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Is the mappability of the centromeres in the GRCh38 genome reference similar to each other?

As far as I can remember when GRCh38 came out, the sequence of the centromeres was determined by a combination of sequencing data and software prediction.

Given the way the sequence of the centromeres has been determined, should we expect Illumina 2x150bp (or shorter, 2x75bp) reads to map relatively equally to all centromere sequences?

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should we expect Illumina 2x150bp (or shorter, 2x75bp) reads to map relatively equally to all centromere sequences?

No. It has long been established that different chromosomes are associated with different centromeric sequences. It is sometimes possible to tell which chr a read is originated from based on its sequence.

The GRCh38 centromeres are trickier. As I remember, the centromeric sequences were computationally generated with a Markov chain (or something alike) modeled after Venter's genome. GRC can distinguish most chromosomes, but not all. Some alpha arrays are placed onto 2 or 4 chromosomes. The original GRCh38 keeps all 4 copies. When you download GRCh38 for mapping purposes, only one copy is retained; additional copies are hard masked along with PARs on chrY.

If you want to know more, see this paper and this.

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I doubt it, unless you are asking if mapping would be similarly bad for all centromeres. Here are some repetitive structures (probably not centromeric) that I've found in the nanopore reads for "human" sample NA12878, produced by the nanopore-WGS consortium:

Repetitive human reads #1

These structures are consistent in that they repeat lots of times, but the internal patterns can be quite different. Here are a few more:

Repetitive human reads #2

Given that centromeres need to be uniquely linkable to a single chromosome, it would make sense to me if the centromere internal structure is unique to each chromosome.

It's possible to have highly-repetitive structures which don't map to each other. While I haven't dug too deeply into the human reads, I've looked at the 5 most-compressible regions in an assembled rodent parasite (Nippostrongylus brasiliensis) genome, and found no internal similarities between them:

Nippo most-compressible regions

One of the issues with assembly from Illumina reads is that these highly-repetitive regions get collapsed into a single repeat (or at best a region up to twice the fragment length). With internal repeat units that have identity of over 98%, assembling the true sequence is very difficult, even with an exact knowledge of paired read separation. Even if this were possible, it can be impossible to correctly place a read because multiple internal units could be identical (or similarly different) to the sequenced read.

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