I'm having a difficulty in grasping the general purpose and concept of indel calling.
What exactly is this process?
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Insertions and deletions (indels) are one type among many different types of genetic variation, such as single nucleotide variants (SNVs), copy number variants (CNVs), and structural variants (SVs). I'll assume here that you know how indels are defined, but are simple trying to understand the importance of discovering and analyzing them.
The goal of indel calling, like the goal of any variant calling, is to identify genetic variants that can subsequently be associated with important phenotypes, esp. disease. For example, if 60% of patients with disease XYZ have an indel in the promoter region of gene 123, then that is information of extreme interest and value in research and in clinical care.
Genome-wide association studies (GWAS) have been trying to correlate SNVs to disease and other phenotypes for years. Much less work has been done with indels, but their discovery and analysis remains an area of intense interest.
As far as the process of indel calling, large indels can usually be found by mapping paired reads and looking for large discrepancies in the expected distance between pairs and the observed distance.
Huh, my average insert size is 400bp, but the aligned read pairs flanking this area are 1200bp apart. Must be an 800bp deletion in there!
Smaller indels are much more difficult to detect using this strategy, since they are harder to distinguish from noise (i.e. the variation in length of sequenced fragments). However, as another answer mentions, many short indels are simply reflected as short gaps in the alignment.
There are two types of INDELs: short indels and long indels. Some put the threshold at 50bp; others choose 1000bp. Short and long indels are called differently.
<50bp short indels are called from read alignment directly. Modern indel callers essentially build a multi-alignment of reads and call an indel with enough read supports. Short indels may break open reading frames.
For Illumina reads, long indels are usually called with split alignment or read pair alignment because mainstream aligners are unable to directly align through a long indel. Long indels are a type of structural variation. They may affect gene structures in a more dramatic way (e.g. delete a whole exon; screw up transcription by transposon insertion; create pseudogenes).
Ultimately, both short and long indels are types of genetic variants. Calling them helps to understand how genetics shapes phenotypes.