HMMs for alignments & Sequence pattern discovery

I519 Introduction to Bioinformatics

Contents Motifs

– We have seen motifs in regular expression– Profiles & consensus

Motif search– sequence motifs represent critical positions that are

conserved in evolution, so search algorithms employing motifs may be used to identify more divergent sequences than methods based on global sequence similarity

PSI-BLAST (similarity search using PSSM, Position Specific Scoring Matrix)

HMM of protein family (a very brief introduction)

Motifs: Profiles and Consensus a G g t a c T t C c A t a c g tAlignment a c g t T A g t a c g t C c A t C c g t a c g G

A 3 0 1 0 3 1 1 0Profile C 2 4 0 0 1 4 0 0 G 0 1 4 0 0 0 3 1 T 0 0 0 5 1 0 1 4

Consensus A C G T A C G T

Line up the patterns by their start indexes

s = (s1, s2, …, st)

Construct matrix profile with frequencies of each nucleotide in columns

Consensus nucleotide in each position has the highest score in column

Profile Representation of Protein Families

Aligned DNA sequences can be represented by a 4 ·n profile matrix reflecting the frequencies of nucleotides in every aligned position.

Protein family can be represented by a Protein family can be represented by a 20·n profile profile representing frequencies of amino acids.representing frequencies of amino acids.

Profiles and HMMs

HMMs can also be used for aligning a HMMs can also be used for aligning a sequence against a profile representing sequence against a profile representing protein family.protein family.

A A 20·n20·n profile profile PP corresponds to corresponds to n n sequentially linked sequentially linked matchmatch states states MM11,,

…,M…,Mnn in the in the profile HMMprofile HMM of of P.P.

Multiple Alignments and Protein Family Classification

Multiple alignment of a protein family shows variations in conservation along the length of a protein

Example: after aligning many globin proteins, the biologists recognized that the helices region in globins are more conserved than others.

What are Profile HMMs ? A Profile HMM is a probabilistic representation of

a multiple alignment. A given multiple alignment (of a protein family) is

used to build a profile HMM. This model then may be used to find and score

less obvious potential matches of new protein sequences.

Profile HMM

A profile HMMA profile HMM

Building a Profile HMM Multiple alignment is used to construct the HMM

model. Assign each column to a Match state in HMM. Add

Insertion and Deletion state. Estimate the emission probabilities according to

amino acid counts in column. Different positions in the protein will have different emission probabilities.

Estimate the transition probabilities between Match, Deletion and Insertion states

The HMM model gets trained to derive the optimal parameters.

States of Profile HMM Match states Match states MM11……MMnn (plus (plus begin/endbegin/end states) states)

Insertion states Insertion states II00II11……IInn

Deletion states Deletion states DD11……DDnn

Transition Probabilities in Profile HMM

log(alog(aMIMI)+log(a)+log(aIMIM) = ) = gap initiation penaltygap initiation penalty

log(alog(aIIII) = gap extension penaltygap extension penalty

Emission Probabilities in Profile HMM

• Probabilty of emitting a symbol Probabilty of emitting a symbol a a at an at an insertion stateinsertion state I Ijj::

eeIjIj(a) = p(a)(a) = p(a)

where where p(a)p(a) is the frequency of the is the frequency of the occurrence of the symbol occurrence of the symbol a a in all the in all the sequences.sequences.

Profile HMM Alignment Define Define vvMM

jj (i)(i) as the logarithmic likelihood score of as the logarithmic likelihood score of

the best path for matching the best path for matching xx11..x..xii to profile HMM to profile HMM

ending with ending with xxii emitted by the state emitted by the state MMjj..

vvIIj j (i) (i) andand v vDD

j j (i) (i) are defined similarly.are defined similarly.

Profile HMM Alignment: Dynamic Programming

vvMMj-1j-1(i-1) + log(a(i-1) + log(aMMj-1,j-1,MMj j ))

vvMMjj(i) = log (e(i) = log (eMMjj(x(xii)/p(x)/p(xii)) + max v)) + max vII

j-1j-1(i-1) + log(a(i-1) + log(aIIj-1j-1,,MMj j ))

vvDDj-1j-1(i-1) + log(a(i-1) + log(aDDj-1j-1,,MMj j ))

vvMMjj(i-1) + log(a(i-1) + log(aMMjj, I, Ijj))

vvIIjj(i) = log (e(i) = log (eIIjj(x(xii)/p(x)/p(xii)) + max v)) + max vII

jj(i-1) + log(a(i-1) + log(aIIjj, I, Ijj))

vvDDjj(i-1) + log(a(i-1) + log(aDDjj, I, Ijj))

Paths in Edit Graph and Profile HMM

A path through an edit graph and the corresponding path through a profile HMM

Making a Collection of HMM for Protein Families

Use Blast to separate a protein database into families of related proteins

Construct a multiple alignment for each protein family.

Construct a profile HMM model and optimize the parameters of the model (transition and emission probabilities).

Align the target sequence against each HMM to find the best fit between a target sequence and an HMM

Application of Profile HMM to Modeling Globin Proteins

Globins represent a large collection of protein sequences

400 globin sequences were randomly selected from all globins and used to construct a multiple alignment.

Multiple alignment was used to assign an initial HMM

This model then get trained repeatedly with model lengths chosen randomly between 145 to 170, to get an HMM model optimized probabilities.

hmmer package Tools for making HMMs and for hmmscan

hmmer3 (as fast as blast)

Sequence Pattern (Motif) Discovery Finding patterns in multiple alignments, or in

unaligned sequences eMotif (a protein pattern database); eBLOCKs Gibbs and MEME

– To infer patterns in unaligned sequences– Gibbs program starts with a fixed pattern length of W and a

random set of locations of the pattern in given input sequences (i.e., the initial pattern is random); and then one sequence is selected at a time randomly and an attempt is made to improve its pattern position.

– MEME uses many similar concepts, but uses the EM (expectation maximization) method.

Utilization of Multiple Alignments Residue conservation

– Jalview Subfamilies

– SCI-PHY– FunShift

Readings Chapter 6