De Novo Assembly Graph

The fundamental structure consists of nodes representing sequences (k-mers or reads) and edges representing overlaps. In a de Bruijn graph, nodes are k-mers of fixed length k, and directed edges connect k-mers that overlap by k-1 bases. In an overlap-layout-consensus (OLC) graph, nodes are full reads and edges are weighted by the length of the overlap. This topology directly encodes the adjacency information needed to traverse the genome.

A bubble is a subgraph where two or more alternative paths diverge from a common source node and converge at a common sink node. These structures represent biological variation (SNPs, indels) or sequencing errors. The assembler must distinguish true variants from artifacts by evaluating coverage depth and topology within the bubble. Resolving bubbles is critical for generating accurate contigs and for directly calling variants from the graph itself.

Genomic repeats longer than the read length cause the graph to collapse into a single path, creating a tangle. This results in fragmented assemblies where distinct genomic loci are erroneously merged. The graph's inability to disambiguate these repeats is the primary limitation of short-read assembly. Long reads can span repeats, introducing long-range edges that resolve tangles and linearize the graph.

Tips are short, dead-end paths in the graph, typically caused by sequencing errors at the ends of reads. They are identified by their low coverage and short length relative to the main graph. A critical preprocessing step is tip clipping, which iteratively removes these spurious structures. This reduces graph complexity and prevents false connections that would fragment the assembly.

To generate contiguous sequences, the graph undergoes simplification. This includes: Path compression, where non-branching linear paths are merged into single nodes representing longer sequences; Transitive edge removal, where redundant edges implied by longer paths are deleted; and Low-coverage node removal, which eliminates nodes likely representing errors. The result is a compact, biologically meaningful representation.

Unlike linear references, an assembly graph can natively represent population variation as alternative paths. This is the foundation of a variation graph or pangenome graph. Instead of calling variants against a single reference, the graph itself becomes the reference, with known haplotypes embedded as distinct routes. This eliminates reference bias, where reads from highly divergent regions fail to align to a linear reference.

A directed graph representing overlaps between sequences of a fixed length k (k-mers). Unlike overlap graphs, nodes represent k-mers and edges represent overlaps of k-1 bases. This approach, central to EULER and Velvet assemblers, dramatically reduces computational complexity by collapsing redundant sequencing reads into a compact path structure, making it ideal for high-coverage short-read data.

A three-stage assembly paradigm best suited for long-read sequencing (PacBio, Oxford Nanopore).

• Overlap: All-vs-all read comparison to find suffix-prefix matches.
• Layout: Clustering overlapping reads into contig layouts.
• Consensus: Deriving the most likely nucleotide sequence via multiple sequence alignment. This method preserves long-range connectivity but scales quadratically with read count.

The selection of the k-mer length is the single most critical parameter in de Bruijn graph assembly. A k-mer that is too short creates unresolvable branching due to repetitive elements collapsing into a single node. A k-mer that is too long fails to connect overlapping reads, fragmenting the graph. Optimal k balances uniqueness against connectivity, often determined empirically using tools like KmerGenie.

A preprocessing step that prunes dead-end paths (tips) from the assembly graph. Tips typically arise from sequencing errors at the ends of reads, where a single base substitution creates a short, low-coverage branch that terminates abruptly. Removing these spurious paths reduces graph complexity and prevents the assembler from generating false, truncated contigs.

The process of identifying and collapsing bubbles—divergent paths in the graph that reconverge after a short distance. Bubbles represent heterozygous variants, sequencing errors, or diploid polymorphisms. A tour bus algorithm or Dijkstra's traversal detects these structures, and the path with higher coverage or quality scores is retained, collapsing the bubble into a single consensus sequence.

The process of ordering and orienting contigs into scaffolds using the distance constraints provided by mate-pair or paired-end libraries. In the graph, these links are represented as long-range edges between contig endpoints. Scaffolding resolves repeats that are shorter than the insert size, bridging gaps filled with ambiguous bases (Ns) to reconstruct chromosome-scale architecture.