Assembling and comparing genomes or transcriptomes using de Bruijn graphs
Daniel Zerbino, Marcel Schulz, Wendy Lee, Ewan Birney and David Haussler

• De Bruijn graphs
• Repeat resolution
• Practical considerations
• Extensions to Velvet

• Traditional assemblers: Phrap, Arachne, Celera, etc.
• Short reads: Edena
• Generally more expensive computationally.
  • Overlaps only allow clean right-to-left and left-to-right overlaps.
  • Transitivity
    • Need to remove the redundant connections.
    • Well studied graph theory problem
• Use whole-read alignments

• Filter out all the reads that are identical or self-contained in another read. Only left-to-right, etc. are allowed.
• Compute all their overlaps.
• Get many transitive redundant connections.
  • Many algorithms are available for transitive reduction.
• You obtain simplified paths through the reads.
  • Get 4 big chunks of reads from the example.
  • Hard to distinguish which reads belong to which copy of the repeat.
• This is how contigs were first built.
• Have to compare all reads against each other.
  • Quadratic. This has become difficult.
  • Correction: quadratic behavior can be reduced to about O(n log n) by doing a clustering before aligning: just like in several fast search techniques, you only attempt to align sequences that share seed hits to relatively short k-mers (much shorter than those needed for de Bruijn graphs, since they only need to reduce the number of hits, not get unique locations in the genome). — Kevin Karplus 2010/04/24 07:51
• Next generation sequencing reads are short, and overlaps between reads are short. They are getting a little longer with newer technology.
• OLC method uses all information in the read at least.

• Some examples: SSAKE, SHARCGS, VCAKE
• Much faster & leaner than the previous
• Less robust to variation and noise
• Essentially simplified de Bruijn graph assemblers
• Build a dictionary of words in the data set.
  • His example is 4mer, but typically 20mer and longer.
• For each, create a node in the hash table.
  • Big dataset. Typically a binary marker to say if present.
• Sometimes at branch have two possible extensions.
• Greedy approach essentially de Bruijn graph with local info only. In this structure you could have many paths through.
• Can throw in reads of different lengths with no problems.

• Currently the most common for NGS: Euler, ALLPATHS, Velvet, ABySS, SOAPdenovo
• Pavel Pevzner popularized in paper from 2001
• Why do we use them?
  • High through-put, cheap, short reads with errors
• Basically a compromise between two previous approaches:
  • Just a k-mer hash
  • … but processed globally
• Graph construction and correction is similar in all assemblers.
• ABySS handles parallel implementation.

• Errors that are created in assembly create spurs/tips that can be easily removed.
• When finding bubbles, remap the branch with the lower coverage back onto the branch with the higher coverage (as not to lose the information).
• Loops can represent tandem repeats.

• First, concatenate the simple graphs without branches into nodes which compact the non-branching runs into a single item.
• Biochemistry of short reads means errors tend to be near the ends.
• If you have errors in the reads in the second half, it creates millions of tips, but they are at least easy to remove later.
• Each read is a path through the graph. The head of the read is still kept, so we're not losing the read placement information.
• We are still left with bubbles.
  • Possibly accumulation of overlapping spurs/tips. More often variation (e.g. SNPs or variation).
  • Would like to keep that information where possible.
  • Could also be a long read. But we don't want to cut the long read in the middle.
• Now we have loops that goes back on itself (not a bubble).

• Algebraic difference:
  • Reads in the OLC methods are atomic (i.e. an arc)
  • Reads in the DB graph are sequential paths through the graph
• …this leads to practical differences
  • DB graphs allow for greater variety of overlaps
  • Overlaps in the OLC approach require a global alignment, not just a shared k-mer
  • OLC methods gets error correction from long reads, while DB graphs requires more work to correct.

• Compare 5mb chunk from 4 species: E. coli, yeast, C. elegans, human
• Increased coverage from 0 to 50x
• N50 on y-axis
• First there is exponential growth as expected, but then the complexity causes trouble unless you have other kinds of information.
• Not using paired-reads information
• You see that the human is a little more complex than E. coli.

• 548 million Solexa reads were generated from a flow-sorted human X chromosome.
  • Fit in 70GB of RAM
  • Numerous short contigs
    • Many contigs: 898,401 contigs
    • Shirt contigs: 260bp N50 (however max of 6,956bp)
  • Overall length: 130Mb
  • How to handle repeats?
• Moral: there are engineering issues to be resolved but the complexity of the graph needs to be handled accordingly.

• Reduced representation (Margulies et al.).
  • Reduced representation using restriction enzymes and gel to cut the problem into tractable bits.
  • Cut chunks from the gel and then sequenced the gel slice separately or at least in different lanes.
  • Then the assembly problem is smaller and more localized instead of whole genome.
• Combined re-mapping and de novo sequencing (Cheetham et al., Pleaseance et al.).
  • Map to reference or similar genome, then re-map locally some stuff that is unique.
  • MAQ (Mapping and Assembly with Quality) and BWA (Burrows-Wheeler Alignment Tool) only allow 3 or 4 mismatches.
  • Can see reads not mapping in a small area with too many SNPs or breakpoint rearrangments.
• Code parallelization (Birol et al., Jeffrey Cook).
  • Only ABySS has published yet
• Improved indexing (Zamin Iqbal and Mario Caccamo).
  • Fit whole genome shotgun onto 200GB
• Use of intermediate remapping (Matthias Haimei).
  • Wanted to parallelize the second level work of building scaffolds, but those are mostly engineering issues.

• The de Bruijn graph for a small organism looks like long-ish contigs, but still makes a hair-ball.

• If all of the paths along the short reads move from one long read (e.g. 100-1kb) to another long read, then you know the sequence from the short reads
• Long reads which are mapped seamlessly into the graph.
• 35bp reads 50x, some long reads (100-1kb) 0-20x
• Played with the length
• The longer your long reads are, the more bridgeable it is and the longer the contigs.
  • Someone might ask: “Why not just assemble the long reads?”

• Equivalent to a Principle Component Analysis or a heat conduction model
  • Find what is the vector that threads its way
• Relies on a (massive) matrix diagonialization
• Comprehensive: all data integrated at once
  • Takes all the data at once in one huge matrix, not too affected by noise. No one has actually tried this approach as it requires too much computation.

• E.g. Arachne, Celera, BAMBUS
• Heuristic approach similar to that used in traditional overlap layout-consensus contigs
  • The traditional approach is contigs with paired-end reads.
  • Find chains connected by contig reads.
• Build a big graph of pairwise connections, simplify, extract obvious linear components
  • Your coverage is huge.
  • Each base pair has to handle 1000 coverage read-pairs. Long reads separated by a mess in the middle. Check possible paths. Find which are acceptable.
  • Find all the reads that start and end on the two long reads. Then consider them all together, much more efficient.
  • 5% or more of mate-pairs can be wrong
  • Hopefully will be able to filter them out.
  • In Velvet use a likelihood approach
  • Have a distance estimate
  • Coverage of A and B, how many would we expect to see? If we see too few, we discard the connection.

• Euler: for each pair of reads, find all possible paths from one read to another
• ABySS: Same as above, but the read-pairs are bundled into node-to-node connections to reduce calculations
• ALLPATHS: Same as above, but the search is limited to localized clouds around pre-computed scaffolds
  • ALLPATHS did better using small localized problems of a single small scaffold for parallelization.

• The Shorty algorithm uses the variance between read pairs anchored on a common contig on k-mer
  • Projected image of the other ends creates possibility of assembling a smaller set, the projection from a node.

• Pick one unique node, follow their paths
  • Velvet used the reverse idea, the projections to a node
• Some of them are unique, pick out those nodes
  • Hit the nodes in the vicinity of the starting contig, got distance information on the immediate vicinity.
  • Uses a greedy algorithm. Find way to next unique node.
• Having a more-precise insert size could help
• Velvet did a size assuming 10% distribution
  • Solexa might have been different
• SOLiD up to 2k, Solexa just 300
• It is difficult to have enough DNA of a narrow range.
• Don't love barcoding because it uses a lot of reagents.

• Di-base encoding has a 4 letter alphabet, but very different behavior to sequence space
  • Double-encoded files use ACGT.
  • Be careful not to confuse it!
  • Different rules for complementarity
    • Just reverse, don't complement them.
• Direct conversion to sequence space is simple but wasteful
  • One error messes up all the remaining bases. This is a huge loss, so do all in colorspace and make a complete assembly, then finally convert to base calls later.
• Conversion must therefore be done at the very end of the process, when the reads are aligned
  • You can then use the transition rules to detect errors. Typically it detects the error after 1 or 2 bp, then corrects.
  • SOLiD has developed tools

• When using different technologies, you have to take into account different technologies
  • Trivial when doing OLC assembly
  • Much more tricky when doing de Bruijn graph assemble, since k-mers are not assigned to reads
  • Different assemblers had different settings (e.g. Newbler)
• 454 had homopolymer issues in flow-space.
• Illumina or ABI are different.
  • Makes it hard to handle errors.
  • Especially in de Bruijn graphs. Applying the correction rules becomes much more complex.
• Newbler may be better for 454.

• Some assemblers have in-built filtering of the reads (e.g. Euler) but not a generality
• Efficient filtering of low quality bases can cut down on the computational cost (memory and time)
  • User-specific, data-space specific solutions
  • No tried and true consistent approach
• Beware that some assemblers require reads of identical length

Oases: de novo transcriptome assembly
How to study mRNA reads which do not map

• People are using next generation sequencing generally because it's cheaper.
• Would have just one path except for alternate splicing.
• Pavel Pevzner mentioned in 2002 that de Bruijn graphs are equivalent to splice graphs, so we can apply those algorithms developed for splice graphs to de Bruijn graphs.

• Create clusters of contigs:
  • Connecting reads
  • Connecting read pairs
  • The genetic locus should create a connected locus, cluster of contigs.
  • Sometimes one cluster gets broken into two, but works pretty well.
• Re-implement traditional algorithms to run on graphs, instead of a reference genome
  • Greedy transitive reduction (Myers, 2005)
  • Motif searches
  • Dynamic assembly of transcripts (Lee, 2003)
    • find the path of highest weight

• Full length transcripts - handles alternative splicing.
  • With skipped exon and one artifact.
• Transcripts from different genes - handles varying coverage levels.
• Alternative splicing events: when possible, distinguished between common AS events.
  • Find donor and acceptor sites on or around junctions.

• Benchmarked within the RGASP competition
• Already 100+ users, some reporting very promising results:
  • N50 = 1886 bp (Monica Britton, UC Davis)
  • 99.8% of aligned transcripts against unigene (Micha Bayer - Scottish Crop Research Institute)

• The number of transcripts and loci are in the ballpark of what they were expecting.
• rl 36, k21 ins size 200
• Map to genome ~90%

• Found an unannotated gene with 7 exons
• Assembler has no notion of the reference genome, but still found one example that mapped very well.

• Mapping
  • Many good mature tools available
  • Easy to compute
  • Simpler to analyze, comes with genetic coords
• De novo
  • Harder than mapping
  • May require special hardware
  • No reference needed
  • Handles novel structures without a priori
• How to get the best of both worlds?

• Solution: the reference-based de Bruijn graph
  • Just throw in the reference genome as long reads.
  • Chucking in long reads and getting short contigs.
  • Preserves the structure of the reference sequences. Not allowed to overlap with self.
    • What they wanted really was to start from a reference genome, then handle it as a little insertion.
  • Integrates alignment information (SAM, BAM file with BWA, Bowtie)
  • Edits, breaks up, reconnects, and extends the “alignment contigs” as necessary
• Applications
  • Comparative transcriptome assembly
  • Cancer RNAseq
  • Comparative assembly

• For transcriptome, using k=21.
• Can use reads as short as 25.
• How many X coverage needed?
• How many genes do you want to catch?
• With genome, want long inserts generally.
• With transcriptome, short inserts are more useful. They have been using 200bp tiny stuff.

Kevin on Wednesday will be talking about:

• Use SOLiD data for ordering and orientation of Pog contigs
• Special purpose scripts
• The data was so noisy