GPSeq in a nutshell
Let's focus on a GPSeq experiment comprising
conditions
:
where with we indicate a negative condition with no restricted cutsites and, thus, no reads. Each condition
is characterized by different number of cells
and reads
, with
and
.
It is important to notice how the maximum resolution of a GPSeq experiment is at single-cutsite, as the cutsite is where de-duplicated reads are located. In other words, the cutsite is GPSeq's unit of measure.
Depending on the restriction enzyme, e.g., 4 bp or 6 bp cutter, cutsites are more or less sparse, allowing to achieve a higher or lower theoretical maximum resolution (). The real maximum resolution (
) is always lower than the theoretical maximum resolution (
), as some reads are lost during sequencing and some cutsites are never digested.
Also, notice that each cutsite can have up to reads as, after de-duplication, a read represents a digestion event occurring in one cell.
Let's define a genomic region located on chromosome
between the genomic coordinates
(first) and
(last). Taking into account that GPSeq captures restriction events, and that we focus only on restricted cutsite, we can define the probability of digesting
as:
where is the number of de-duplicated reads mapping to
in condition
, and
is the number of cutsites in
in condition
considered in the analysis.
In other words, we normalize the number of restriction events in a genomic region by the number of restriction events in the condition and the number of considered cutsites in the region itself; this makes comparable across different regions and different conditions.
The number of reads in the region in condition
is:
where is the ![i]-th cutsite in
. Remember that a cutsite
is, essentially, a small region; then:
In other words, we consider a cutsite ![s] as belonging to region when region and site are on the same chromosome and the site start position is included in the region.
Additionally, we degine a non-empty cutsite as a cutsite with at least a mapped de-duplicated read, corresponding to a cutsite being restricted in a cell and being sampled during the sequencing run.
Let's consider a genomic region comprising
units (single/grouped-cutsites, see 2.d), we can define a mean (
) and variance (
) of the restriction events count in the units of the window.
Please, not that is a sample variance (normalized over
).