This document discusses a method for accurately reconstructing repeats from long read sequencing data. It involves computing all substrings that occur in different positions in the genome from each read, clustering these substrings into groups corresponding to distinct repeats, and modeling each repeat based on the clustered strings. Key aspects include handling different replication modes like whole, prefix, substring, and periodic repeats. The method is fast and can automatically reconstruct all repeats in a genome de novo from noisy long reads.

1. ACCURATE
REPEAT
RECONSTRUCTION
FROM LONG READS
fabio cunial
myers lab

2. ASSEMBLE ENTIRE CHROMOSOMES
INCLUDING TELOMERES, CENTROMERES, HETEROCHROMATIN.

3. ASSEMBLE ENTIRE CHROMOSOMES
INCLUDING TELOMERES, CENTROMERES, HETEROCHROMATIN.
Using long reads:
sampled uniformly at random from the genome
uniform error probability along each read

4. unknown genome
overlap graph
read
⩾k
⩾k
"ASSEMBLE"
Myers. "Building fragment assembly string graphs." ECCB 2005.

5. unknown genome
overlap graph
read
⩾k
"ASSEMBLE"
jason chinMyers. "Building fragment assembly string graphs." ECCB 2005.

6. overlap graph
long repeat long repeat
"ENTIRE CHROMOSOMES"?
jason chin

7. overlap graph
long repeat long repeat
"ENTIRE CHROMOSOMES"?
jason chin

8. overlap graph
long repeat long repeat
"ENTIRE CHROMOSOMES"?
jason chin

9. multiple solutions
safety: return only maximal parts that
belong to all solutions.
jason chin
Kececioglu, Myers. "Combinatorial algorithms for DNA sequence assembly." Algorithmica 1995.
Tomescu, Medvedev. "Safe and complete contig assembly via omnitigs." RECOMB 2016.
"ENTIRE CHROMOSOMES"?
long repeat long repeat

10. RESOLVING LONG REPEATS
every sequence of 4 repetitive units is unique in the genome
long repeat ≈ unique sequence of "repetitive units"
⩾k

11. RESOLVING LONG REPEATS
adaptive to units
⩾4 units
long repeat ≈ unique sequence of "repetitive units"
every sequence of 4 repetitive units is unique in the genome

12. REPEAT RECONSTRUCTION
1. For every read, compute all substrings that occur
in a different position of the genome.
2. Cluster all such substrings into groups
that correspond to distinct repeats.
3. Given the set of strings in each cluster,
compute a model of the corresponding repeat.

13. repeat reconstruction
accurate, comprehensive assembly
faster assembly
understanding the combinatorial
structure of all repeats

14. INPUT
position on a read ⩾10 Kbp
quality
score
15% error≈

15. INPUT
position on a read ⩾10 Kbp
quality
score
15% error≈
Myers. "Efficient local alignment discovery amongst noisy long reads." WABI 2014.

16. KEY IDEA #1: MAXIMALITY
For every read, compute all substrings that occur
in a different position of the genome.
right-maximal alignment

17. KEY IDEA #2: REPLICATION MODES
unknown genome

18. KEY IDEA #2: REPLICATION MODES
unknown genome

19. KEY IDEA #2: REPLICATION MODES
unknown genome

20. KEY IDEA #2: REPLICATION MODES

21. WHOLE REPLICATION
left- and right-maximal alignments,
left-maximal with low quality to the right,
right-maximal with low quality to the left,
factors contained in a left-maximal alignment with same start and
in a right-maximal alignment with same end.
substrings =
boundaries = local maxima in the density of maximal events
Ram, Gray. "Density estimation trees." ACM SIGKDD 2011.

22. WHOLE REPLICATION

23. PREFIX REPLICATION
biased
unbiased

24. PREFIX REPLICATION
⩽a ⩾b
⩽c
DAG

25. PREFIX REPLICATION
⩽a ⩾b
⩽c
DAG
length of a longest path in a
connected component
n.connectedcomponents
τ
Iteratively search for a longest path
of length at least τ from each alignment

26. PREFIX REPLICATION
⩽a ⩾b
⩽c
DAG
length of a longest path in a
connected component
n.connectedcomponents
τ
Iteratively search for a longest path
of length at least τ from each alignment
Mark alignments as not to be used for splitting:

27. SUBSTRING REPLICATION
⩽a
⩾b
⩾c
⩽d
...
DAG, longest paths, split using peaks of density, etc.

28. PERIODIC REGIONS

29. PERIODIC REGIONS

30. PERIODIC REGIONS

31. PERIODIC REGIONS

32. PERIODIC REGIONS

33. PERIODIC REGIONS

34. PERIODIC REGIONS

35. EXTENSIONS
The same substring can replicate
by prefixes and suffixes
Whole repeats shorter than min. alignment length
Unbiased internal deletion/insertion
Preferences in internal deletion/insertion lengths
Whole instances vs. partial instances
Preferences in prefix/suffix lengths
Periodic prefix/suffix
Frequency of a repeat in the genome
Period estimation
Periodic regions and splitting
distance between pairs of consecutive
alignments in longest path
n.pairs

36. REPEAT RECONSTRUCTION
1. For every read, compute all substrings that occur
in a different position of the genome.
2. Cluster all such substrings into groups
that correspond to distinct repeats.
3. Given the set of strings in each cluster,
compute a model of the corresponding repeat.

37. 242 components, 7 periodic.
drosophila
whole (65%)
prefix/suffix (18.5%)
substring (10.5%)
periodic (1%)
prefix+suffix (4%)

38. CONCLUSIONS
Heuristics, but the input is very noisy
and set cover can be reduced to our problem.
Fast (hundreds of μs per alignment),
embarrassingly parallel.

39. CONCLUSIONS
Repeats can be highly overlapping,
and can replicate in multiple ways simultaneously.
Long repetitive regions of the genome
really consist of smaller units

40. CONCLUSIONS
The signal is strong enough that a de novo, automatic
reconstruction of all repeats is within reach.

41. ACCURATE
REPEAT
RECONSTRUCTION
FROM LONG READS
fabio cunial
myers lab

43. REPEAT RECONSTRUCTION ⇒ FASTER ASSEMBLY
Compute
alignments
Build repeat
models
Match models Compute
alignments
just outside
matches