force Motif Search 1. BruteForceMotifSearch(DNA, t, n,l) 2. bestscore ß 0 3. for each s=(s 1,s 2,..., s t ) from (1,1... 1) to (n-l+1,..., n-l+1) 4. if (Score(s,DNA) > bestscore) 5. bestscore ß Score(s, DNA) 6. bestmotif ß (s 1,s 2,..., s t ) 7. return bestmotif

34 Running Time of BruteForceMotifSearch That means that for t = 8, n = 1000, l = 10 Must perform 7.322E+25 computations Assuming each computation takes a cycle on a 3 GHz CPU, it would take 7.33 billion years to search all the possibilities This algorithm is not practical Lets explore some ways to speed it up

35 Some Motif Finding Programs CONSENSUS Hertz, Stromo (1989) GibbsDNA Lawrence et al (1993) MEME Bailey, Elkan (1995) RandomProjections Buhler, Tompa (2002) MULTIPROFILER Keich, Pevzner (2002) MITRA Eskin, Pevzner (2002) Pattern Branching Price, Pevzner (2003) RISO Carvalho et al (2006) MUSA Mendes at al (2006)