Zero insert size means :
1. mate unmapped. (or)
2. Multi mapped read. (or)
3. Mate mapped to different 'Chr/scaffold/contig'
And may be others, but its good to look at the flag (column 2) and check whats happening.
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I am not sure If I understand you right but this is the histogram I am talking about
So do I need to see all the sam file flags?
What genome are you working with? If the genome that you have used for reference mapping is not assembled into Chromosomes, with mate pair data, this may be possible, as the two pairs of a read mapped to different contigs/scaffolds as mate pair will have large inserts (3kb/5kb/10kb). Hence, it is normal to have zero insert size for a mate pair data aligned to a draft genome.
But, could you let me know whats the size of the mate pair fragment during library prep?
Library size is 8 kb and this big zero column I could not explain it, so according to your answer shall I count it as pairs that mapped to different locus?! or you have other suggestion? could it be library preparation problem?
Which genome is it? Is it assembled to Chromosome level? If not, you can not comment on wetlab. Wet lab personnel may have checked the library size before sequencing with instrument such as BioAnalyzer. Check with them if they have insert size profile?
Maize genome and I mapped it against reference from genbank