Banana Slug Genomics

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Workaround for broken symlinks on head and children nodes
  - Check assemblies/Pog/map-colorspace-5/Makefile for the workaround
    - explicitly assigns working directory rather than using cwd

  - Kevin has been working on H. Pylori, which is a much more challenging genome than Pog. MAy have developed some new methods for dealing with genome assembly
  - One trick is a method to estimate how frequently a contig appears in a genome.
    - Look at reads/base. For long regions, reads/base is roughly constant.
    - Expect to have more reads/base in repeat regions.
    - This measure is more noisy with smaller regions
  - Estimated gap size is helpful for interpolating smaller contigs between other contigs.
    - Short fragments can fit in regions with large estimated gap size.
  - Biological tricks:
    - c->b->a->b'->d
    - an inversion of b->a->b' turns the scaffold into c->b->a'->b'->d

Burrows-Wheeler Transform (BWT)
  - The algorithm behind bowtie, bwa, soap2 and possibly a few other mapping algorithms.
  - The strength of this is it allows you to map short reads to a large genome rapidly and without alot of memory.
  - Dependent on a reference genome.
  - Indexes the genome and produces a fairly compact genome.
  - The current implementations are all optimized for short reads.
  - The algorithm inherently gets worse as the reads get longer.
  - Longer reads will have to be broken into shorter pieces, indexed the reads separately and piece them back together.

What is the Burrows-Wheeler Transform and where did it come from?
  - Came from data compression.
  - Original idea was to make a string and take an invertible string.
  - The converted string would be much easier to compress than the original string. 
  - Also used for bzip.
  - Example of how BWT works:
    - **Note must, have an end marker at the end of the string**
    - Take the initial string (GOOGOL$) and all rotations:
      - GOOGOL$
      - OOGOL$G
      - OGOL$GO
      - GOL$GOO
      - OL$GOOG
      - L$GOOGO
    - Sort them Lexographically
      - $GOOGOL
      - GOL$GOO
      - GOOGOL$
      - L$GOOGO
      - OGOL$GO
      - OL$GOOG
      - OOGOL$G
    - The BWT is the last column Array **B**
      - **1** $GOOGO**L**
      - **2** GOL$GO**O**
      - **3** GOOGOL**$**
      - **4** L$GOOG**O**
      - **5** OGOL$G**O**
      - **6** OL$GOO**G**
      - **7** OOGOL$**G**
    - How do you invert this thing and get the original string back?
      - You know the all the letters in your original string. You know how to sort them alphabetically.
        - This gives you the first column
      - You know the first and the last are paired together.
        - Take all the pairs you get from putting the first and last column together and reproduce the 2nd column.
    - What is this really representing?
      - You can also keep track of the permutation you did when you did the sorting. The array which maps position in BWT to original sorted array is know as the **S**
        - 0=>**6** $GOOGOL 
        - 1=>**3** GOL$GOO
        - 2=>**0** GOOGOL$
        - 3=>**5** L$GOOGO
        - 4=>**2** OGOL$GO
        - 5=>**4** OL$GOOG
        - 6=>**1** OOGOL$G
      - These numbers are also a method of keeping track of the transform
    - Let's say you have a repeated subsequence
      - Take "GO" for example.
      - All the repeated subsequences are clumped together (0 & 3) **GO**O**GO**L
    - There's another way of looking at this from a computer science perspective
      - Trie
        - The branching structure of the tree
        - The branching is based on the alphabet. The branching factor is the number of letters in your alphabet.
        - BWT is aka a Prefix Trie
        - [Insert Diagram] See the BWA paper for the picture [Fast and Accurate Short read alignment with Burrows-Wheeler Transform, Heng Li and Richard Durbin, bioinformatics 2009]
      - It turns out there is a nice simple correspondence between the trie and the array of numbers in the BWT.
      - Let's say you want to find a subsequence [OG] in the Trie.
        - Invert the string and trace the path back to the first character. Each possibility is a child of that node.
        - The table representation can also find all string starting with [OG] (4,4)
        - Each node in the tree corresponds to a range from the array of the BWT.
        - [GO] has range (1,2)
      - Trie is not stored, but enough data to recalculate the trie is stored.
  - Algorithm
    - C is the number of letters in the first letter of the BWT matrix lexicographically before a. [G=>1,L=>3,O=>4)
    - O(a,i) = # occurrences of letter a within B[0..1]
    - R_(aw) = C(a) + O(a,R_(w)-1)+1, where a is a prefix letter and w is a word. R_ is the lower bound
    - R-(aw) = C(a) + O(a, r-(w), where a is a prefix letter and w is a word. R- is the upper bound
    - Let's see if we can map "GO"
      - R_(nil) = 0
      - R-(nil) = 6
      - R_("O") = c(O) + O("O", -1) +1 = 4
      - R-("O") = c(O) + O("O") + 1 = 6
      - R_("GO") = 
  - Kevin recommends reading the paper. [Fast and Accurate Short read alignment with Burrows-Wheeler Transform, Heng Li and Richard Durbin, bioinformatics 2009]
Banana Slug Genomics

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