15-780: Graduate Artificial Intelligence. Computational biology: Sequence alignment and profile HMMs

Transcription

1 5-78: Graduate rtificial Intelligence omputational biology: Sequence alignment and profile HMMs

2 entral dogma DN GGGG transcription mrn UGGUUUGUG translation Protein PEPIDE 2

3 omparison of Different Organisms Genome size Num. of genes E. coli Yeast Worm.5* 8.5* 8 * 8 4,2 6, 8,4 Fly.8* 8 3,6 Human 3* 8 25, Plant.3* 8 25, 3

4 ssigning function to proteins One of the main goals of molecular (and computational) biology. here are 25 human genes and the vast majority of their functions is still unknown Several ways to determine function - Direct experiments (knockout, overexpression) - Interacting partners - 3D structures - Sequence homology Hard Easier 4

5 Function from sequence homology We have a query gene: GGGG Given a database containing genes with known function, our goal is to find similar genes from this database (possibly in another organism) When we find such gene we predict the function of the query gene to be similar to the resulting database gene Problems - How do we determine similarity? 5

6 Sequence analysis techniques major area of research within computational biology. Initially, based on deterministic or heuristic alignment methods More recently, based on probabilistic inference methods 6

7 Sequence analysis raditional - Dynamic programming - Blast Probabilsitic - Profile HMMs 7

8 Pairwise sequence alignment G G G G G G 8

9 Pairwise sequence alignment G G G G We cannot expect the alignments to be perfect. Major reasons include insertion, deletion and substitutions. We need to allow gaps in the resulting alignment. G G 9

10 Scoring lignments lignments can be scored by comparing the resulting alignment to a background (random) model. Independent Related P ( x, y I ) =! q i x i! j q x j P ( x, y M ) =! i p x i y i Score for alignment: S s( x i, y i ) =! i where: s ( a, b) = pa, log( q q a b b )

11 P ( x, y I ) Scoring lignments lignments can be scored by comparing the resulting alignment to a background (random) model. In other Independent words, we are trying to find Related an alignment that maximizes the likelihood ratio of the aligned pair compared to the background model q P ( x, y M ) p =! q i x i! j x j =! i x i y i Score for alignment: S s( x i, y i ) =! i where: s ( a, b) = pa, log( q q a b b )

12 omputing optimal alignment: he Needham-Wuncsh algorithm F(i,j)+s(x i,x j ) F(i,j) = max F(i,j)+d F(i,j)+d d is a penalty for a gap G F(i,j) F(i,j) F(i,j) F(i,j) 2

13 Example ssume a simple model where S(a,b) = if a=b and -5 otherwise. lso, assume that d = G

14 Example ssume a simple model where S(a,b) = if a=b and -5 otherwise. lso, assume that d = G F(i,j)+s(x i,x j ) -5-6 F(i,j) = max F(i,j)+d F(i,j)+d

15 Example ssume a simple model where S(a,b) = if a=b and -5 otherwise. lso, assume that d = G F(i,j)+s(x i,x j ) -5-6 F(i,j) = max F(i,j)+d F(i,j)+d

16 Example ssume a simple model where S(a,b) = if a=b and -5 otherwise. lso, assume that d = G F(i,j)+s(x i,x j ) -5-6 F(i,j) = max F(i,j)+d F(i,j)+d

17 Example ssume a simple model where S(a,b) = if a=b and -5 otherwise. lso, assume that d = G

18 Example ssume a simple model where S(a,b) = if a=b and -5 otherwise. lso, assume that d = G

19 Example ssume a simple model where S(a,b) = if a=b and -5 otherwise. lso, assume that d = G G

20 Running time he running time of an alignment algorithms if O(n 2 ) his doesn t sound too bad, or is it? he time requirement for doing global sequence alignment is too high in many cases. onsider a database with tens of thousands of sequences. Looking through all these sequences for the best alignment is too time consuming. In many cases, a much faster heuristic approach can achieve equally good results. 2

21 BLS: Basic Local lignment Search ool Heuristic alignment method, first presented in 99. he biggest success of computational biology to date. Since it was suggested, a number of new and improved version where presented (psi-bls). urrently available with almost all public databases. 2

22 BLS (cont.) Sequence is composed of a list of words. Uses a dictionary (3 for and for nucleotides). ll matches to database are recorded. 22

23 BLS Hits are extended in both direction if they are less than X bases away from each other. ll sequences reaching a certain score are returned, and a complete alignment is performed. 23

24 24

25 Sequence analysis raditional - Dynamic programming - Blast Probabilsitic - Profile HMMs 25

26 Protein families Proteins can be classified into families (and further into sub families etc.) specific family includes proteins with similar high level functions For example: - ranscription factors - Receptors - Etc. Family assignment is an important first step towards function prediction 26

27 Multiple lignment Process Process of aligning three or more sequences with each other Fine for offline computations We can determine such alignment by generalizing the algorithm to align two sequences What s the complexity of this? 27

28 Multiple lignment: Reasons for differences Substitutions Insertions Deletions 28

29 Biological Motivation: Given a single amino acid target sequence of unknown protein we want to infer the family of the resulting protein. 29

30 Methods for haracterizing a Protein Family Objective: Given a number of related sequences, encapsulate what they have in common in such a way that we can recognize other members of the family. Some standard methods for characterization: Multiple lignments Regular Expressions onsensus Sequences Hidden Markov Models 3

31 Designing HMMs: onsensus (match) states We first include states to output the consensus sequence :.8 :.8 :.8 :.8 :.2 G:.2 :.2 G:.2 3

32 Designing HMMs: Insertions We next add states to allow insertions start.4 :.2 :.4 : G:.2 : :.8 :.8 :.8.4 :.8 :.2 G:.2 :.2 G:.2 32

33 Designing HMMs: Deletions Finally we add states with no output to allow for deletions start O O O.4 :.2 :.4 : G:.2 : :.8 :.8 :.8.4 :.8 :.2 G:.2 :.2 G:.2 33

34 Scoring our simple HMM # - G G G vrs: #2 - HMM: # = Score of -.97 #2 Score of 6.7 (Log odds) 34

35 ligning and raining HMMs raining from a Multiple lignment raining from unaligned sequences ligning a sequence to a model an be used to create an alignment an be used to score a sequence an be used to interpret a sequence 35

36 raining from an existing alignment Start with a predetermined number of states in your HMM. For each position in the model, assign a MLE column in the multiple alignment that is estimates relatively conserved. Emission probabilities are set according to amino acid counts in columns. ransition probabilities are set according to how many sequences make use of a given delete or insert state. 36

37 Remember the simple example hose six positions in model. Highlighted area was selected to be modeled by an insert due to variability. an also do neat tricks for picking length of model, such as model pruning. 37

38 ligning sequences to a model Now that we have a profile model, let s use it! ompute the likelihood of the best set of states for this sequence We know how to do this: he Viterbi algortthm ime: O(N*M) 38

39 So what do we do with an alignment to a model? Design statistical tests to determine how likely it is to get this score from a random (gene) sequence Use several protein family models for classifying new proteins, assign protein to most highly scoring family. 39

40 raining from unaligned Baum-Welch algorithm sequences Start with a model whose length matches the average length of the sequences and with random emission and transition probabilities. lign all the sequences to the model. Use the alignment to alter the emission and transition probabilities Repeat. ontinue until the model stops changing By-product: It produces a multiple alignment 4

41 raining from unaligned continued dvantages: You take full advantage of the expressiveness of your HMM. You might not have a multiple alignment on hand. Disadvantages: HMM training methods are local optimizers, you may not get the best alignment or the best model unless you re very careful. an be alleviated by starting from a logical model instead of a random one. 4

42 Profile HMM Effectiveness Overview dvantages: Very expressive profiling method ransparent method: You can view and interpret the model produced Very effective at detecting remote homologs Disadvantages: Slow full search on a database of 4, sequences can take 5 hours Have to avoid over-fitting and locally optimal models 42

43 Limitations Markov hains Probabilities of states are supposed to be independent P(x) P(y) P(y) must be independent of P(x), and vice versa his usually isn t true 43

44 Protein Structure 44

45 Summary Initial methods for sequence alignment relied on combinatorial and dynamic programming methods. hese methods do not generalize well for multiple sequence alignment and for searching large databases. State of the art methods rely on I techniques, primarily variants of HMMs to overcome this problem. 45

46 46