Askar Gafurov, Brona Brejova, Paul Medvedev. Markov chains improve the significance computation of overlapping genomeannotations. Bioinformatics, 38(Suppl 1):i203-i211. 2022.

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MOTIVATION: Genome annotations are a common way to represent genomic features
such as genes, regulatory elements or epigenetic modifications. The amount of
overlap between two annotations is often used to ascertain if there is an
underlying biological connection between them. In order to distinguish between
true biological association and overlap by pure chance, a robust measure of
significance is required. One common way to do this is to determine if the number
of intervals in the reference annotation that intersect the query annotation is
statistically significant. However, currently employed statistical frameworks are
often either inefficient or inaccurate when computing P-values on the scale of
the whole human genome. RESULTS: We show that finding the P-values under the
typically used 'gold' null hypothesis is NP-hard. This motivates us to
reformulate the null hypothesis using Markov chains. To be able to measure the
fidelity of our Markovian null hypothesis, we develop a fast direct sampling
algorithm to estimate the P-value under the gold null hypothesis. We then present
an open-source software tool MCDP that computes the P-values under the Markovian 
null hypothesis in O(m2+n) time and O(m) memory, where m and n are the numbers of
intervals in the reference and query annotations, respectively. Notably, MCDP
runtime and memory usage are independent from the genome length, allowing it to
outperform previous approaches in runtime and memory usage by orders of magnitude
on human genome annotations, while maintaining the same level of accuracy.
AVAILABILITY AND IMPLEMENTATION: The software is available at All data for reproducibility are
available at
SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics