Whole Genome Assembly

1
Whole Genome Assembly

• The problem biological sequencing is gives
  relatively short fragments (clones) of DNA.
• How the whole genome can be reconstructed?
• Two general approaches were implemented
• clone-by-clone
• shotgun sequencing the one discussed here
• The results were almost identical

2
Mapping using Clones

• Clone
• A large fragment of genomic DNA obtained using
  restriction enzymes
• One can make faithful copies of a clone large
  number of times from a small number of initial
  clones.
• All location information for a clone is assumed
  to be lost. For instance it is not known
• Which chromosome a clone belongs to
• Whether two clones overlap
• What base-pair sequence the clone has etc.

3
Clone Library

• A large set of clones Clone Library is created
• Locations of the clones are assumed to be
  uniformly random distributed
• The sizes of all clone are roughly same.
• G Genome length, L Clone Length,
• N Clones in a library
• Coverage NL/G c
• (c is the expected number of clones covering any
  location of the genome.)
• If the coverage is at least 3 for a base, it is
  assumed to be sure.

4
Clone Library
Genome
Clone Library
Minimal Tiling Path
5
Clone Libraries Commonly Used
6
Example Genome Sizes

• Bacteriophage lambda (virus),
  50,000
• Escherichia Coli (bacterium),
  5,000,000
• Saccharomyces cerevisiae (yeast), 10,000,000
• Caenorhabditis elegans (worm), 100,000,000
• Drosophila melanogaster (fruitfly),
  200,000,000
• Homo sapiens (human), 3,000,000,000

7
Example

• A BAC library for human
• G 3,300 Mb, L 180 Kb, N 96,000
• c NL/G 96 103 180 103/ (3.3 109) 6¼
• 96,000 randomly chosen BACs from the human genome
  provide a 6 library.
• Certain regions of the genome may be difficult to
  clone and hence may not be represented in the
  library.
• A Tiling Path is a subset of clones that
  minimally cover the genome.
• Removal of any clone from the tiling path
  will leave some location of the genome uncovered.

8
Mapping A Single Clone

• Provide a clone with additional information a
  finger print
• Restriction Pattern
• End Sequencing (500 base pairs on each end)
• Probes (Hybridization probes, etc.)
• Restriction Pattern
• Take a clone and completely digest it into small
  pieces (restriction fragments) by a restriction
  enzyme.
• The restriction fragments and their order are
  always the same for that clone.

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• Restriction Patterns are to expansive for large
  genome projects
• Mapping with probes is much cheaper. Probes may
  be short random sequences or extracted from DNA.
• STS (sequence tag sites) are long enough DNA
  pieces so that are unique with very probability.
  Probing is usually done at the ends of clones.

10
Sequence Assembly

• Idealized Assembly with probes can be formalized
  as following problem (assuming no error in the
  read sequence)
• Shortest Common Superstring Problem
• Given a collection of n strings F f1, f2, ,
  fn, find the shortest string that is a
  superstring of every string in F.
  

11
Example

• F actcc, gagca, ccctac, agg
• Each of these is a superstring of everything in F
  (because each contains everything in F as a
  substring)
• actccgagcaccctacagg
• actcccctacaggagca
• aggagcactccctac
• overlaps in bold shortest one is best.

12
About the SCS Problem

• No algorithm is known which is guaranteed to
  find the best solution (i.e. the shortest
  supersrting) in reasonable time for large cases.
• We can never guarantee finding the correct/best
  superstring (all genome construction problems
  are large).
• Thats not all even if we would have a solution
  there are still hard problems

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• Problems of SCS solution
• Does not allow experimental errors need to have
  perfect superstring.
• The orientation of each fragment must be known
  unrealistic.
• May not be the biological solutions if there are
  many long repeats, it is almost impossible to
  reconstruct exact original sequence.

14
Example of the repeats problem

• Real sequence may include
• agactactactactga, and the covering fragments
  may be
• agactactact and actactactga
• which will be collapsed by solving the SCS to
  agactactactga,
• overlapping too many of the act repeats.

15
Fragment Assembly

• Despite the issues, we need to put the fragments
  together somehow so
• Approximate methods are used, which are
  algorithms that try to find good (may be not
  best) solutions quickly.
• Repeats are dealt with by focussing extra
  biotechnology effort to get large sequenced
  fragments (large reads) around certain areas
  which might contain multiple repeats.

16
Overlap multigraphs
A useful data structure for addressing the SCS is
the overlap multigraph of the set of strings.
This is denoted OM(F) for a set of strings
(fragments) F. First, an illustration for the
set of fragments
4
2
maryha
teass
ryhad
hite
2
1
3
1
2
aswhit
lambit
ssnow
tlela
1
3
4
3
2
2
little
yhadali
lelam
1
2
2
tsfle
2
1
4
leecew
ecewas
Edge between two frags is labelled by length of
overlap
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More formally
OM(F) is a directed graph in which we have an
edge from fa to fb whenever there is a nonzero
overlap between the suffix of fa and the prefix
of fb. The edge is labelled with the largest
overlap between them. A Hamiltonian path in a
directed graph is a path which visits every node
in the graph precisely once. Any Hamiltonian
path in an overlap multigraph corresponds to a
superstring. Finally, finding the SCS
corresponds to finding the Hamiltionian path with
maximal weight (adding up the edges on the path)

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Example
4
2
maryha
teass
ryhad
hite
2
1
3
1
2
aswhit
lambit
tlela
1
3
ssnow
4
3
2
2
little
yhadali
lelam
1
2
2
tsfle
2
1
4
leecew
ecewas
The red path is the longest H path in this case,
and leads to the correct sequence. But in genome
sequencing, it is rarely so easy the graph is
immensely larger, and there are very many H
paths.
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How its done

• Basic approach is this (where an edge is start,
  finish)
• 1. build the OM(F) graph
• 2. Sort the edges in ascending order of
  weight, breaking ties randomly
• 3. Iteratively choose the highest weighted
  edge (first in the list) with the following
  properties
• -- does not have finish same as start or
  finish of a previously chosen edge (i.e. does not
  form a cycle)
• -- does not have start same as start of a
  previously chosen edge (i.e. were building a
  path, not a tree) .

20
Reconstruction

• To deal with experimental errors, we need to
  introduce the concept of a distance between
  sequences.
• Substring edit distance the cost of every
  insertion, deletion, or substitution is one unit
  distance. Exception deletions in the
  extremities of the second sequence has no cost.
• If we measure substring edit distances between
  strings, then we can mandate a string S such that
  either f or its reverse complement f must be an
  approximate substring of S at error level e.

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Given a collection F of f strings, and an error
tolerance e between 0 and 1, we need to find the
shortest possible string S such that for every f,
we have dist (f, S) lt ef. Find a string
S as short as possible such that either f (or
its reverse complement) must be an approximate
substring of S at error level e. This means that
we are allowed an average e errors for each base
in f. If e 0.05 we are allowed 5 errors per
hundred bases. Example If a GCGATAG and b
CAGTCGCTGATCGTACG, then the best alignment
is -----GC-GATAG---- CAGTCGCTGATCGTACG
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The next step

• When short reads (few hundreds of bp) are
  assembled into contigs - long sequences by some
  of the techniques they are to be assembled to
  supercontigs (or scaffolds) and places at right
  locations on the genome.

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The order of the whole genome assembly
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Placing the assembly on the genome

• A sequence tag is a short sequence that is unique
  among the whole genome.
• Genetic map contains many sequence tags and their
  locations.
• Align the super contigs to the genome according
  to the tags.

25
Review of WGS

• WGS Whole Genome Shotgun sequencing
• 1. Create clone library
• 2. Assembly the overlapped reads into contigs
• 3. Assembly the contigs into super contigs.
• 4. Align the super contigs to the genome
• 5. Genome Finishing filling the possible gaps
  between supercontigs by additional sequencing