Comparative Genome Maps

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Comparative Genome Maps

• CSCI 7000-005 Computational Genomics
• Debra Goldberg
• debg_at_hms.harvard.edu

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What is a comparative map?
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Why construct comparative maps?

• Identify isolate genes
• Crops drought resistance, yield, nutrition...
• Human disease genes, drug response,
• Infer ancestral relationships
• Discover principles of evolution
• Chromosome
• Gene family
• key to understanding the human genome

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Why automate?

• Time consuming, laborious
• Needs to be redone frequently
• Codify a common set of principles
• Nadeau and Sankoff warn of arbitrary nature of
  comparative map construction

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Definitions

• Marker identifiable chromosomal locus
• Homology genes with common ancester
• Homeology chromosomal regions derived from a
  common ancestral linkage group
• Synteny loci on the same chromosome
• Colinearity syntenic regions with conserved gene
  order

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Input/Output

• Input
• genetic maps of 2 species
• marker/gene correspondences (homologs)
• Output
• a comparative map
• homeologies identified

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Map construction
Go from this
to this
Maize 1 (target), Rice (base) Wilson et al.
Genetics 1999
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Chromosome labeling
Maize 1 (target), Rice (base) Wilson et al.
Genetics 1999
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A natural model?
Maize 1 (target), Rice (base) Wilson et al.
Genetics 1999
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Scoring
10L
3L
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Assumptions

• Accept published marker order
• All linkage groups of base are unique
• Simplistic homeology criteria
• At least one homeologous region

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A natural model?
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A natural model?
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A natural model?
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A natural model?
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Dynamic programming

• li location of homolog to marker i
• Si,a penalty (score) for an optimal labeling
  of the submap from marker i to the end, when
  labeling begins with label a

a 1 ... i ... n
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Recurrence relation

• Sn,a m ?(a, ln)Si,a m ?(a, li) min
  (Si1,b s ?(a,b) )

a ... n ... ln
b?L
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Problem with linear model

• s 2

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The stack model
d
f
e
c
c
b
b
b
a

• Segment at top of the stack can be
• pushed (remembered), later popped
• replaced
• Push and replace cost s -- pop is free.

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Scoring
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Dynamic programming

• Si,j,a score for an optimal labeling of
• submap from marker i to marker j
• when labeling begins with label a -- i.e.,
  marker i is labeled a

a 1 ... i ... j ... n
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Recurrence relation

• Si,i,a m ?(a, li)
• Si,j,a min
• m ?(a, li) min (Si1,j,b s ?(a,b) )
• min Si,k,a Sk1,j,a

b?L
iltkltj
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Results infers evolutionary events
Wilson et al.
Maize 1 (target) Rice (base)
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Problem Incomplete input

• Gene order not always fully resolved.
• Co-located genes can be ordered to give most
  parsimonious labeling.

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The reordering algorithm

• Uses a compression scheme
• Within a megalocus, group genes by location of
  related gene.
• Order these groups
• First, last groups interact with nearby genes
• Any ordering of internal groups is equally
  parsimonious

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The reordering algorithm
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The reordering algorithm
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Definitions

• ? extended to distance to a set A of labels
• 0 if a ? A,
• 1 otherwise
• S the set of indices of supernode start
  elements
• For simplicity, call supernode i ? S

?(a, A)
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Definitions

• For i ? S
• ni markers in i
• ni(a) markers in i with a homolog on a
• li set of labels matching markers in i
• li a ? L ni(a) ? 1,

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Definitions

• pi(c) gives mismatched marker and segment
  boundary penalties for label c

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Definitions

• p(i,a,b) gives the total mismatched marker and
  segment boundary penalties attributed to hidden
  markers

? (pi(c)) m ?i (a,b) for i?S, a?b p(i,a,b)
? (m ni(c)) m ?i (a,b) for i?S,
ab 0 otherwise.
c ? a,b
c ? a
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Definitions

• For i ? S
• ? i(a,b) labels in a,b without matching
  marker in i
• ? i(a,b) ?(a, li) ?(b, li)
• ? i(a,b) ? 0,1,2

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Definitions

• ?i (a,b) corrects if mismatch marker penalties
  assigned twice for same marker in the recurrence
  and in p(i,a,b)
• For example
• ?i (a,b) 0 if ? i(a,b) 0(if a, b are both
  represented in supernode)
• ?i (a,a) -2 if ? i(a,a) gt 0(if a is not
  represented in supernode)

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Recurrence relation

• Si,i,a m ?(a, li)

Si,j,a min m ?(a, li) min (Si1,j,b s
?(a,b) p(i,a,b)) min Si,k,a Sk1,j,a
b?L
iltkltj k ? S
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Results Fewer mismatches

• stack reordering

Mouse 5 (target) Human (base)
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Results Mismatches placed between segments

• stack reordering

Mouse 8 (target) Human (base)
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Results Detects new segments

• stack reordering

Mouse 13 (target) Human (base)
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Summary

• Finds optimal comparative map
• Arranges markers in most parsimonious way
• First algorithm to use megalocus data
• Fast, objective, simple to use
• Biologically meaningful results

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Summary

• Global view
• Biologically meaningful results
• Provides testable hypotheses
• Robust
• not species-specific
• high/low resolution, genetic/physical maps
• stable to errors in marker order

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Future Directions

• Algorithmic extensions
• 3rd species
• polyploidy
• search for ancient duplications
• Deduce history of evolutionary events
• makes genome rearrangement measures tractable and
  robust
• infer common ancestor

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Future Directions

• Block-segmental sequence comparisons
• non-local sequence alignment
• protein domains
• 2D block-segmental comparisons
• comparison of regulatory networks
• image processing

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Acknowledgments

• NSF
• AAUW
• David and Lucile Packard Foundation
• USDA
• Cooperative State Research Education and
  Extension Service
• ONR

• Jon Kleinberg
• Susan McCouch
• Chris Pelkie
• Sandra Harrington
• Sam Cartinhour
• Dave Schneider