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## PowerPoint Slideshow about ' Short Read Mapper' - tobit

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Outline

Outline

Outline

Outline

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

Outline

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

Biological Motivation

- 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

Biological Motivation

- 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

Biological Motivation

- 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

Biological Motivation

- 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

Outline

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

Computer Science Problem

- 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

Computer Science Problem

- Problem Layout

…

T

C

A

G

A

A

G

A

Short read length L

- Allow up to D mismatches per short read

Computer Science Problem

- 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

Trivial Solution

Algorithm

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

- Easy to explain, easy to code

C

A

G

A

A

G

A

A

T

A

A

Trivial SolutionExample: Let L = 4, D = 2

Reference:

Short Read:

3 mismatches

C

A

G

A

A

G

A

A

T

A

A

Trivial SolutionExample: Let L = 4, D = 2

Reference:

Short Read:

3 mismatches

C

A

G

A

A

G

A

A

T

A

A

Trivial SolutionExample: 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

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

Hash Index Solution

- 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

Hash Index Solution

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

Hash Index Solution

- 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

Hash Index Solution

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

Hash Index Solution

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 Solution

Hash Index Example

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

0

1

…

228

229

…

Hash Index Solution

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

…

Hash Index Solution

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

Hash Index Solution

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

Example

Short Read: TCGAAACTGAGT

TCGA

AACT

GAGT

Hash Index Solution

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

Hash Index Solution

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

Hash Index Solution

Much better performance!

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

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

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