Gribskov Profile. Hidden Markov Models. Building a Hidden Markov Model #$ %&

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3 Gribskov Profile #$ %& Hidden Markov Models Building a Hidden Markov Model "!

4 Proteins, DNA and other genomic features can be classified into families of related sequences and structures How to detect these similarities: & Related sequences can diverge beyond recognition with standard sequence comparison methods $ %& %&

5 What is a Gribskov Profile?! " POS A C D E F G H L S T Y Gap

6 Differences between Gribskov Profiles and common sequence comparison methods ' (

7 What is needed to create a Gribskov Profile? 1 seq1.pep ~CCGTL seq2.pep GCGSL~ seq3.pep ~CGHSV seq4.pep ~CGGTL seq5.pep CCGSS~ $ ) * +,,-. '

8 ( */01,2# 1 seq1.pep ~CCGTL seq2.pep GCGSL~ seq3.pep ~CGHSV seq4.pep ~CGGTL seq5.pep CCGSS~,. 2 A C D E. W Y Gap 2,

9 The profile is filled using the * 20 M (p,a) = b=1 W (p,b) * Y (a,b) W (p,b) = n(b,p)/ N R Y (a,b) 8 6 * /01 /0#1 78 /081 9: /#081 5!

10 A B C D E F G H I K L M N P Q R S T V W X Y Z A 4 B -2 6 C D E F G H I K L M N P Q R S T V W X Y Z W C #$%!

11 The profile is filled using the * 20 M (p,a) = b=1 W (p,b) * Y (a,b) W (p,b) = n(b,p)/ N R Y (a,b) 8 6 * /01 5! /0#1 78 /081 9: /#081 : /#081 7(,

12 20 M (p,a) = b=1 W (p,b) * Y (a,b) M (1,A) = b=1 W (1,b) * Y (A,b) M (1,A) = ( W (1,A) * Y (A,A) ) + (W (1,C) * Y (A,C) ) ++ ( W (1, Y) *Y (A,Y) ) 1 seq1.pep ~CCGTL seq2.pep GCGSL~ seq3.pep ~CGHSV seq4.pep ~CGGTL seq5.pep CCGSS~ M (1,A) = ( 0.025/6 * 4) + ( 1/6 * 0 ) ++ ( 0.025/6 * -1) M (1,C) = b=1 W (1,b) * Y (C,b) &.0.,-;5! &''()* POS A C D E F G H L S T Y Gap

13 &''()* +&''()*,+ - &'*9 + % &'*9+ &*9 +. &*9 + / &(*0+ $ &)* 1 seq1.pep ~CCGTL seq2.pep GCGSL~ seq3.pep ~CGHSV seq4.pep ~CGGTL seq5.pep CCGSS~ /##$$'<17 2 /#1=, /#1= 3 /$1= 4 /$1= - /'1= + /<1 Probability of any sequence is calculated in the same way POS A C D E F G H L S T Y Gap

14 Gribskov Profile #$ %& Hidden Markov Models Building a Hidden Markov Model "!

15 Markov Models are probabilistic, models, with a solid statistical foundation In contrast to patterns and profiles, HMMs allow consistent treatment of insertions and deletions C P=0.6 P=0.1 P=0.2 P=0.09 P=0.01 A T G C - In contrast to patterns and profiles, Markov Models take into account the information about neighboring residues.

16 Domain 1 (active binding site) ATGTCGTCGTCG Domain 2 (never found, inactive) ATGTGGTCGTCG Domain 3 (never found, inactive) Domain 4 (active) ATGTCATCGTCG ATGTGATCGTCG Markov Model is based on active domains only!! )$ 30/' )' 40 /#1-7.-0/$1-7.- )# -0 / /$ )$ -0/ /$ )$ +0/'1 > 72. ) +0/'1 > 72.

17 Markov Models take into account additional information about neighboring residues. First order Markov Model Fifth order Markov Model # 0 ' /?1

18 !! Gene finding Protein secondary structure prediction Protein homology recognition Phylogenetic analysis Radiation hybrid mapping Profile HMM libraries Genetic linkage mapping &# ) 5#2-339* & "2-33$* &1 "2-333* &4 5'2-33$* &< "2-336* &+:;<=(>7+ * &1 "2-33$*

19 -2- %2% -2% %2 > + - &* + - & * + % &* + % & * ; +&?8@@*, + - &* & * -2% + % &* %2

20 "3 "3 < -" "- -" "- > +,&"%/* + ',&"%/* +,&"%/* + (,&"%/* +,&"/* + ',&* +,&"3/* + (,&* +,&".* + ',&"-* +,&"-* + (,&".*

21 Markov Models assume that sequences are generated independently of the model Applied to time series or to linear sequences

22 ! < - % > - % 2 # A C D E F G H I... Y, # A C D E F G H I... Y 3 : A C D E F G H I... Y

23 ! < - % > - % 2 #, # 3 : )

24 ! < - % > - % 2 #, # 3 : ' 0

25 "! P(sequence) is the product of the emission and transition probabilities Any sequence can be represented by a path through the model ##: < > A C C C Y Y

26 " ##: +&*,".0" >3..+. # : +&'*,".$0"- +&*"""""" <.3.4@.4@.3> #.-.4+ # A> A> :., > > /##: A> > Different state paths through the model can generate the same sequence Correct probability of a sequence <

27 " Forward Algorithm + This solution is computationally unfeasible for long sequences & Viterbi Algorithm '

28 # $ &7. * <.3.4@.4@.3> > A.3.4+ #..2.4@.- #..2-.A > #.-.4 A A> :.,3.4@ : 2.> > # # : ).)22),,)33 +&''A* /1 )B , 2 "-% /#1 ) , 3 4 "-/ ".$ "% "- "%% /# /#1, ,3 /:1 ) > /:1 3 7.A>9.,37.,, +&''A*,+&* =; 0+&'* =- 0+&*

29 % # <..- +&''A*,+&* &'* % 0 +&'*..+ 0+&A*..> A.3.4+ #..2.4@ #.- /##:17/1 )B 9C/#1 )2 =/#1 2 D9 /#1, 9C/:1 ), =/:1, D..2-.A> A A> :.,3.4@ : 2.> > /1 2 7/1 ). /#1, 7/#1 )2 =/#1 2 /#1 3 7/#1, /#1, 7.-C/#1 )2 )20, =/#1 2 20, D /:1 4 7/:1 )3 =/:1 3 /:1 )3 7..2C/#1, 9, ) D /:1 3 7.,3C/#1, 9, D

30 $ The score that a sequence obtains with an HMM measures the probability of that sequence to belong to a family, group, class. Global scoring Local scoring The alignment type is part of the model and must be specified before creating the HMM and not when using it

31 <B#EF GH ""F G H B "!, 0

32 Gribskov Profile #$ %& Hidden Markov Models Building an Hidden Markov Model "!

33 HMM can be estimated from sequences Sequences used to estimate or train the model are called Training data 1 seq1.pep ~CCGTL seq2.pep GCGSL~ seq3.pep ~CGHSV seq4.pep ~CGGTL seq5.pep CCGSS~

34 $ Model overspecialization ) 0 &( Solutions Sequence weighting 2crd XFTNVSCTTSKECWSVCKRLHNTSGRGKCMCMK 1bah XFTNVSXTTSKECWSVCQRLHNTSGRGKCMXMK 1sxm TIINVKCTSPKQCSKPCKELYGSSAGaKCMNGK 1lir XFTQESCTASNQCWSICRRLHNTNRG.KCMNSK 2mbt XFTNVSCSASSQCWPVCKKLFGTYRG.KCINGK % $& * (

35 $ Solutions Model overspecialization Sequence weighting based on tree structures ), ##8 $##8 ). & ) 3 6##8 ) - ) 4 ) + ##: 6##I6##: ) 2 ##8 & & )7)2=), ),7)3=)4 )27),7.-9). )37.-9),7.,-9).

36 $ Solutions Model overspecialization Maximum discrimination weighting 8 & 0 & )*0 ' &

37 $ Model overspecialization Position-specific weighting method (Henikoff) 8 & 5 %5 872;9% 8 ' & : ' ; +. B.- "-%/"/ + / C>.- "-%/"/ 2crd XFTNVSCTTSKECWSVCQRLHNT 1bah XFTNVSXTTSKECWSVCQRLHNT 1sxm TIINVKCTSPKQCSKPCKELYGS 1lir XFTQESCTASNQCWSICRRLHNT 2mbt XFTNVSCSASSQCWPVCKKLFGT

38 $ Overfitting caused by insufficient training data ' '2A. <IE<$$!"6"6EI:5 <IE<$$!"6"6EI:5 <I"J<$$J6J6'JI: ):E)$$")"666"I:6! K Solutions Regularization using prior information B K 2 B & ' & = = ' & 4=2 4=,. <2.=2 4=,.

39 To build an HMM it is necessary to estimate (( E5B85 1 seq1.pep ~CCGTL seq2.pep GCGSL~ seq3.pep ~CGHSV seq4.pep ~CGGTL seq5.pep CCGSS~ *

40 but usually 5B'E5B85 L K &&

41 & Baum-Welch Algorithm Iterative algorithm which maximizes the probability of the training sequences in the model Maximizes the likelihood of the model That it is the joint probability of all sequences in the training set given a particular set of parameters

42 $'( $ 1- INITIALIZATION STEP Arbitrary model parameters Convergence 2- FORWARD AND BACKWARDS ALGORITHM Calculate all emission and transition probabilities in all possible paths using the existing parameters. Calculate f k (i) and b k (i) * greater variation new parameters that maximize the probabilities of the training sequences little variation 3- EXPECTED VALUES Calculate the expected number of times each transition [A kl kl ] or emission [E k (b)] is used given the training sequence and using f k (i) and b k (i) 5- Log LIKELIHOOD Calculation of the model likelihood with these new parameters. 4- NEW MODEL PARAMETERS Calculate new transitions and emission values using the the expected A kl kl and E k (b)

43 $ Avoid a local maximum Solutions Use of heuristic methods & & * ' ' ' &

44 !! Gene finding Protein secondary structure prediction Protein homology recognition Phylogenetic analysis Radiation hybrid mapping Profile HMM libraries Genetic linkage mapping &# ) 5#2-339* & "2-33$* &1 "2-333* &4 5'2-33$* &< "2-336* &+:;<=(>7+ * &1 "2-33$*

45 ! HMM DO NOT deal well with correlations between residues, because they assume that each residue depends only on one underlying state. Example: prediction of RNA secondary structure Conserved RNA base pairs induce long-range pairwise correlations; one position might be any residue, but the base-paired partner must be complementary. An HMM state path has no way of 'remembering' what a distant state generated.

46 For gene finding several signals must be recognized and combined into a prediction of exons and introns < < + 2 """ :D :D! #

47 An HMM for unspliced genes x xxxxxxxxatgccc ccc ccctaaxxxxxxxx Four models are combined together using Viterbi algorithm to find the most probable pathway

48 An HMM for spliced genes!! needed to use three different models of introns for each reading frame (

49 An HMM for spliced genes * * CCC GTxxxxxx interior intron xxxxxxag CCC 3 CCC C GTxxxxxx interior intron xxxxxxag CC CCC 4 - CCC CC GTxxxxxx interior intron xxxxxxag C CCC - 4 ### All models are combined together using the Viterbi algorithm to find the most probable pathway

50 !$ HMMalign HMMBuild HMMconvert HMMemit TMhmm Genescan HMM scan HMMsearch! ) %&! #))& $ % * ) K 5 & %&

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52 & 8& 4M 8K I "*( I

53 & #< '<8 Let s create a profile Hidden Markov model from our group of aligned sequences. hmmbuild HmmerBuild

54 &

55 !$ )* ProfileMake ' ProfileGap ProfileSearch ' E N8 5 N8 ProfileSegments +< TProfileGap TProfileSearch $ TProfileSegments

56 E5B85 * e k (b) = E k (b)/ b E k (b ) * % The expected transition probability is calculated in the same way / 1 a kl (b)=a kl (b)/ l E kl (b )

57 % 4 C!D + P(x)= π ( x, π) ( f k (i) = P(x 1 x i., π i = k) % x i,f+&!*!

58 $ What if.. G!,F+ 4 P(x, π i = k)= P(x 1 x i., π i = k) P(x 1+1 x L π i = k) f k (i) b k (i) ( + P(π i = k x)= f k (i) b k (i) / P(x)