Theory and Models

Introduction

In MAVIS structural variants (SVs) are defined by a pair of breakpoints

And a breakpoint is defined by

1. chromosome
2. base-pair range (start, end). This has a length of 1 for exact calls and more for uncertain/non-specific calls
3. orientation. This is Left or Right with respect to the positive/forward strand. This defines which portion of the genome is ‘retained’
4. strand. (only applicable to stranded transcriptome libraries)

So then a breakpoint pair is any two intervals on the reference genome which are adjacent in the mutant genome

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Evidence

There are many ways that single reads or paired-end reads can act as support for an SV call.

Figure 6. In the figure above the red rectangle represents a deletion structural variant. The arrows are types of single or paired-end reads supporting the event: flanking read pairs (F), split reads (S), half-mapped reads (H), and spanning reads (N).

Types of Flanking evidence

One of the most confusing parts about working with contig and paired-end reads is relating them to the breakpoint so that you can determine which types will support an event. The flanking read types we outline here are similarly described by IGV. We have used similar coloring for the read pairs in the following diagrams to facilitate ease of use for those already familiar with viewing bam files in IGV.

Note

The major assumptions here are that the ‘normal’ read-pair is a read pair which has one read on the positive/forward strand and its partner on the negative/reverse strand. It is assumed that partners share a read name, as is the case for Illumina reads.

Deletion

For a deletion, we expect the flanking reads to be in the normal orientation but that the fragment size should be abnormal (for large deletions).

Figure 7. Flanking read pair evidence for a deletion event. the read pairs will have a larger than expected fragment size when mapped to the reference genome because in the mutant genome they are closer together, owing to the deletion event. (B1) The first breakpoint which has a left orientation. (B2) The second breakpoint which has a right orientation. Both breakpoints would be on the positive strand (assuming that the input is stranded) which means that the first read in the pair would be on the positive strand and the second read in the pair would be on the negative/reverse strand.

Insertion

Figure 8. Flanking read pair evidence for an insertion event. The read pairs will have a smaller than expected fragment size when mapped to the reference genome because in the mutant genome they are father apart, owing to the insertion event. (B1) The first breakpoint which has a left orientation. (B2) The second breakpoint which has a right orientation. Both breakpoints would be on the positive strand (assuming that the input is stranded) which means that the first read in the pair would be on the positive strand and the second read in the pair would be on the negative/reverse strand.

Duplication

Figure 9. Flanking read pair evidence for a tandem duplication event. The read pairs will have an abnormal orientation but still the same strands as the normal read pair. (B1) The first breakpoint will be on the positive strand and have a right orientation. (B2) The second breakpoint will be on the positive strand and have a left orientation.

Inversion

Figure 10. Flanking read pair evidence for an inversion. Both breakpoints have left orientation.

Figure 11. Flanking read pair evidence for an inversion. Both breakpoints have right orientation.

Translocation

Figure 12. Flanking read pair evidence for a translocation. (B1) the first breakpoint with a left orientation. (B2) the second breakpoint with a right orientation.

Figure 13. Flanking read pair evidence for a translocation. (B1) the first breakpoint with a right orientation. (B2) the second breakpoint with a left orientation.

Inverted Translocation

Figure 14. Flanking read pair evidence for an inverted translocation. Both breakpoints have left orientation.

Figure 15. Flanking read pair evidence for an inverted translocation. Both breakpoints have right orientation.

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Compatible Flanking Pairs

For insertion and duplication events compatible flanking pairs are collected. This means that flanking pairs that support a duplication may be used as compatible flanking evidence for an insertion (in the same region) and similarly flanking pairs which support an insertion may be compatible flanking evidence for a duplication

Figure 16. The event depicted above may be called as either a duplication or an insertion (depending on the input call). If the even were called as a duplication the reads in green would be the flanking supoprt and the reads in blue would be given as compatible flanking support. If the event were called as an insertion the reverse would apply.

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Calculating the Evidence Window

Figure 17. Basic Terms used in describing read pairs are shown above: fragment size: the distance between the pair; read length: the length of the read; fragment size: the combined length of both reads and the fragment size

We make some base assumptions with regards to paired-end read data:

Note

the distribution of fragment sizes approximately follows a normal distribution

Note

the most common fragment size is the unmutated ‘normal’ fragment

With the above assumptions we take the median fragment size to be the expected normal.

Given that we expect mutations and therefore abnormal fragment sizes, we use a modified method to calculate the median standard deviation (see code below). We calculate the squared distance away from the median for each fragment and then take a fraction of this to be ‘normal’ variation. So the most abnormal portion is ignored, assuming it is supposed to be abnormal. This results in a calculation as follows.

from statistics import median
import math

fragments = [abs(read.template_length) for read in reads]  # the fragment sizes of the reads
f = 0.95 # fraction
m = median(fragments) # get the median fragment size value
X = [math.pow(i - m, 2) for i in fragments]  # take the square error for each point
end = int(round(len(X) * f))
X = sorted(X)[0:end]
stdev = math.sqrt(sum(X) / len(X))

This gives us an idea of when to judge an fragment size as abnormal and where we expect our normal read pairs fragment sizes to fall.

Figure 18. Distribution of fragment sizes (absolute values) of proper read pairs. The black curve representings the fit for a normal distribution using the standard deviation calculated with all data points. The blue curve is the expected distribution using a 0.95 fraction of the data. The thick vertical black line is the median and the thin black lines are standard deviations away from the median.

As we can see from the diagram above, removing the outliers reproduces the observed distribution better than using all data points

We use this in two ways

1. to find flanking evidence supporting deletions and insertions
2. to estimate the window size for where we will need to read from the bam when looking for evidence for a given event

The _generate_window() function uses the above concepts. The user will define the median_fragment_size the stdev_fragment_size , and the stdev_count_abnormal parameters defined in the VALIDATION_DEFAULTS class.

If the library has a transcriptome protocol this becomes a bit more complicated and we must take into account the possible annotations when calculating the evidence window. see _generate_window() for more

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Calling Breakpoints by Flanking Evidence

Breakpoints are called by contig, split-read, or flanking pairs evidence. Contigs and split reads are used to call exact breakpoints, where breakpoints called by flanking reads are generally assigned a probabilistic range.

The metrics used here are similar to those used in calculating the evidence window. We use the max_expected_fragment_size as the outer limit of how large the range can be. This is further refined taking into account the range spanned by the flanking read pair evidence and the position of the opposing breakpoint.

Figure 19. Calculation of the left-oriented breakpoint by flanking reads. Reads mapped to the breakpoint are shown in grey. The read on the right (black outline, no fill) demonstrates the read length used to narrow the right side bound of the estimated breakpoint interval.

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Determining Flanking support

Figure 20. After a breakpoint has been called we can narrow the interval of expected fragment sizes using the size of the event. (Left) The colored portion of the graph represents the range in fragment sizes we expect for a normal/unmutated genome. (Right) For a deletion event we expect the fragment size to be bigger, outside the normal range. Reads that would flank the breakpoint should follow a similar distribution to the normal genome but the median will be shifted by the size of the event. The shaded portion of the graph represents the range in fragment sizes we expect for flanking pairs supporting the deletion event.

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Classifying Events

The following decision tree is used in classifying events based on their breakpoints. Only valid combinations have been shown. see classify()

Figure 21. Classification Decision Tree. The above diagram details the decsion logic for classifying events based on the orientation, strand and chromosomes or their respective breakpoints

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Assembling Contigs

During validation, for each breakpoint pair, we attempt to assemble a contig to represent the sequence across the breakpoints. This is assembled from the supporting reads (split read, half-mapped read, flanking read pair, and spanning read) which have already been collected for the given event. The sequence from each read and its reverse complement are assembled into contigs using a DeBruijn graph. For strand specific events, we then attempt to resolve the sequence strand of the contig.

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Annotating Events

We make the following assumptions when determining the annotations for each event

Note

If both breakpoints are in the same gene, they must also be in the same transcript

Note

If the breakpoint intervals overlap we do not annotate encompassed genes

Note

Encompassed and ‘nearest’ genes are reported without respect to strand

There are specific questions we want annotation to answer. We collect gene level annotations which describes things like what gene is near the breakpoint (useful in the case of a potential promoter swap); what genes (besides the one selected) also overlap the breakpoint; what genes are encompassed between the breakpoints (for example in a deletion event the genes that would be deleted).

Figure 22. Gene level annotations at each breakpoint. Note: genes which fall between a breakpoint pair, encompassed genes, will not be present for interchromosomal events (translocations)

Next there are the fusion-product level annotations. If the event result in a fusion transcript, the sequence of the fusion transcript is computed. This is translated to a putative amino acid sequence from which protein metrics such as the possible ORFs and domain sequences can be computed.

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Predicting Splicing Patterns

After the events have been called and an annotation has been attached, we often want to predict information about the putative fusion protein, which may be a product. In some cases, when a fusion transcript disrupts a splice-site, it is not clear what the processed fusion transcript may be. MAVIS will calculate all possibilities according to the following model.

Figure 23. The default splicing pattern is a list of pairs of donor and acceptor splice sites

For a given list of non-abrogated splice sites (listed 5’ to 3’ on the strand of the transcript) donor splice sites are paired with all following as seen below

Figure 24. Multiple abrogated acceptors sites. As one can see above this situation will result in 3 different splicing patterns depending on which donor is paired with the 2nd acceptor site

Figure 25. Multiple abrogated donor sites. As one can see above this situation will result in 3 different splicing patterns depending on which acceptor is paired with the 2nd donor site

More complex examples are drawn below. There are five classifications (SPLICE_TYPE) for the different splicing patterns:

1. Retained intron (RETAIN)
2. Skipped exon (SKIP)
3. Multiple retained introns (MULTI_RETAIN)
4. Multiple skipped exons (MULTI_SKIP)
5. Some combination of retained introns and skipped exons (COMPLEX)

Figure 26. Splicing scenarios

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Pairing Similar Events

After breakpoints have been called and annotated we often need to see if the same event was found in different samples. To do this we will need to compare events between genome and transcriptome libraries. For this, the following model is proposed. To compare events between different protocol (genome vs transcriptome) we use the annotation overlying the genome breakpoint and the splicing model we defined above to predict where we would expect to find the transcriptomic breakpoints. This gives rise to the following basic cases.

Note

In all cases the predicted breakpoint is either the same as the genomic breakpoint, or it is the same as the nearest retained donor/acceptor to the breakpoint.

Figure 27. (A-D) The breakpoint lands in an exon and the five prime portion of the transcript is retained. (A) The original splicing pattern showing the placement of the genomic breakpoint and the retained five prime portion. (B) The first splice site following the breakpoint is a donor and the second donor is used. (C) The first splice site following the breakpoint is a donor and the first donor is used. (D) The first splice site following the breakpoint is an acceptor. (E-H) The breakpoint lands in an exon and the three prime portion of the transcript is retained. (E) The original splicing pattern showing the placement of the genomic breakpoint and the retained three prime portion. (F) The first splice site prior to the breakpoint is an acceptor and the first acceptor is used. (G) The first splice site prior to the breakpoint is an acceptor and the second acceptor is used. (H) The first splice site prior to the breakpoint is a donor