pasio 1.1.2

Description:

pasio 1.1.2

PASIO
Pasio is a tool for denosing DNA coverage profiles coming from high-throughput sequencing data.
Example of experiments pasio works well on is ChIP-seq, DNAse-seq, ATAC-seq.
It takes a .bed file of counts (integer values, normalization is not supported). And produces
tsv file with genome splited into segments which coverage can be treated as equal.
Pasio runs on both Python 2 and 3 (Python 2 interpreter runs a bit faster).
The only dependencies are numpy and scipy.
Defaults are reasonable for fast yet almost precise computation, so usually it is enough to run:
pasio input.bedgraph

PASIO can read and write to gzipped files (filename should have .gz extension).
Installation
PASIO works with Python 2.7.1+ and Python 3.4+. The tool is available on PyPA, so you can install it using pip:
python -m pip install pasio

Note that pip install wrapper to run pasio without specifying python. One can use one of two options to run it:
pasio <options>...
python -m pasio <options>...

The latter option can be useful if you want to run it using a certain python version.
Underlying math
PASIO is a program to segment chromatin accessibility profile. It accepts a bedgraph file
with coverage of position by DNase cuts (e.g. by 5'-ends of DNase-seq)
and splits each contig/chromosome into segments with different accessibilites in an optimal way.
Method is based on two assumptions:

cuts are introduced by Poisson process P(λ) with λ depending on segment
λ are distributed as λ ~ Г(α, β) = β^α * λ^{α - 1} * exp(-βλ) / Г(α)

α and β are the only parameters of segmentation.
Then we can derive (logarithmic) marginal likelyhood logML to be optimized.
logML for a single segment S of length L with coverages (S_1, S_2, ...S_L) and total coverage C = \sum_i(S_i) will be:
logML(S,α,β) = α*log(β) − log(Γ(α)) + log(Γ(C + α)) − (C + α) * log(L + β) − \sum_i log (S_i!)
Here α*log(β) − log(Γ(α)) can be treated as a penalty for segment creation (and is approximately proportional to α*log(β/α)).
Total logML(α,β) is a sum of logarithmic marginal likelihoods for all segments: logML(α,β) = \sum_S logML(S,α,β).
Given a chromosome coverage profile, term \sum_S {\sum_i log (S_i!)} doesn't depend on segmentation.
Value \sum_S {log(Γ(C + α)) − (C + α) * log(L + β)} is refered as a self score of a segment.
We optimize only segmentation-dependent part of logML which is termed just score.
This score is a sum of self score of a segment and a penalty for segment creation.
Program design
split_bedgraph loads bedgraph file chromosome by chromosome, splits them into segments and writes into output tsv file.
Coverage counts are stored internally with 1-nt resolution.
Splitting is proceeded in two steps: (a) reduce a list of candidate split points (sometimes this step is omitted),
(b) choose splits from a list of candidates and calculate score of segmentation.
The first step is performed with one of so called reducers. The second step is performed
with one of splitters (each splitter also implements a reducer interface but not vice versa).
Splitters and reducers:

The most basic splitter is SquareSplitter which implements dynamic programming algorithm
with O(N^2) complexity where N is a number of split candidates. Other splitters/reducers perform
some heuristical optimisations on top of SquareSplitter
SlidingWindowReducer tries to segment not an entire contig (chromosome) but shorter parts of contig.
So they scan a sequence with a sliding window and remove split candidates which are unlikely.
Each window is processed using some base splitter (typically SquareSplitter).
Candidates from different windows are then aggregated.
RoundReducer perform the same procedure and repeat it for several rounds or until list of split candidates converges.
NotZeroReducer discards (all) splits if all points of an interval under consideration are zeros.
NotConstantReducer discards splits between same-valued points.
ReducerCombiner accept a list of reducers to be sequentially applied. The last reducer can also be a splitter.
In that case combiner allows for splitting and scoring a segmentation. To transform any reducer into splitter one can combine
that reducer with NopSplitter - so that split candidates obtained by reducer will be treated as
final splitting and NopSplitter make it possible to calculate its score.

Splits denote segment boundaries to the left of position. Adjacent splits a and b form semi-closed interval [a, b)
E.g. for coverage counts [99,99,99, 1,1,1] splits should be [0, 3, 6].
So that we have two segments: [0, 3) and [3, 6).
Splits and split candidates are stored as numpy arrays and always include both inner split points and segment boundaries, i.e. point just before config start and right after the contig end.
One can also treat splits as positions between-elements (like in python slices)
counts: | 99 99 99 | 1 1 1 |
splits candidates: 0 1 2 3 4 5 6
splits: 0 3 6

Splitters invoke LogMarginalLikelyhoodComputer which can compute logML for a splitting (and for each segment).
LogMarginalLikelyhoodComputer store cumulative sums of coverage counts at split candidates
and also distances between candidates. It allows one to efficiently compute logML and doesn't need
to recalculate total segment coverages each time.
In order to efficiently compute log(x) and log(Г(x)) we precompute values for some first million of integer numbers x.
Computation efficiency restricts us to integer values of α and β. Segment lengths are naturally integer,
coverage counts (and total segment counts) are also integer because they represent numbers of cuts.
LogComputer and LogGammaComputer store precomputed values and know how to calculate these values efficiently.