Chapter 6 Profiles and Hidden Markov Models

The following approaches can also be used to identify distantly related members to a family of protein (or DNA) sequences Position-specific scoring matrix (PSSM) Profile Hidden Markov Model These methods work by providing a statistical frame where the probability of residues or nucleotides at specific sequences are tested Thus, in multiple alignments, information on all the members in the alignment is retained.

Position-specific scoring matrices Position Sequence 1A T G T C G Sequence 2A A G A C T Sequence 3T A C T C A Sequence 4C G G A G G Sequence 5 A A C C T G Pos123456Overall Freq. A T G C Pos A T G C Pos A T G C Frequencies of observations in a position Normalised to overall frequencies Converted to log 2

Pos A T G C Match AACTCG to the PSSM matrix: = = ~80 Thus, the sequence AACTCG is 80 times more likely to fit than a random 6 nucleotide sequence

Profiles Profiles are PSSMs that include gap penalty information This is not a trivial problem, and is incorporated in Position specific iterated (PSI) BLAST A normal BLASTP is performed with the query sequence, homologs obtained, and a multiple alignment performed A Profile is based on this alignment The profile is used to search the database again, and a new profile is created by adding in newly identified homologs This process is repeated until no new homologs are identified PSI-BLAST very sensitive approach to search for distant relatives of a family High sensitivity can generate high false positive count Inclusion of false positives can lead to profile drift User can visually inspect each iteration result to decide on inclusion of sequences Typically 3-5 iterations sufficient to identiofy distant homologs

Markov Model and Hidden Markov Model A Markov chain described a series of events or states There is a certain probability to move from one state to the next state This is known as the transition probability Sequences can also be seen as Markov chains where the occurrence of a given nucleotide may depend on the preceding nucleotide Zero order Markov model described a state that is independent of a previous state First order Markov model state is dependent on direct precursor (i.e., di- nucleotide sequences) Second order Markov model, depends on three nucleotides, for example codons Thus frequency of transitions in tri-mers may be different in coding and non- coding regions of the genome The Markov model is therefore applicable to finding genes in genomes In a Markov model all states are observable 1 P 12 2 P 23 3 P 34 4 P 45 5

Hidden Markov model 1 2 2’ 3 3’ 4 4’ 5 P 12 P 23 P 34 P 45 P 12’ P 23’ P 34’ P 45’ A Markov model may consist of observable states and unobservable or “hidden” states The hidden states also affect the outcome of the observed states In a sequence alignment, a gap is an unobserved state that influences to probability of the next nucleotide The probability of going from one state to the next state is called the transition probability In DNA, there are four symbols or states: G, A, T and C (20 in proteins) The probability value associated with each symbol is the emission probability To calculate the probability of a particular path, the transition and emission probabilities of all possible paths have to be considered Begin stateEnd state Observable states Hidden states

A0.80 C0.02 G0.10 T0.08 Emission probability A0.11 C0.08 G0.32 T Transition probability State 1State 2 This particular Markov model has a probability of 0.80 X 0.40 X 0.32 = 0.102to generate the sequence AG This particular model shows that the sequence AT has the highest probability to occur Where do these numbers come from? A Markov model has to be “trained” with examples A simple two state example

Training The frequencies of occurrence of nucleotides in a multiply aligned sequence is used to calculate the emission and transition probabilities of each symbol at each state The trained HMM is then used to test how well a new sequence fits to the model The use a HMM for gaps sequence alignments, a state can either be a match/mismatch (mismatch is low probability match) (observable) Insertion (hidden) Deletion (hidden) B D1 I1 M1 D2 I2 M2 D3 I3 M3 I4 E There is one optimal path from B to E that describes the most probable sequence and the optimal alignment to the multiply aligned sequence family

Viterbi algorithm

Bubblesort indexvalue The algorithm Two loops The outer loop starts at index max-1 and decrements by -1 with every loop The inner loop starts at 0 and increments by +1 to the value of the outer loop Compare values at index and at index+1 in the inner loop If value[index]<value[index+1], swap them Continue until outer loop is 1 max 0 A brief interlude, looking at algorithms…

indexvalue Outer loop = 9 Inner loop = 0 indexvalue Outer loop = 9 Inner loop = 0 indexvalue Outer loop = 9 Inner loop = 0 indexvalue Outer loop = 9 Inner loop = 0 indexvalue Outer loop = 9 Inner loop = 0 indexvalue Outer loop = 9 Inner loop = 0 indexvalue Outer loop = 9 Inner loop = 0 indexvalue Outer loop = 9 Inner loop = 0 indexvalue Outer loop = 9 Inner loop = 0 indexvalue Outer loop = 9 Inner loop = 0 Outerloop=9 Smallest number is now at the bottom

indexvalue Outer loop = 9 Inner loop = 0 indexvalue Outer loop = 9 Inner loop = 0 indexvalue Outer loop = 9 Inner loop = 0 indexvalue Outer loop = 9 Inner loop = 0 indexvalue Outer loop = 9 Inner loop = 0 indexvalue Outer loop = 9 Inner loop = 0 indexvalue Outer loop = 9 Inner loop = 0 indexvalue Outer loop = 9 Inner loop = 0 indexvalue Outer loop = 9 Inner loop = 0 Outerloop=9 Next smallest number is now at the bottom-1

import random def bubblesort(list_of_numbers): for outer_loop in range(len(list_of_numbers)-1, 0, -1): for index in range(outer_loop): if list_of_numbers[index] < list_of_numbers[index + 1]: temporary = list_of_numbers[index] list_of_numbers[index] = list_of_numbers[index + 1] list_of_numbers[index + 1] = temporary return list_of_numbers numbers=range(10) #get a list of numbers from 0 to 9 random.shuffle(numbers) # shuffle the numbers print "In random order: ", numbers print "In order: ", bubblesort(numbers) Python code for Bubblesort algorithm

def qsort2(L): if len(L)<=1: return L pivot=L[0] less= [x for x in L if x<pivot] equal= [x for x in L if x==pivot] greater= [x for x in L if x>pivot] return qsort2(less)+equal+qsort2(greater) Quicksort

Applications of HMMs HMMs include predictive information of insertions and deletions separately Not arbitrary “gap penalties” Once HMMs are trained, can be used to identify distant family members in a database Can be used for protein family classification Advanced gene and promoter prediction Transmembrane protein prediction Protein fold recognition Nucleosome positions HMMer ( suite of linux programshttp://hmmer.wustl.edu/ hmmalign, aligns sequences to an HMM profile.hmmalign hmmbuild, build a hidden Markov model from an alignment.hmmbuild hmmcalibrate, calibrate HMM search statistics.hmmcalibrate hmmconvert, convert between profile HMM file formats.hmmconvert hmmemit, generate sequences from a profile HMM.hmmemit hmmfetch, retrieve specific HMM from an HMM database.hmmfetch hmmindex, create SSI index for an HMM database.hmmindex hmmpfam, search one or more sequences against HMM database.hmmpfam hmmsearch, search a sequence database with a profile HMM.hmmsearch

Chapter 7 Protein Motif and Domain Prediction

A motif is a conserved sequence aa long Eg. Zn-finger motif Domain is aa in length Eg. transmembrane domain Motifs and domains are often evolutionally conserved Useful to identify functions of proteins that should little homology over full sequence Motifs and domains often identified by PSSM and HMMs Motifs or domains can be stored in a database Unknown proteins can be matched to this database to identify motifs and domains and illuminate possible protein fundctions Motifs domains can be stored as regular expression ([ST]-X-[RK]) Or as PSSM or HMMs

Regular expressions E-X(2)-[FHM]-X(4)-{P}-L Invariant Conserved in square [] brackets Disallowed in curly {} brackets Nonspecific shown by X Repetions by number in round () brackets PROSITE ( High number of false negatives Database must be continually updated PSSM, profiles and HMMs incorporate statistical information and are much more accurate

PRINTS Matches smaller regions of a motifs called “fingerprints” to query BLOCKS PSSM or aligned sequences used to define blocks that are larger than motifs ProDom Database generated with PSI-BLAST Pfam Contains HMMs of seeded smaller alignment from SWISSPROT and trEMBL SMART Database of HMMs based on manual structural alignments or PSI- BLAST profiles

Protein family databases COG (Cluster of orthologous groups) All against all comparison of all sequenced genomes If best fit is obtained in prokaryotes, archeae and eukaryotes, defined as cluster Clusters can be searched to identify possible function of unknown protein ProtoNet Pairwise BLAST alignment of all protein sequences in SWISSPROT Query sequence searched against this database

Finding distant/little conserved motifs Expectation Maximization Use predicted alignment of sequences Calculate PSSM Iterate over used sequences and modify PSSM to better fit each in turn Gibbs Motif sampling Use estimated alignment of all but one sequence Calculate PSSM Recalculate PSSM with one left-out sequence Iterate process to convergence setting

Weblogo Graphical representation of the motif sequence Highly conserved residues are shown as larger symbols Ambiguity indicated Helix-turn-helix motif of E. coli CAP family protein