Deeper look into Genome Assembly algorithms

Contributors

Authors:

Anthony Bretaudeau

Simon Gladman

Anton Nekrutenko

Delphine Lariviere

Questions

What are the main types of assembly algorithms?
How do they perform with short and long reads?
How to improve assemblies using other technologies?

last_modification Last modification: Dec 28, 2020

Different types of input data

Short reads (Illumina): numerous 👍, high quality 👍, cheap 👍, short 👎
Long reads (PacBio, Nanopore): longer 👍, fewer 👎, (many) more errors 👎

Genome Assembly can be done with:

only short reads
only long reads
both (hybrid assembly)

Specific algorithms for each

Genome Assembly algorithms

Detect overlaps between reads to build the longest possible sequences

Algorithms use graphs to represent overlapping reads/words

Two steps:

Build a (huge) graph while reading the input data
Try to find the longest paths traversing the graph

Two main types of algorithms:

Short reads: de Bruijn Graphs
Long reads: OLC (Overlap Layout Consensus)

OLC (Overlap Layout Consensus)

The older, first used for Sanger sequencing

Compare all reads, look for read overlaps

If a suffix of one read is similar to a prefix of another read…

TCTATATCTCGGCTCTAGG    <- read 1
    ||||||| |||||||
    TATCTCGACTCTAGGCC  <- read 2

…then they may overlap within the genome.

Directed graphs

We build a directed graph where directed edges connect nodes representing overlapping reads: Image showing example reads represented as nodes, and an overlap between two reads as an edge

Directed graph representing overlapping reads. (Image from Ben Langmead).

Directed graphs

For example, consider these 15 three letter reads:

TAA AAT ATG TGC GCC CCA CAT ATG TGG GGG GGA GAT ATG TGT GTT

We’re lucky, we know the corresponding genome sequence is TAATGCCATGGGATGTT

So the 15 reads can be represented as the following directed graph:

A graph representing the 15 overlapping example reads

However, in real life we do not know the actual genome! All we have is a collection of reads. Let’s first build an overlap graph by connecting two 3-mers if suffix of one is equal to the prefix of the other:

Overlap graph. All possible overlap connections for our 3-mer collection. (Fig. 4.7 from CP)

So to determine the sequence of the underlying genome we are looking for a path in this graph that visits every node (3-mer) once. Such path is called Hamiltonian path and it may not be unique.

For example for our 3-mer collection there are two possible Hamiltonian paths:

First possible Hamiltonian path Second possible Hamiltonian path

Two Hamiltonian paths for the 15 3-mers. Edges spelling “genomes” TAATGCCATGGGATGTT and TAATGGGATGCCATGTT are highlighted in black. (Fig. 4.9. from [CP](http://bioinformaticsalgorithms.com/)).

The reason for this “duality” is the fact that we have a repeat: 3-mer ATG is present three times in our data (green, red, and blue). Repeats cause a lot of trouble in genome assembly.

Limits of OLC

Computationally intensive
Doesn’t perform well with Illumina (massive amount of short reads)

=> deBruijn Graphs

de Bruijn Graphs

Based on a counter-intuitive idea

Hash all reads in overlapping fixed-length words
Words = k-mers of size k
Build a directed graph where nodes are k-mers and edges represent overlaps between k-mers

What are K-mers?

K-mers are subwords of length k of a string

K-mers de Bruijn graph

Example with 4 english words

Read errors

.image-75[ Example of english words with errors ]

Coverage (or sequencing depth)

The number of unique reads that contain a given nucleotide in the reconstructed sequence.

Aligned reads showing the notion of coverage

Source: Wikimedia

Estimated coverage

(number of reads x read length) / estimated size of the genome

1,000,000 reads x 150bp / 10Mb = 15X

More coverage

Errors won’t be duplicated in every read
Most reads will be error free
We can count the frequency of each k-mer
Annotate the graph with the frequencies
Use the frequency data to clean the de Bruijn graph

More coverage depth will help overcome errors!

Read errors revisited

Graph annotated with coverage

de Bruijn graph assembly process

Select a value for k
“Hash” the reads (make the kmers)
Count the kmers
Make the de Bruijn graph
Perform graph simplification steps
Read off contigs from simplified graph

Make contigs

Find an unbalanced node in the graph
Follow the chain of nodes and “read off” the bases to produce the contigs
Where there is an ambiguous divergence/convergence, stop the current contig and start a new one.
Re-trace the reads through the contigs to help with repeat resolution

Assembly in real life

In this topic we’ve learned about two ways of representing the relationship between reads derived from a genome we are trying to assemble:

Overlap graphs - nodes are reads, edges are overlaps between reads.
De Bruijn graphs - nodes are overlaps, edges are reads.

Overlap graph

An example overlap graph

de Bruijn Graph - same data

An example de Bruijn graph

Whatever the representation will be it will be messy:

An example of a real-life, noisy graph

A fragment of a very large De Bruijn graph (Image from BL).

There are multiple reasons for such messiness:

Sequence errors

Sequencing machines do not give perfect data. This results in spurious deviations on the graph. Some sequencing technologies such as Oxford Nanopore have very high error rate of ~15%.

Graph components resulting from sequencing errors (Image from BL).

Ploidy

As we discussed earlier humans are diploid and there are multiple differences between maternal and paternal genomes. This creates “bubbles” on assembly graphs:

Bubbles due to a heterozygous site (Image from BL).

Repeats

As we’ve seen the third law of assembly is unbeatable. As a result some regions of the genome simply cannot be resolved and are reported in segments called contigs: