“Multiple indexes and multiple alignments” Presenting:Siddharth Jonathan Scribing:Susan Tang...

“Multiple indexes and multiple alignments”

Presenting: Siddharth Jonathan

Scribing: Susan Tang

DFLW: Neda Nategh

Upcoming:

10/24: “Evolution of Multidomain Proteins” Wissam Kazan

“Human Migrations” Anjalee Sujanani

10/26: “Comparison of Networks Across Species” Chuan Sheng Foo

“Repetitive DNA Detection and Classification”Vijay Krishnan

CS374 Presentation - Searching Biological Sequence Databases 2

CS374Algorithms in Biology

Searching Biological Sequence Databases

Siddharth Jonathan

Outline

• Background

• Problem

• Typhon Overview

• Typhon Components

• Results

Background

• Sequence Alignment

• Multiple Alignment Databases

• Probabilistic Profile

• Phylogenetic Tree

Sequence Alignment

• Identifying regions of similarity in the genome, proteins etc.

• Types– Global– Local

• Seeded• Non-seeded

• Why is it important?– Comparative analysis of genomes– Producing Phylogenetic trees– Understanding newly sequenced genomes

Seeds – A Review

A seed, P = a set of ordered list of w positions

i.e. P = {x1, x2, …, xw} w = weight of P = |P|

s = span of P = xw – x1 + 1

Ex:P = {0, 1, 4, 5}

w = 4s = 5 – 0 + 1 = 6

Indexing in Seeded Local Alignment algorithms

…G A T T A C C A G A T T A C C A G A T T A …

Gene Sequence S

Seed A = {0,1,2,3}

GATT S,0

ATTA S,1

The same idea holds for non-contiguous seeds as well!

Average number of seeds indexed per position is called the Budget

Seeded Local Alignment Algorithms

• BLAST

• BLAT

• BLASTZ

• Exonerate

• Usage of multiple seeds, spaced seeds

• What do they have in common?

• Indexing!

Multiple alignmentSpecies 1Species 2

Phylogenetic Tree

Probabilistic Profile

Each cell corresponds to one position in the alignment…

We’ll learn what information it carries very shortly!

Regions

The Problem

Say, we have a database of multiple alignments

So what’s the challenge?

Find local alignments for the query

Candidate seeds

The Problem Statement

Budget

Can we do better?

Make use of information implicit in multiple alignment for

selecting which seeds to index for a given position

The Problem Statement - Typhon

Probabilistic Profile Candidate Seeds

Budget

Indexing Scheme that indexes only a subset of candidate seeds at each position

Overall Architecture of Typhon

Step 1: Probabilistic Profile Construction

• 6 tuple for each position in the multiple alignment

• Ppresent – existence probability

• PA

• PC

• PT

• PG

• Pid – Probability that the corresponding query position has the consensus character

Conditional Probability that the homologous position contains A,C,T,G given that a homologous position exists.

Nucleotide with highest such value is called the consensus character

Calculation of Probabilistic Profile

PPresent=100%

PA=75%

PC=25%

Propagation of values up the tree to the root is a tricky problem!

Calculating probabilistic profile

• PPresent and PN calculated independently• PPresent Weighted average of children’s

PPresent values.• Weights proportional to the inverse of the

branch length• PN calculated through Felsentein’s

algorithm with a Kimura Matrix • Pid = max(PN) (This is calculated at the root)

Region Decomposition

ATTGGAACCCAGGCCA----AATT-GCGCC-----AA-TT------G----C-----ATGG-G-----ATGCCCAAAAAAT

ATTGGAACTCAGGCCA----AATT--CGCC-----AA-T-------G----C-----AT--G------ATGCCCATAAAAT

ATTGGAACCCAGGCCA----AATT-CG--C-----A-TT-------G----T-----A-GGG------ATGCCCAAAAAAT

ATTGGAACCCAGGCCA----A-TTGC-G-C-----AAT-T------G-----C----ATGGGG-----ATGCCCATAAAAT

1 2 3 2 1

Each region is characterized by a PPresent and a Pid

How do we come up with these regions?

Hidden Markov Models (HMM)

Given an observation sequence

Predict the sequence of Hidden states

Region Decomposition – Simple Method

• Come up with a set of region classes (states)

• Construct an HMM

• Looking at the observation sequence, try to determine the most likely parse– Viterbi algorithm

• Problem – Need to determine classes at the beginning

Alternative

• Split the Profile into 2 classes at a time

• Use 2 stage HMM

• Stop until bound on number of region classes is reached

Region Decomposition with HMM

Step 3: Seed Indexing

What are we trying to do?

1 2 1 3

Candidate Seeds

A D C B C E D

The Goal

• Maximize expected number of regions matched to a homologue

Seed Assignment

• 2 Approaches:– General Method– Greedy Approximation

General Method - Terminology

Region Classes

Size of the candidate set

Object[i][j]

Calculation of number of matching regions(done for each cell in the previous table)

Probability that a region matches a homologue

Conditional Probability that the seeds match the region and its homologue

given that it exists

Number of regionsX X

‘PPresentPhit |C|

General Method - Explained

PPresent* P1

hit * |C|PPresent* P2

hit * |C|

PPresent* P1

hit * |C|

PPresent* P1

hit * |C|

PPresent* P1

hit * |C|

Region Class 1

Region Class 2

Region Class 3

Region Class 4

Number of Candidate Seeds

1 2 3 4 5

Some Terminology

• Weight– Total Length of all regions in a region class *

# of seeds indexed at each position– Sort of like the Budget for a region

• Value– Expected Number of Regions matched.

(previous calculation)

Solving the Seed Assignment Problem

PPresent* P1

hit * |C|

PPresent* P1

hit * |C|

PPresent* P1

hit * |C|

PPresent* P1

hit * |C|

Region Class 1

Region Class 2

Region Class 3

Region Class 4

1 2 3 4 5

Solving the Seed Assignment Problem

Weight, Value

Region Class 1

Region Class 2

Region Class 3

Region Class 4

1 2 3 4 5

Solving the Seed Assignment ProblemBudget =112

Weight, Value

Region Class 1

Region Class 2

Region Class 3

Region Class 4

1 2 3 4 5

Looks Familiar?

• Closely related to the Knapsack Problem, a well studied problem in Computer Science

Approximate Solution

• Faster

• Space Efficient

• New Terminology : – Density of an object = Value/Weight

Approximate Solution – General Intuition

• Select objects in order of decreasing density

• Disallow more than one object per row

Approximate Method in Action

Candidate Set

Object[1,1]

Density=V/W=3

Object[2,1]

Density=V/W=2

Object[3,1]

Density=V/W=5

Object[4,1]

Density=V/W=4

Object[3,2]

Density=V/W=6

What are the new values of Weight, Value and Density?

Value = additional number of regions matched

Weight = amount of budget used by this one seed.

And keep track of the Budget!

Results

• Considerations– Sensitivity– Speed– Space

Sensitivity Results

• Experimental Setup

• Detection of Hypothetical Homologous Alignments (HHA)

• Typhon Vs Standard

Sensitivity Comparison

Effect of Multiple Alignment on Sensitivity

Running time Comparison

• Time spent building the index– Typhon takes longer

• Time spent scanning the index

• Typhon 3-4 times slower at run time which is reasonable

Scanning time

Conclusion

• Information implicit from Multiple Alignments helps search sensitivity

• Variable allocation of seeds by region classes helps (Typhon)

• Space and time complexities of Typhon comparable to STANDARD

• Most effective for queries far from each species in the alignment

Questions?

Acknowledgements

• Serafim Batzoglou , George Asimenos , Jason Flannick

“Multiple indexes and multiple alignments” Presenting:Siddharth Jonathan Scribing:Susan Tang...

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