May 16. Gene Finding

Transcription

1 Gene Finding

2 j T[j,k] k i Q is a set of states T is a matrix of transition probabilities T[j,k]: probability of moving from state j to state k Σ is a set of symbols e j (S) is the probability of emitting S while in state j. Automaton M=(Q,T, π,σ,e) At 9irst, M goes to initial state j with probability π j In state j, M emits a symbol from Σ according to e j, and moves to state k with probability T[j,k]., 2016

3 k S 1 S i-1 j S i P max (i,j M) = max k P max (i- 1,k) T[k,j] e j (S i ) (Viterbi) P sum (i,j M) = k (P sum (i- 1,k) T[k,j]) e j (S i ), 2016

4 E F (H)=0.5 E L (H)=0.1 M=(Q,T, π,σ,e), 2016

5 E F (H)= E L (H)=0.1 H H T T T is the observed sequence P_max(2,F) e-1 4.5e-2 1.3e-2 5.8e e-2 5.4e-2 1.6e e-3, 2016

6 HMMs allow us to model position speci9ic gap penalties, and allow for automated training to get a good alignment. Patterns/Pro9iles/HMMs allow us to represent families and foucs on key residues Each has its advantages and disadvantages, and needs special algorithms to query ef9iciently.

7 Input: a protein sequence of unknown function. To get function: Compare against a database of protein sequences with known function. Create a database of multiple alignment of diverged family members. Search using patterns such as regular expressions Search using pro9iles Search using HMMs In all cases, search domains, not the entire sequence

8 A number of databases capture proteins (domains) using various representations Each domain is also associated with structure/ function information, parsed from the literature. Each database has speci9ic query mechanisms that allow us to compare our sequences against them, and assign function HMM 3D

9 What is a Gene? 5/16/16 CSE 182

10 In our discussion of BLAST, we alternated between looking at DNA, and protein sequences, treating them as strings. DNA, RNA, and proteins are the 3 important molecules What is the relation between the three?

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12 We de9ine a gene as a location on the genome that codes for proteins. The genic information is used to manufacture proteins through transcription, and translation. There is a unique mapping from triplets to amino- acids 5/16/16 CSE 182

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15 Transcription start ATAGATGATGTACGATGAGAATGTGATTAATG Translation start Donor Acceptor

16 The ribosomal machinery reads mrna. Each triplet is translated into a unique amino- acid until the STOP codon is encountered. There is also a special signal where translation starts, usually at the ATG (M) codon. 5/16/16 CSE 182

17 The ribosomal machinery reads mrna. Each triplet is translated into a unique amino- acid until the STOP codon is encountered. There is also a special signal where translation starts, usually at the ATG (M) codon. Given a DNA sequence, how many ways can you translate it? 5/16/16 CSE 182

18 The gene can lie on any strand (relative to the reference genome) The code can be in one of 3 frames. Frame 1 Frame 2 Frame 3 S R V * W R V Q Y S G * S I V D AGTAGAGTATAGTGGACG TCATCTCATATCACCTGC -ve strand

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20 ATG 5 UTR exon 3 UTR Translation start intron Transcription start Donor splice site 5/16/16 CSE 182 Acceptor

21 Eukaryotic gene de9initions: Location that codes for a protein The transcript sequence(s) that encodes the protein The protein sequence(s) Suppose you want to know all of the genes in an organism. This was a major problem in the 70s. PhDs, and careers were spent isolating a single gene sequence. All of that changed with better reagents and the development of high throughput methods like EST sequencing 5/16/16 CSE 182

22 Proteins are the molecular machinery of the cell. Drugs target proteins, binding to activate/inhibit.

23 Only a few (protein) targets were known in1970s The focus was on designing drugs that interact with the target.

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26 It is possible to extract all of the mrna from a cell. However, mrna is unstable An enzyme called reverse transcriptase is used to make a DNA copy of the RNA. Use DNA polymerase to get a complementary DNA strand. Sequence the (stable) cdna from both ends. This leads to a collection of transcripts/expressed sequences (ESTs). Many might be from the same gene AAAA TTTT AAAA TTTT 5/16/16 CSE 182

27 The expressed transcript (mrna) has a poly- A tail at the end, which can be used as a template for Reverse Transcriptase. This collection of DNA has only the spliced message! It is sampled at random and sequenced from one (3 /5 ) or both ends. Each message is sampled many times. The resulting collection of sequences is called an EST database AAAA TTTT AAAA TTTT 5/16/16 CSE 182

28 Often, reverse transcriptase breaks off early. Why is this a good thing? The 3 end may not have a much coding sequence. We can assemble the 5 end to get more of the coding sequence 5/16/16 CSE 182

29 Newer methods like RNA- seq offer a more comprehensive sampling of the set of transcripts: They can be used for gene 9inding, but, Differences in expression/abundance of transcripts The gene sequence is in small pieces The fragments must still be mapped back to the genome to get the coordinates. There are other features of the gene that are not revealed by transcript sequencing

30 Given Genomic DNA, identify all the coordinates of the gene TRIVIA QUIZ! What is the name of the FIRST gene 9inding program? (google testcode) ATG 5 UTR Translation start intron exon 3 UTR Donor splice site Transcription start Acceptor

31 Given genomic DNA, does it contain a gene (or not)? Key idea: The distributions of nucleotides is different in coding (translated exons) and non- coding regions. Therefore, a statistical test can be used to discriminate between coding and non- coding regions.

32 You are given a collection of exons, and a collection of intergenic sequence. Count the number of occurrences of ATGATG in Introns and Exons. Suppose 1% of the hexamers in Exons are ATGATG Only 0.01% of the hexamers in Intergenic are ATGATG How can you use this idea to 9ind genes?

33 Frequencies (X10-5 ) AAAAAA AAAAAC AAAAAG AAAAAT I E X 5 10 Compute a frequency count for all hexamers. Exons, Intergenic and the sequence X are all vectors in a multi-dimensional space Use this to decide whether a sequence X is exonic/ intergenic.

34 Plot the following vectors E= [10, 20] I = [10, 5] V 3 = [6, 10] V 4 = [9, 15] Is V 3 more like E or more like I? V 3 E 5 I

35 Normalize V = V/ V All vectors have the same length (lie on the unit circle) Next, compute the angle to E, and I. Choose the feature that is closer (smaller angle. β E V 3 I E - score(v 3 ) = α α + β α

36 Fickett and Tung (1992) compared various measures Measures that preserve the triplet frame are the most successful. Genscan uses a 5th order Markov Model

37 Exon Intron AAAAAA 20 1 AAAAAC AAAAAG 5 30 AAAAAT 3.. A AAAAA C AAAAC Tot G AAAAG Pr EXON [AAAAAACGAGAC..] =T[AAAAA,A] T[AAAAA,C] T[AAAAC,G] T[AAACG,A] = (20/78) (50/78).

38 " CodingDifferential[x] = log Pr Exon [x] % $ ' # Pr Intron [x]& The coding differential can be computed as the log odds of the probability that a sequence is an exon vs. and intron. In Genscan, separate transition matrices are trained for each frame, as different frames have different hexamer distributions

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40 Plot the coding score using a sliding window of 9ixed length. The (large) exons will show up reliably. Not enough to predict gene boundaries reliably Coding

41 Signals at exon boundaries are precise but not speci9ic. Coding signals are speci9ic but not precise. When combined they can be effective ATG GT AG Coding

42 We can compute the following: E- score[i,j] I- score[i,j] D- score[i] A- score[i] Goal is to 9ind coordinates that maximize the total score i j

43 Ex: Grail II. Used statistical techniques to combine various signals into a coherent gene structure. It was not easy to train on many parameters. Guigo & Bursett test revealed that accuracy was still very low. Problem with multiple genes in a genomic region

44 An HMM is the best way to model and optimize the combination of signals Here, we will use a simpler approach which is essentially the same as the Viterbi algorithm for HMMs, but without the formalism.

45 i 1 i 2 i 3 i 4 IIIIIEEEEEEIIIIIIEEEEEEIIIIEEEEEE IIIII Identifying a gene is equivalent to labeling each nucleotide as E/I/intergenic etc. These labels are the hidden states For simplicity, consider only two states E and I

46 i 1 i 2 i 3 i 4 IIIIIEEEEEEIIIIIIEEEEEEIIIIEEEEEE IIIII Given a labeling L, we can score it as I- score[0..i 1-1] + E- score[i 1..i 2 ] + D- score[i 2 +1] + I- score[i i 3-1] + A- score[i 3-1] + E- score[i 3..i 4 ] +. Goal is to compute a labeling with maximum score.

47 De9ine V E (i) = Best score of a labeling of the pre9ix 1..i such that the i- th position is labeled E De9ine V I (i) = Best score of a labeling of the pre9ix 1..i such that the i- th position is labeled I Why is it enough to compute V E (i) & V I (i)?

48 # E_score[ j i] + V V E (i) = max I ( j 1) j<i $ % +A_score[ j 1]} j i # I_score[ j..i] + V V I (i) = max E ( j 1) j<i $ % +D_score[ j]} j i

49 Note that we deal with two states, and consider all paths that move between the two states. E I i

50 We did not deal with the boundary cases in the recurrence. Instead of labeling with two states, we can label with multiple states, E init, E 9in, E mid, I, I G (intergenic) I G I Note: all links are not shown here E fin E mid E init

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52 Gene 9inding can be interpreted as a d.p. approach that threads genomic sequence through the states of a gene HMM. E init, E 9in, E mid, I, I G (intergenic) I G I E fin Note: all links are not shown here E mid E init i

53 A probabilistic model for each of the states (ex: Exon, Splice site) needs to be described In standard HMMs, there is an exponential distribution on the duration of time spent in a state. This is violated by many states of the gene structure HMM. Solution is to model these using generalized HMMs.

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55 Each state also emits a duration for which it will cycle in the same state. The time is generated according to a random process that depends on the state.

56 q k j i F k (i) = P q k (X j,i ) f qk ( j i +1) a lk j<i l Q F l ( j) Duration Prob.: Probability that you stayed in state q k for j-i+1 steps Emission Prob.: Probability that you emitted X i..x j in state q k (given by the 5th order markov model) Forward Prob: Probability that you emitted i symbols and ended up in state q k

57 Various signals distinguish coding regions from non- coding HMMs are a reasonable model for Gene structures, and provide a uniform method for combining various signals. Further improvement may come from improved signal detection

58 Coding versus non- coding Splice Signals Translation start ATG 5 UTR exon 3 UTR Translation start intron Transcription start Donor splice site Acceptor

59 The donor site marks the junction where an exon ends, and an intron begins. For gene 9inding, we are interested in computing a probability D[i] = Prob[Donor site at position i] Approach: Collect a large number of donor sites, align, and look for a signal.

60 Fixed length for the splice signal. Each position is generated independently according to a distribution Figure shows data from > 1200 donor sites AAGGTGAGT CCGGTAAGT GAGGTGAGG TAGGTAAGG

61 Various signals distinguish coding regions from non- coding HMMs are a reasonable model for Gene structures, and provide a uniform method for combining various signals. Further improvement may come from improved signal detection

62 Nature Science

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64 Gene prediction is harder with alternative splicing. One approach might be to use comparative methods to detect genes Given a similar mrna/protein (from another species, perhaps?), can you 9ind the best parse of a genomic sequence that matches that target sequence Yes, with a variant on alignment algorithms that penalize separately for introns, versus other gaps.

65 Pr[GGTA] is a donor site? 0.5*0.5 Pr[CGTA] is a donor site? 0.5*0.5 Is something wrong with this explanation? GGTA GGTA GGTA GGTA CGTG CGTG CGTG CGTG

66 PWMs do not capture correlations between positions Many position pairs in the Donor signal are correlated

67 Choose the position i which has the highest correlation score. Split sequences into two: those which have the consensus at position i, and the remaining. Recurse until <Terminating conditions> Stop if #sequences is small enough

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69 Various signals distinguish coding regions from non- coding HMMs are a reasonable model for Gene structures, and provide a uniform method for combining various signals. Further improvement may come from improved signal detection

70 Nature Science

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72 Gene prediction is harder with alternative splicing. One approach might be to use comparative methods to detect genes Given a similar mrna/protein (from another species, perhaps?), can you 9ind the best parse of a genomic sequence that matches that target sequence Yes, with a variant on alignment algorithms that penalize separately for introns, versus other gaps.

73 Procrustes/Sim4: mrna vs. genomic Genewise: proteins versus genomic CEM: genomic versus genomic Twinscan: Combines comparative and de novo approach. Mass Spec related? Later in the class we will consider mass spectrometry data. Can we use this data to identify genes in eukaryotic genomes? (Research project)

74 RefSeq and other databases maintain sequences of full- length transcripts/ genes. We can query using sequence.

75 Sequence Comparison (BLAST & other tools) Protein Motifs: Pro9iles/Regular Expression/ HMMs Discovering protein coding genes Gene 9inding HMMs DNA signals (splice signals) How is the genomic sequence itself obtained? ESTs Gene finding Protein sequence analysis