A Hidden Markov model for A Hidden Markov model for progressive multiple alignmentprogressive multiple alignment

-Ari Loytynoja and Michel -Ari Loytynoja and Michel C.MilinkovitchC.Milinkovitch

Presnted by Santosh Kumar KodicherlaPresnted by Santosh Kumar Kodicherla

HMM ApplicationsHMM Applications

Hidden Markov Model is used to find optimal Hidden Markov Model is used to find optimal value in many applications like:value in many applications like:

1. In Membrane Helix1. In Membrane Helix

2. In finding a dice whether its Fair dice or 2. In finding a dice whether its Fair dice or

not.not.

3.Decesion tree applications, Neural 3.Decesion tree applications, Neural Networks etc.Networks etc.

Working of HMM for Simple Pair Working of HMM for Simple Pair wise Alignmentwise Alignment

We check The two sequences and built the We check The two sequences and built the unknown parent. (Similarity is maximum).unknown parent. (Similarity is maximum).

This forms the basis for Current Algorithm.This forms the basis for Current Algorithm.

Seq1 Seq2

Parent

Steps in HMM WorksSteps in HMM Works

AlignmentsAlignments

Pairwise AlignmentPairwise Alignment PDGIVTSIGSNLTIACRVS PPLASSSLGATIRLSCTLS

Multiple Alignment Multiple Alignment DREIYGAVGSQVTLHCSFW

TQDERKLLHTTASLRCSLK PAWLTVSEGANATFTCSLS LPDWTVQNGKNLTLQCFAD

LDKKEAIQGGIVRVNCSVP SSFTHLDQGERLNLSCSIP DAQFEVIKGQTIEVRCESI LSSKVVESGEDIVLQCAVN PAVFKDNPTEDVEYCCVAD

Systems and ModelsSystems and Models

Building Multiple alignment with Decreasing Building Multiple alignment with Decreasing Similarity.Similarity.

Compute probabilistic alignmentCompute probabilistic alignment Keep Track of child pointers.Keep Track of child pointers. For each site Vector probabilities of alternate For each site Vector probabilities of alternate

characters A/C/G/T/- is calculated.characters A/C/G/T/- is calculated. New node generated is aligned with another New node generated is aligned with another

internal sequence and cont.internal sequence and cont. Once root node is defined for multiple Once root node is defined for multiple

alignments ,we use recursive back tracking to alignments ,we use recursive back tracking to generate multiple alignments. generate multiple alignments.

Substitution ModelSubstitution Model Consider Seqx, Seqy- generate Seqz(Parent)Consider Seqx, Seqy- generate Seqz(Parent) Terms:Terms: PPaa(X(Xii) –Probability Seq X) –Probability Seq Xii has character ‘ a ‘. has character ‘ a ‘. If a char is observed it is given a prob=1.If a char is observed it is given a prob=1. Character ‘a’ has a background probability qCharacter ‘a’ has a background probability qaa

a Evolves b, this represented as Sa Evolves b, this represented as Sab.ab.

Comparing characters, Substitution.Comparing characters, Substitution.

GAP:GAP: PPxi,yixi,yi= represents prob. X= represents prob. Xii,Y,Yii are aligned and generate Z are aligned and generate Zi.i.

For all the character states ‘a’ in ZFor all the character states ‘a’ in Zk-k-

– pxi ,y j = pzk (xi , y j ) =∑pzk=a(xi , y j ).

pzk=a(xi , y j ) = qa ∑b sab pb(xi ) ∑b sab pb(y j )

Steps in Algorithm:Steps in Algorithm:

1.1. Look back HM Model.Look back HM Model.

2.2. Pair wise alignmentPair wise alignment

3.3. Calculate Posterior Probability.Calculate Posterior Probability.

4.4. Multiple AlignmentMultiple Alignment

5.5. Testing AlgorithmTesting Algorithm

Look back HM Model Look back HM Model – Defines 3 states,Defines 3 states,

Match M, x-insert ,y-insert.Match M, x-insert ,y-insert.

-Calculate probabilities of -Calculate probabilities of Moving from M to X or Y Moving from M to X or Y represented as δ.represented as δ.

-Probability to stay at insert ‘ε ‘.-Probability to stay at insert ‘ε ‘.

-Probability to move back to M.-Probability to move back to M.

Pair wise alignment :Pair wise alignment :

In Dynamic prog, we In Dynamic prog, we define matrix and makes define matrix and makes recursive calls, by recursive calls, by choosing best path.choosing best path.

Use Backtracking to find Use Backtracking to find the best path.the best path.

Veterbi path to get the Veterbi path to get the best alignment path.best alignment path.

Used to find the parent Used to find the parent vector which represents vector which represents both childs.both childs.

Forward and backward recursions.Forward and backward recursions.

Multiple Alignment Observations.Multiple Alignment Observations.

The pair wise algorithm works progressively The pair wise algorithm works progressively from tip of the node to root of tree.from tip of the node to root of tree.

Once root node is defined multiple Once root node is defined multiple alignments can be generated.alignments can be generated.

If a gap is introduced in the process , the If a gap is introduced in the process , the recursive call does not proceed.recursive call does not proceed.

At a given column most of sequences are At a given column most of sequences are well aligned except few which may contain well aligned except few which may contain Gaps.Gaps.

Testing the new AlgorithmTesting the new Algorithm