RNA Pol II transcription model and interpretation of GRO-seq data

Abstract

A mixture model and statistical method is proposed to interpret the distribution of reads from a nascent transcriptional assay, such as global run-on sequencing (GRO-seq) data. The model is annotation agnostic and leverages on current understanding of the behavior of RNA polymerase II. Briefly, it assumes that polymerase loads at key positions (transcription start sites) within the genome. Once loaded, polymerase either remains in the initiation form (with some probability) or transitions into an elongating form (with the remaining probability). The model can be fit genome-wide, allowing patterns of Pol II behavior to be assessed on each distinct transcript. Furthermore, it allows for the first time a principled approach to distinguishing the initiation signal from the elongation signal; in particular, it implies a data driven method for calculating the pausing index, a commonly used metric that informs on the behavior of RNA polymerase II. We demonstrate that this approach improves on existing analyses of GRO-seq data and uncovers a novel biological understanding of the impact of knocking down the Male Specific Lethal (MSL) complex in Drosophilia melanogaster.

Appendix: Double geometric distribution

A random variable X is said to have a (possibly asymmetric) Double Geometric distribution with parameters (u, d) when it has the same distribution as $(-U)+D$, where U and D are independent Geometric random variables with means $(1/u-1)$ and $(1/d-1)$, respectively. In particular, the probability mass function of X is

$$\begin{aligned} p_{u,d}(k)=\frac{ud}{u+d-ud}\cdot \left\{ \begin{array}{lcl} (1-u)^{-k} &{} \quad \hbox {for} &{} k\le 0;\\ (1-d)^k &{} \quad \hbox {for} &{} k\ge 0. \end{array}\right. \end{aligned}$$

In this case, we write $X\sim DoubleGeometric(u,d)$. More generally, given an integer i, we write $X\sim DoubleGeometric(i,u,d)$ to mean that $(X-i)\sim DoubleGeometric(u,d)$.

If $X\sim DoubleGeometric(i,u,d)$ then

• (1) $(i-X)\sim Geometric(u)$ when $X\le i$; and

• (2) $(X-i)\sim Geometric(d)$ when $X\ge i$.

These two properties justify the Double Geometric terminology.