Finding the location and unit length of repetitive sequences within a long read

After discovering a few difficulties with genome assembly, I’ve taken an interest in finding and categorising repetitive DNA sequences, such as this one from Nippostrongylus brasiliensis [each base is colour-coded as A: green; C: blue; G: yellow; T: red]:

[FASTA file associated with this sequence can be found here]

These sequences with large repeat unit sizes are only detectable (and assembleable) using long reads (e.g. PacBio, nanopore) because any subsequence smaller than the unit length will not be able to distinguish between sequencing error and hitting a different location within the repeat structure. I have been tracking these sequences down in a bulk fashion by two methods:

1. Running an all-vs-all mapping, and looking for sequences that map to themselves lots of times
2. Carrying out a compression of the sequence (e.g. bzip2), and finding sequences that have a compression rate that is substantially higher than normal

After I’ve found a suspicious sequence, I then want to be able to categorise the repeat (e.g. major repeat length, number of tandem repeats, repetitive sequence). This is where I’m getting stuck.

For doing a “look, shiny” demonstration, I currently have a very manual process of getting these sequences into a format that I can visualise. My process is as follows:

1. Use LAST to produce a dot plot of self-mapping for the mapping
2. Visually identify the repetitive region, and extract out the region from the sequence
3. Use a combination of fold -w <width> and less -S to visually inspect the sequence with various potential repeat unit widths to find the most likely repeat unit size
4. Display the sequence in a rectangular and circular fashion using my own script, wrapping at the repeat unit length

But that process is by no means feasible when I’ve got thousands of potential repetitive sequences to fish through.

Is there any better way to do this? Given an arbitrary DNA sequence of length >10kb, how can I (in an automated fashion) find both the location of the repeat region, and also the unit length (bearing in mind that there might be multiple repeat structures, with unit lengths from 30bp to 10kb)?

An example sequence can be found here, which has a ~21kb repeat region with ~171bp repeat units about 1/3 of the way into the sequence.

A Kmer-based Analysis

I’ve now seen human sequences with repetitive regions in excess of 10kb (i.e. out of the range of most linked-read applications). My current idea is centred around creating hash tables of short sequences (currently 13-mers) and tracking their location:

1. Process the sequence, storing the location of each kmer
2. For each kmer, find out how many times it appears in the sequence
3. For repeated kmers, find out how much of a gap there is between the next time that kmer occurs
4. Report the median and modal gap length of repeated kmers, and statistics associated with their frequency in the sequence

Some local repetitive regions may be lost in the statistics with this approach, it’s hard to tell if there are multiple repetitive regions within a single sequence, and if the repeat units are themselves slightly repetitive (enough that a kmer is duplicated within a repeat unit), then the algorithm will under-report the repetitiveness (see step 3).

 $ repaver.r -style dotplot -prefix dotplot MAOA_chrX_43645715-43756016.fa
 $ repaver.r -style profile -prefix profile MAOA_chrX_43645715-43756016.fa
 $ repaver.r -style semicircular -prefix semi MAOA_chrX_43645715-43756016.fa