tools.md

bbglab/deepCSA: Tools explanation

Table of contents

• Introduction

Introduction

Here, you can find an explanation of the different computations, tools or metrics implemented in deepCSA.

Publications with detailed explanation

We are in the process of completing the documentation, but in the meantime you can check the recently published paper and its supplementary material for more details.

Adjusted mutation density

This can be found in the mutdensityadj folder of the deepCSA output.

Goal

The goal is to define a mean mutation density estimate for a specific subset of mutation sites. For example, we might be interested in measuring what is the mutation density at the set of missense mutation sites -- i.e., mutation sites in the CDS that induce missense mutations.

Motivation

In the context of bulk-ultradeep sequencing, there are several factors that can influence the occurrence of mutations at a given site.

• trinucleotide context of the site

• neutral mutagenesis, defined as:

  • normalized profile: vector of relative mutabilities for each trinucleotide context

  • exposure associated with the profile, expressed as mutation burden

• sequencing depth of the site

• selection of the site

We would like to define a way to compute the mutation density that corrects for potential confounders like depth and triplet content, thus rendering the estimates more comparable. For example, the missense sites in gene A may imply that more missense mutations per site are observed than in gene B, even if both genes are subject to the same exact mutational process.

Given a collection $\mathcal{C}=\{i\}$ of mutation sites (e.g. missense mutations) and a number of mutations $m$ observed in this context, we would like to come up with an expression of the type $m/L$, where $L$ denotes the effective number of sites.

Assuming even depth $D$ for simplicity, the current flat method would simply take :

$$L=\frac{1}{3}\cdot|\mathcal{C}|\cdot D$$

Assumptions

Throughout we make the following assumptions:

• the only way mutations come about is by neutral mutagenesis

• discrepancies between neutral mutagenesis and the observed mutations are due to selection

Definitions/Notation

Mutation sites are defined as specific single base nucleotide changes. Each mutation site corresponds to a tri-nucleotide context of the form $F_5RF_3>A$ where $F_5, F_3$ are the 5' and 3' flanking nucleotides, respectively, R is the reference nucleotide and A is the alternate allele. Therefore, there are 3 mutation sites per genomic position.

Let $\{P_c\}$ be the relative mutabilities per trinucleotide context $c$: given a mutation site with tri-nucleotide context $c_1$, we expect to observe $P_{c_1}/P_{c_2}$ more mutations than in a mutation site with triplet context $c_2$. For a more univocal definition, we may want to impose the following condition:

$$\sum_c P_c = 1$$

Note that in order to render absolute mutabilities, the $P_c$ should be multiplied by a suitable scaling factor $\alpha$.

Let $D_i$ be the sequencing depth at mutation site $i$.

Let $m$ denote the total number of mutations observed in the target class -- i.e., mapping to the prescribed collection of mutation sites where we are interested to compute the mutation density.

For each mutation site $i$, we will denote $c(i)$ its triplet context.

Method description

Given a collection $\mathcal{C}=\{i\}$ of mutation sites (e.g. missense mutations) and a number of mutations $m$ observed in this context, we want to compute an effective length $L$ that represents the entire collection of sites

$$L=\sum_{i\in\mathcal{C}} P_{c(i)}\cdot D_i$$

Note that this definition of length has an arbitrary interpretation, because of the multiple possible choices that we can make for the relative mutational profile. To render a universal length, we must set a scale to represent the mutational profile with a concrete meaning. What would be a good practical reference?

One possibility would be to choose a scaling factor $\alpha$ that represents an absolute mutability equivalent to an expected 1 mutation per megabase in one mappable copy of the genome.

If $n_c$ is the number of mutation sites with trinucleotide context $c$ comprised in the mappable genome and $G$ is the total length of the mappable genome (expressed in nucleotides), $\alpha$ must be such that:

$$\alpha\sum_c n_cP_c = G / 10^6$$

Because $G=\frac{1}{3}\sum_c n_c$, we can compute $\alpha$:

$$\hat\alpha = \frac{G}{10^6\cdot\sum_c n_cP_c} = \frac{1}{3\cdot 10^6} \frac{\sum_c n_c}{\sum_c n_cP_c}$$

Applying this scaling, the effective length would take the following form:

$$L=\hat\alpha\sum_i P_{c(i)}\cdot D_i = \hat\alpha\sum_c \left( P_c\cdot \sum_{i\in c} D_i \right)$$

Units

Defining the mutation density as $m/L$, according to the preceding explanation, the units in which the readout is expressed are the following: mutations / Mb sequenced.

Omega

For more explanations on omega go to the corresponding repo.

Site comparison

The site comparison step takes advantage of the computation of mutabilities in omega, and then compares these mutabilities either by residue, residue change or nucleotide change.

Mutational signatures

We provide two different strategies for signature analysis.

• Using SigProfilerAssignment with a set of known SBS signatures

• Using a Hierarchical Dirichlet Process algorithm developed by Nicola Robets and compacted by the McGranahan lab into a wrapped version.

Additionally one could run SigProfilerExtractor on the data but this needs to be done externally.