greedy algorithms and genome rearrangements an introduction to bioinformatics algorithms (jones and...

Greedy Algorithms And Genome RearrangementsAn Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Turnip vs. Cabbage: Look and Taste DifferentAlthough cabbages and turnips share a recent common ancestor, they look and taste differentAn Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Turnip vs Cabbage: Comparing Gene Sequences Yields No Evolutionary InformationAn Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Turnip vs Cabbage: Almost Identical mtDNA gene sequencesIn 1980s Jeffrey Palmer studied evolution of plant organelles by comparing mitochondrial genomes of the cabbage and turnip

99% similarity between genes

These surprisingly identical gene sequences differed in gene order

This study helped pave the way to analyzing genome rearrangements in molecular evolutionAn Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Turnip vs Cabbage: Different mtDNA Gene OrderGene order comparison:

An Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Turnip vs Cabbage: Different mtDNA Gene OrderGene order comparison:

An Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Turnip vs Cabbage: Different mtDNA Gene OrderGene order comparison:

An Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Turnip vs Cabbage: Different mtDNA Gene OrderGene order comparison:

An Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Turnip vs Cabbage: Different mtDNA Gene OrderGene order comparison:BeforeAfterEvolution is manifested as the divergence in gene orderAn Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Transforming Cabbage into TurnipAn Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

What are the similarity blocks and how to find them?What is the architecture of the ancestral genome?What is the evolutionary scenario for transforming one genome into the other?Unknown ancestor ~ 75 million years agoMouse (X chrom.)

Human (X chrom.)Genome rearrangementsAn Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

History of Chromosome XRat Consortium, Nature, 2004An Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

A Genetic Anomaly

Reversals

Blocks represent conserved genes.1, 2, 3, 4, 5, 6, 7, 8, 9, 10An Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Reversals132410568971, 2, 3, -8, -7, -6, -5, -4, 9, 10Blocks represent conserved genes.In the course of evolution or in a clinical context, blocks 1,,10 could be misread as 1, 2, 3, -8, -7, -6, -5, -4, 9, 10.An Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Reversals and Breakpoints132410568971, 2, 3, -8, -7, -6, -5, -4, 9, 10The reversion introduced two breakpoints (disruptions in order).An Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Reversals: Example5 ATGCCTGTACTA 33 TACGGACATGAT 55 ATGTACAGGCTA 33 TACATGTCCGAT 5Break and Invert

An Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Types of RearrangementsReversal1 2 3 4 5 61 2 -5 -4 -3 6Translocation1 2 3 4 5 61 2 6 4 5 3 1 2 3 4 5 61 2 3 4 5 6FusionFissionAn Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Comparative Genomic Architectures: Mouse vs Human GenomeHumans and mice have similar genomes, but their genes are ordered differently~245 rearrangementsReversalsFusionsFissionsTranslocation

An Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Waardenburgs Syndrome: Mouse Provides Insight into Human Genetic DisorderWaardenburgs syndrome is characterized by pigmentary dysphasiaGene implicated in the disease was linked to human chromosome 2 but it was not clear where exactly it is located on chromosome 2 An Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Waardenburgs syndrome and splotch miceA breed of mice (with splotch gene) had similar symptoms caused by the same type of gene as in humans

Scientists succeeded in identifying location of gene responsible for disorder in mice

Finding the gene in mice gives clues to where the same gene is located in humansAn Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Comparative Genomic Architecture of Human and Mouse Genomes To locate where corresponding gene is in humans, we have to analyze the relative architecture of human and mouse genomesAn Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Pevzner, P. and Tesler, G. (2003). Human and mouse genomic sequences reveal extensive breakpoint reuse in mammalian evolution. PNAS, 100 (13): 7672-7677.

Reversals: Example p = A B C D E F G H r(3,5)

A B E D C F G H

An Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.infoNote: we will ignore directionality of synteny blocks for the sake of simplicity

Reversals: Example p = A B C D E F G H r(3,5)

A B E D C F G H

r(5,6)

A B E D F C G HAn Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Reversals and Gene OrdersGene order is represented by a permutation p: p = p 1 ------ p i-1 p i p i+1 ------ p j-1 p j p j+1 ----- p n

p 1 ------ p i-1 p j p j-1 ------ p i+1 p i p j+1 ----- pn

Reversal r ( i, j ) reverses (flips) the elements from i to j in p r(i,j)An Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Reversal Distance Problem

Goal: Given two permutations, find the shortest series of reversals that transforms one into another

Input: Permutations p and s

Output: A series of reversals r1,rt transforming p into s, such that t is minimum

t : reversal distance between p and sd(p, s) : smallest possible value of t, given p and s

An Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Sorting By Reversals Problem

Goal: Given a permutation, find a shortest series of reversals that transforms it into the identity permutation (1 2 n )

Input: Permutation p

Output: A series of reversals r1, rt transforming p into the identity permutation such that t is minimum An Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Sorting By Reversals: Examplet =d(p ) = reversal distance of pExample : p = 3 4 2 1 5 6 7 10 9 8 4 3 2 1 5 6 7 10 9 8 4 3 2 1 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 So d(p ) = 3An Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Sorting by reversals: 5 stepsAn Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Sheet1

Step 0: p2-4-35-8-7-61

Step 1:2345-8-7-61

Step 2:23456781

Step 3:2345678-1

Step 4:-8-7-6-5-4-3-2-1

Step 5: g12345678

Step 0:2-4-35-8-7-61

Step 1:2345-8-7-61

Step 2:-5-4-3-2-8-7-61

Step 3:-5-4-3-2-1678

Step 4:12345678

Sheet2

Sheet3

Sorting by reversals: 4 stepsAn Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Sheet1

Step 0:2-4-35-8-7-61

Step 1:2345-8-7-61

Step 2:23456781

Step 3:2345678-1

Step 4:-8-7-6-5-4-3-2-1

Step 5:12345678

Step 0: p2-4-35-8-7-61

Step 1:2345-8-7-61

Step 2:-5-4-3-2-8-7-61

Step 3:-5-4-3-2-1678

Step 4: g12345678

Sheet2

Sheet3

Sorting by reversals: 4 stepsWhat is the minimum reversal distance for this permutation? Can it be sorted in 3 steps? An Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Sheet1

Step 0:2-4-35-8-7-61

Step 1:2345-8-7-61

Step 2:23456781

Step 3:2345678-1

Step 4:-8-7-6-5-4-3-2-1

Step 5:12345678

Step 0: p2-4-35-8-7-61

Step 1:2345-8-7-61

Step 2:-5-4-3-2-8-7-61

Step 3:-5-4-3-2-1678

Step 4: g12345678

Sheet2

Sheet3

Pancake Flipping ProblemThe chef is sloppy; he prepares an unordered stack of pancakes of different sizesThe waiter wants to rearrange them (so that the smallest winds up on top, and so on, down to the largest at the bottom)He does it by flipping over several from the top, repeating this as many times as necessaryChristos Papadimitrou and William Gates flip pancakesAn Introduction to Bioinformatics Algorithms (Jones and Pevzner) www.bioalgorithms.info

Pancake Flipping Problem: Formulation

Goal: Given a stack of n pancakes, what is the minimum number of flips to rearrange them into perfect stack?Input: Permutation pOutput: A series of prefix reversa