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This document describes Cortex, a de novo genome assembler that uses colored de Bruijn graphs to assemble multiple genomes simultaneously and detect genetic variants without reference sequences. It discusses four approaches Cortex uses: bubble calling to detect variants from repeats or errors, path divergence to find complex variants, multiple-sample analysis to improve accuracy, and genotyping known loci. The document outlines the algorithms and implementations of these approaches, and provides examples of use cases and limitations.
![BC implementation
get_super_node(n, G):
path1 = traverse forward, until reach node with in/out degree != 1
path2 = traverse forward, until reach node with in/out degree != 1
return union(path1, path2)
bubble_caller(G):
for each node n in G:
if outdegree(n) == 2 and not_visited(n):
mark_as_visited(n)
(<n1,e1>,<n2,e2>) = get_outedges(n, G)
path1 = get_super_node(n1, G)
path2 = get_super_node(n2, G)
mark_as_visited(path1[0] .. path1[-1])
mark_as_visited(path2[0] .. path2[-1])
if path1[-1] == path2[-1] and
orientation(path1[-1] == orientation(path2[-1]):
bubble_found = true
8 / 22](https://image.slidesharecdn.com/slides5-130814060729-phpapp01/85/Slides5-8-320.jpg)
![PD implementation
path_devergence(L, M, ref):
for i in [0 .. len(ref)]:
s = get_supernode_in_sample_color(n) #may be null
b = get_first_position_differ(ref,s)
if s != null and b > 0 and
s[b–L–1+j] == n[i+j] for j = [0 .. L-1]:
for j = [i+L+1 .. i+M]:
if s[len(s) – L+k] == ref[j+k] for k = [0 .. L-1]:
variant_found = true
break
10 / 22](https://image.slidesharecdn.com/slides5-130814060729-phpapp01/85/Slides5-10-320.jpg)
Slides5
- 1. De novo assembly and genotyping of variants using colored de Bruijn graphs Iqbal et al. 2012 Kolmogorov Mikhail 2013
- 2. Challenges • Detecting genetic variants that are highly divergent from a reference • Detecting genetic variants between samples when there is no available reference sequence 2 / 22
- 3. Mapping-based approaches limitations ● Sample may contain sequence absent or divergent from the reference ● Reference sequences, particularly of higher eukaryotes are incomplete, notably in telomeric and pericentromeric regions ● Some samples may have no available reference sequence 3 / 22
- 4. Cortex! ● De novo assmebler capable of assembling multiple eukaryote genomes simultaneously ● Focus on detecting and characterising genetic variation ● Alignment free ● Accuracy of variant calling may be improved by adding reference sequence 4 / 22
- 5. Colored graph ● De Brujin graph with colored nodes and edges ● Different colors may reflect HTS data from multiple samples, experiments, reference sequences, known variant sequences 5 / 22
- 6. Variant calling aproaches ●Bubble calling ●Path divergence ●Multiple-sample analysis ●Genotyping 6 / 22
- 7. First approach: Bubble calling ● Bubbles can be induced by variants, repeats or sequencing errors ● Variants can be separated from repeats by including reference sequence ● When multiple samples available, it`s possible to estimate likelihood of bubble type 7 / 22
- 8. BC implementation get_super_node(n, G): path1 = traverse forward, until reach node with in/out degree != 1 path2 = traverse forward, until reach node with in/out degree != 1 return union(path1, path2) bubble_caller(G): for each node n in G: if outdegree(n) == 2 and not_visited(n): mark_as_visited(n) (<n1,e1>,<n2,e2>) = get_outedges(n, G) path1 = get_super_node(n1, G) path2 = get_super_node(n2, G) mark_as_visited(path1[0] .. path1[-1]) mark_as_visited(path2[0] .. path2[-1]) if path1[-1] == path2[-1] and orientation(path1[-1] == orientation(path2[-1]): bubble_found = true 8 / 22
- 9. Second approach: Path divergence ● Complex variants are unlikely to generate clean bubbles ● In some cases (particularly deletions), path complexity is restricted to reference allele ● Such cases may be identified by following reference sequence and track places, where it diverges from sample graph 9 / 22
- 10. PD implementation path_devergence(L, M, ref): for i in [0 .. len(ref)]: s = get_supernode_in_sample_color(n) #may be null b = get_first_position_differ(ref,s) if s != null and b > 0 and s[b–L–1+j] == n[i+j] for j = [0 .. L-1]: for j = [i+L+1 .. i+M]: if s[len(s) – L+k] == ref[j+k] for k = [0 .. L-1]: variant_found = true break 10 / 22
- 11. Third approach: Multiple-sample analysis ●The joint analysis of HTS data from multiple samples can improve the accuracy and false discovery rate of variant detection substantially ●Maintaining separate colors for each sample gives an additional information about whether a bubble is likely to be induced by repeats or errors ●Approach can be used when there is no suitable reference 11 / 22
- 12. Classification of graph structures ● Given colored de Brujin graph, with each color representing single diploid individual from single population ● Need to classify pair of paths (for example, bubble branches) as either alleles of variant, repeats or errors 12 / 22
- 13. Information sources ● Total coverage of two sides ● Average allele-balance (the distribution of coverages between the two branches) ● Variance of allele-balance across samples 13 / 22
- 14. Structure differences ●Repeat: normal coverage, intermediate balance, no variance between samples. ●Variance: normal coverage, but each individual has a 0, 1 or 2 copy of allele 1 (and 2, 1 or 0 of allele 2). ●Error: low coverage on error branch 14 / 22
- 15. Models ●Coverage modelles as over-dispersed Poisson distribution ●Variant: Binominal distribution for allele-balance ●Repeat / Error: Beta distribution for allele-balance ●A site is classified as Variant / Repeat / Error if the log- likelihood of the data under that model is at least 10 greater than the other models (log10 Bayess Factor at least 10) 15 / 22
- 16. Fourth approach: Genotyping ●Colored de Bruijn graphs can be used to genotype samples at known loci even when coverage is insufficient to enable variant assembly ●Graph is constructed of the reference sequence, known allelic variants and data from the sample ●The likelihood of possible genotype is calculated accounting for the graph structure 16 / 22
- 17. Genotyping algorithm ●We have a graph with one color for each known allele, one color for reference genome (with site in question named X) and one color for sample ●For any pair of alleles γ1 , γ2 we define a likelihood function 17 / 22
- 18. Likelihood function ●Ignore all segments of alleles, which are present in reference minus X ●Decompose both alleles into sections, that are shared (si ) and uniqe (ui ) and count nuber of reads in each ●Count number of nodes n in both sample graph and joint graph of all known alleles except γ1 and γ2 — these are sequencing errors ●For each section of length li probability of ri reads arriwing within the section is given by a Poisson distribution with rate θi = λli on shared segments and θi / 2 on unique 18 / 22
- 19. Colored graph implementation ● Graph encoded impicitly, within a hash table ● Kmers and their reverse complements are stored in a same node ● Hash table value is array of integers, representing coverage for each color ● For each kmer, one binary flag is used for each nucleotide to track, if corresponding edge is present ● Memory usage per node: 8(k / 32) + 5c + 1 bytes 19 / 22
- 20. Use cases ● Variant calling in a high coverage human genome ● Detection of novel sequence from population graphs of low-coverage samples ● Using population information to classify bubble structures ● Genotyping simple and complex variants 20 / 22
- 21. Limitations ● Not using paired reads information ● Greater need for error correction, as kmer size increases ● Potential of a graph explosion, as more individuals are included in the graph 21 / 22
- 22. Thanks for attention 22 / 22