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Short Read Mapper

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Short Read Mapper

Brian S. Lam

CS124

- Biological Motivation
- Computer Science Problem
- Trivial Solution
- Hash Index Solution
- Future Direction

- Biological Motivation
- Computer Science Problem
- Trivial Solution
- Hash Index Solution
- Future Direction

- Goal: read the DNA sequence of an individual
- 2 types of methods
- Full Genome Sequencing (FGS): reads the entire DNA sequence at once
- Shotgun sequencing: divides DNA into many short reads, and then a computer program reassembles them

- Shotgun sequencing sounds more complicated, why use it?
- Faster
- Cheaper

- However, there are downsides:
- We have to reassemble the short reads
- We must have a reference genomewhich is similar to the one we’re sequencing

- Q: How do we reassemble the short reads?
- They are randomly ordered
- They will not exactly match the reference genome

- Basically like doing a puzzle, but sometimes the pieces don’t fit

- Q: How do we reassemble the short reads?
- A: Re-sequencing
- Assume that the difference between the reference genome and our reads is very small
- Find the “best fit” position for each short read

- Complications:
- Mutations (i.e. SNPs)
- Read errors
- Insertions, deletions, repeated regions

- Biological Motivation
- Computer Science Problem
- Trivial Solution
- Hash Index Solution
- Future Direction

- We can ignore the biology, and this becomes substring mapping problem
- Allow a certain number of mismatches to account for SNPs
- Ignore other complications such as read errors, insertions, deletions, repeated regions, etc.
- This is for simplicity

- Problem Layout

…

T

C

A

G

A

A

G

A

Short read length L

- Allow up to D mismatches per short read

- Assumptions
- There are at most D mutations in any substring of length L
- Any 2 substrings of length L in our sequence differ by at least 2Dpositions

- What this means:
- All short reads will map to exactly ONE position

- Biological Motivation
- Computer Science Problem
- Trivial Solution
- Hash Index Solution
- Future Direction

Algorithm

For each short read, slide across reference genome until we find a position with < D mismatches

- Easy to explain, easy to code

T

C

A

G

A

A

G

A

A

T

A

A

Example: Let L = 4, D = 2

Reference:

Short Read:

3 mismatches

T

C

A

G

A

A

G

A

A

T

A

A

Example: Let L = 4, D = 2

Reference:

Short Read:

3 mismatches

T

C

A

G

A

A

G

A

A

T

A

A

Example: Let L = 4, D = 2

Reference:

Short Read:

1 mismatch

SNP

1 < D, so this is the correct position, and the second base in the short read is a SNP

However, simplicity has its cost…

?

This is way too slow!

- Biological Motivation
- Computer Science Problem
- Trivial Solution
- Hash Index Solution
- Future Direction

- Idea: If we allow D mismatches, and we break the short read into D+1 pieces, then there is at least one piece that will match perfectly

Algorithm

- Store the index of each substring of length L/(D+1) in a hash index
- Break short reads into pieces of length L/(D+1), and look up possible matching indices in hash index
- Use trivial algorithm to check whether the short read actually matches this position

- Harder to explain, harder to code

- Hashing Function
- We want every substring to map to a unique key
- There are four bases: A, C, G, andT
- If we interpret the string as a base-4 number, we get a unique mapping
- Let A = 0, C = 1, G = 2, T = 3

Hashing Function Example

TGCA → 32104 →

3 x 43

+ 2 x 42

+ 1 x 41

+ 0 x 40

228

This is our key into the hash index

Hashing Function Example

TGCA → 32104 →

3 x 43

+ 2 x 42

+ 1 x 41

+ 0 x 40

228

Step 1) Populating the Hash Index

- Calculate the key length based on the short read length (L) and number of allowed mismatches (D)
- Add index of every substring of key length in the reference genome to the hash index

Hash Index Example

- Assume key length is 4, and reference genome starts with TGCA
- From the example, key(TGCA) = 228

0

1

…

228

229

…

0

Hash Index Example

- Assume key length is 4, and reference genome starts with TGCA
- From the example, key(TGCA) = 228

0

1

…

index

next

228

229

…

Step 2) Break short reads into pieces and look up possible matching indices in hash index

Step 2) Break short reads into pieces and look up possible matching indices in hash index

Example

Short Read: TCGAAACTGAGT

TCGA

AACT

GAGT

Step 2) Break short reads into pieces and look up possible matching indices in hash index

Example

Short Read: TCGAAACTGAGT

TCGA

AACT

GAGT

Look these key values up in the hash index

Step 3) Use the trivial algorithm to check these possible matching positions against the short read

Much better performance!

- Biological Motivation
- Computer Science Problem
- Trivial Solution
- Hash Index Solution
- Future Direction

- Efficiency
- Although the hash index algorithm is faster, it uses a lot of memory

- Robustness
- I ignored insertions, deletions, and repeated regions
- These are all real complications that must be dealt with to get accurate results

Questions?