Motif finding: Lecture 1 CS 498 CXZ

From DNA to Protein: In words 1.DNA = nucleotide sequence Alphabet size = 4 (A,C,G,T) 2.DNA  mRNA (single stranded) Alphabet size = 4 (A,C,G,U) 3.mRNA  amino acid sequence Alphabet size = 20 4.Amino acid sequence “folds” into 3- dimensional molecule called protein AATACGAAGTAA AAUACGAAGUAA Asn Thr Lys Stop

Gene expression Process of making a protein from a gene as template Transcription, then translation Can be regulated

Transcription Process of making a single stranded mRNA using double stranded DNA as template Only genes are transcribed, not all DNA

Step 1: From DNA to mRNA Transcription SOURCE:

GENE ACAGTGA TRANSCRIPTION FACTOR PROTEIN Transcriptional regulation

GENE ACAGTGA TRANSCRIPTION FACTOR PROTEIN Transcriptional regulation

The importance of gene regulation

Genetic regulatory network controlling the development of the body plan of the sea urchin embryo Davidson et al., Science, 295(5560):

That was the “circuit” responsible for development of the sea urchin embryo Nodes = genes Switches = gene regulation Change the switches and the circuit changes Gene regulation significance: –Development of an organism –Functioning of the organism –Evolution of organisms

Binding sites and motifs

Binding sites Binding sites of transcription factor “Bicoid”, collected experimentally

T A A T C C C Motif(“Consensus String”)

W A A T C C N Motif W = T or A N = A,C,G,T

Motif Common sequence “pattern” in the binding sites of a transcription factor A succinct way of capturing variability among the binding sites

A C G T Alternative way to represent motif Position weight matrix (PWM) Or simply, “weight matrix”

Motif representation Consensus string –May allow “degenerate” symbols in string, e.g., N = A/C/G/T; W = A/T; S = C/G; R = A/G; Y = T/C etc. Position weight matrix –More powerful representation –Probabilistic treatment

The motif finding problem Suppose a transcription factor (TF) controls five different genes Each of the five genes should have binding sites for TF in their promoter region Gene 1 Gene 2 Gene 3 Gene 4 Gene 5 Binding sites for TF

The motif finding problem Now suppose we are given the promoter regions of the five genes G1, G2, … G5 Can we find the binding sites of TF, without knowing about them a priori ? –Binding sites are similar to each other, but not necessarily identical This is the motif finding problem To find a motif that represents binding sites of an unknown TF

A variant of motif finding Given a motif (e.g., consensus string, or weight matrix), find the binding sites in an input sequence For consensus string, problem is trivial –For each position l in input sequence, check if substring starting at position l matches the motif. For weight matrix, not so trivial

Binding sites from a weight matrix motif A C G T W A C G T Counts of each base In each column Probability of each base In each column W  k = probability of base  in column k Given a string s of length l = 7 s = s 1 s 2 …s l Pr(s | W) = Example: Pr(CTAATCCG) = 0.67 x 0.89 x 1 x 1 x 0.89 x 1 x 0.89 x 0.11

Binding sites from a weight matrix motif Given sequence S (e.g., 1000 base-pairs long) For each substring s of S, –Compute Pr(s|W) –If Pr(s|W) > some threshold, call that a binding site Look at S, as well as its “reverse complement” –Rev.Compl. of AGTTACACCA is TGGTGTAACT –(That’s what is on the other strand of DNA)

Ab initio motif finding The original motif finding problem To find a motif that represents binding sites of an unknown TF

Ab initio motif finding Define a motif score, find the motif with maximum score over all possible motifs in search space (motif model) Consensus string model => exhaustive search algorithm, guarantee on finding the optimal motif PWM model => local search, not guaranteed to find optimal motif.

Ab initio motif finding - consensus string motifs A precise motif model defines the search space (I.e., a list of all candidate motifs). The motif model also prescribes exactly how to determine if a substring is a match to a particular motif. Define motif model precisely

Ab initio motif finding - consensus string motifs E.g., string over alphabet {A,C,G,T} of fixed length l. If l = 4, all 256 strings AAAA, AAAT, AAAC, …, TTTT, are “candidate motifs”. E.g., string over alphabet {A,C,G,T} of fixed length l, and allowing up to d mismatches. If AAAA is a motif, and d=1, then AAAT, AATA etc. are also counted as matches to motif. E.g., string over extended alphabet {A,C,G,T,N} of fixed length l. Here “N” stands for any character (A,C,G,or T.) –If AANAA is the motif, then AACAA, AAGAA, AATAA or AAAAA are all counted as matches to this motif.

Ab initio motif finding - consensus string motifs Define a motif score, i.e., a real number associated with each candidate motif, in relation to the input sequences. E.g., count N s of a motif s in input sequences(s). E.g., some function of the motif count N s. –E.g., Z s = (N s - E s )/  s – E s is the expected count of motif s in random sequences; and –  s is the variance of the count in random sequences

Ab initio motif finding - consensus string motifs For each motif s in the search space, –Compute the score of s Output the highest scoring motifs. This is the “enumerative” algorithm. Guaranteed to produce the optimal motif, since every possible motif is considered. Guarantee possible due to small search space. (E.g., 4 l where l is the motif length). Cant handle large values of l (e.g., > 10) : exponential growth of running time.

Ab initio motif finding - PWM motifs Local search techniques, e.g., Gibbs sampling Expectation Maximization Greedy

Gibbs sampling: The search space Input: a set of sequences {S 1,S 2,…,S n } Input: motif length l Candidate motif: A set of substrings {s 1,s 2,…,s n }, each of length l, one from each S i. Search space: all possible candidate motifs –O(L n ) where L is length of each S i.

Gibbs sampling: algorithm Consider any candidate motif {s 1,s 2,…,s n },where each s i is of length l Let W  k be the frequency of base  in the k th position of the candidate motif –Pr(s|W) = Let “background” (genome-wide) frequency of nucleotide  be q 

Gibbs sampling: algorithm Let current motif be W t = {s 1,s 2,…,s n } Pick one s i to replace For each substring s’ in S i, replace s i with s’ and compute

Gibbs sampling: algorithm Pick s’ with probability proportional to Pr(s’) as computed Replace s i with s’ to obtain new current motif M t+1 Keep updating motif Report the motif with maximum score