Improving kallisto quantification accuracy by filtering the gene set

In my previous post Road testing kallisto, I presented the results of a simulation study to test the accuracy of kallisto. Specifically, I hypothesised that kallisto would perform poorly for transcripts with little or no unique sequence and I wanted to use the simulation to flag these transcripts in my downstream analysis. The simulation was therefore intentionally naive and ignored biases from library preparation and sequencing so I could focus on the accuracy of quantification with “near perfect” sequence reads. The simulation results broadly fitted my expectations but also threw up a few more questions in the comments section. I’m going to post an update for each of the following questions:

  1. What’s the impact of including low-support transcripts on the quantification of well-supported transcripts?
  2. The correlation between truth and estimated counts drops off as a transcript has fewer unique k-mers. Is this also reflected in the bootstrap variances?
  3. How does kallisto compare to sailfish, salmon and cufflinks?
    • This comparison will come with caveats because of the way the reads were simulated

For this post I’ll focus on the first question.

The impact of including low-support transcripts on the quantification of well-supported transcripts

Previously I showed that the 9 DAZ2 transcripts (Ensembl v82) are very poorly quantified by kallisto. DAZ genes contain variable numbers of a repeated 72-bp exon (DAZ repeats) and I noted that transcript models for DAZ2 overlapped one another perfectly with regards to the splice sites, so some isoforms differ only in the number of DAZ repeats, hence 8/9 of the isoforms had no unique kmers whatsoever. I further suggested that the inclusion of low-support transcript models in the gene set may be reducing the accuracy of quantification for the high-support transcripts. I then suggested this was likely to be a problem at many other loci and filtering out low-support transcripts may be beneficial.

To test this, I created two genesets, “Filtered” and “Unfiltered“, both containing transcripts from hg38 Ensembl v82 protein-coding genes. For the “Filtered” gene set I removed all transcripts with a low-support level (>3 ; No supporting non-suspect EST or mRNA). For the “Unfiltered” gene set, I retained all transcripts. I then compared the accuracy of quantification over all transcripts with a support level of 1-3.

We would expect this filtering to increase the fraction of unique 31-mers in the remaining transcripts. Figure 1 demonstrates that this is indeed the case.

kmers filtered vs unfiltered

Figure 1. Distribution of fraction of unique 31-mers per transcript in the filtered and unfiltered gene sets

Figure 2 is a re-representation of the the previous figure showing the correlation between the sum of ground truths across the 30 simulations and the sum of estimated counts, with separate panels for the two gene sets. The two panels only show quantification over the high-support transcripts. There’s a clear but slight decrease in the accuracy of quantification when using the unfiltered gene set. With the arbitrary threshold of 1.5-fold that I used previously, 278 / 97375 (0.28%) are flagged as “poor” accuracy, compared to 448 / 97375 (0.46%) when we include the low-support transcripts. Honestly, I was expecting a bigger change but this hard thresholding somewhat masks the overall decrease in accuracy.

kallisto Filtering geneset improves accuracy

Figure.2 Filtering low-support transcripts improves the quantification accuracy for high-support transcripts with kallisto

Figure 3 shows the same plot but focusing on the DAZ genes. All the transcript models for DAZ4 are support level 5 so this gene is not included. When the gene set is not filtered, one of the DAZ1 (ENSG00000188120) transcripts is accurately quantified, with the other transcripts having zero or close-to-zero estimated counts across the 30 simulations. The filtering leads to a much improved quantification accuracy for the other DAZ1 transcript and one of the DAZ2 (ENSG00000205944) transcripts. However, there is no real improvement for the remaining transcripts, with two now considerably over-estimated and the other 4 showing no improvement.

Kallisto filtering improves DAZ gene accuracy

Figure 3. Improvement in quantification of DAZ gene transcripts when low-support transcripts are filtered out

The other important metric when assessing the accuracy of quantification is the Pearson’s correlation coefficient (r) between the ground truth and estimate counts across the simulations. For the majority of transcripts r>0.9 even when using the unfiltered gene set, however there is a noticeable improvement when the gene set is filtered (Figure 4).

kallisto_geneset_correlation_dist_zoom

Figure 4. Distribution of Pearson’s correlation coefficients between ground truths and kallisto estimated counts across 30 simulations. Transcripts were quantified using a filtered and unfiltered gene set

We would expect the greatest improvement where the correlation is low with the unfiltered gene set and the filtering leads to a large gain in the fraction of unique 31-mers. To show this, Figure 5 presents the gain in fraction of unqiue 31-mers (x-axis) against the improvement in correlation with the filtered geneset (y-axis), split by the correlation when using the unfiltered geneset. The transcripts in the top left panel showed very poor correlation with the unfiltered gene set (<0.5), so improvements here may be partly affected by regression to the mean. Looking at the other panels which show the transcripts with correlation >0.5 when using the unfiltered gene set, we can see that as the gain in fraction of unique 31-mers approaches 1 the improvement in the correlation tends towards the maximum possible improvement. Even those transcripts which only show a very slight gain in the fraction of unique 31-mers show a considerable improvement in the correlation. This is in line with my observation in the previous post that kallisto shows a much better performance for transcripts with > 0.05 unique kmers. 11047 / 97375 (11.3%) of high-support transcripts show at least a 0.05 increase in the fraction of unique kmers.

Transcripts unique kmers improved accuracy

Figure 5. Change in correlation when using the filtered gene set relative to the unfiltered gene set, split by the gain in fraction of unique 31-kmers and the correlation in the unfiltered gene set

Summary

The figures I’ve shown here fit perfectly with the expectation that filtering out the low-support transcripts increases the fraction of unique kmers in a subset of the remaining transcripts, in turn improving the accuracy of the estimated counts from kallisto. Removing the 44023 low-support transcripts improves the accuracy of the sum of estimates for the high-support transcripts, but the improvement is only slight. Whether this gain is worth removing 44023 isoforms is really down to how much you believe these low-support isoforms. Personally, I worry that a lot of these low-support transcripts are spurious models from poor transcript assembly.

The DAZ genes provide an insight into a very hard-to-quantify set of transcripts, indicating that there are gains to be made from filtering out the low-support transcripts but in some instances these will be minimal. Indeed, in some cases, even transcripts we know are real are just going to be near-impossible to quantify with short-read RNA-Seq due to their sequence similarity with other transcripts from the same locus and/or homologous loci.

The improvement to the correlation across the 30 simulations is somewhat clearer than the improvement in the sum of estimates, and most prominent where the gain in unique kmers is greatest, as expected. 11.2% of transcripts show a significant improvement in the fraction of kmers which seems to me a worthwhile gain for the loss of the low-support transcripts from the gene set. The next step will be to explore the effect of the filtering on differential expression analysis, since this is what I want to use kallisto for, and I expect this will be it’s major use case.

UPDATE (22/10/15):

In response to Ian’s question below, I had a look at whether removing a random selection of transcript models has a similar impact on the accuracy of the remaining models. To do this, I identified the number of transcripts which would be removed by the transcript support level (TSL) filtering for each gene_id and removed a random set (of the same size) of transcript models for the gene_id. This should ensure the comparison is “fair” with regards to the complexity of the loci at which transcript models are removed and the total number of transcript models filtered out.

My expectation was that low-support transcripts would be contaminated by transcript models from incomplete transcript assembly and would therefore be shorter and show a greater overlap with other transcript models from the same locus. I therefore expected that the removal of the random transcripts would also increase the fraction of unique kmers, as suggested by Ian, but that the effect would be greater when the low-support transcripts were removed.  It turns out I was wrong! Figure 6 shows the distribution of fraction unique 31-mers with the unfiltered, TSL-filtered and randomly filtered annotations. The random filtering actually leads to a slightly greater increase in the fraction unqiue 31-mers for the remaining transcripts. This also leads to an slightly greater correlation for the remaining transcripts (Figure 7).

So what about the length and overlap of the low support transcripts? Well it turns out the transcript models do decrease in length from TSL1-4, but oddly transcripts with TSL 5 (“no single transcript supports the model structure”) are very similar in length to TSL1 transcripts (Figure 8). To compare the overlap between the transcript models, I took a short cut and just used the fraction unique kmers as a proxy. Transcripts which have more overlap with other transcripts from the same locus will have a lower fraction of unique kmers. This is complicated by homology between gene loci but good enough for a quick check I think. Figure 9 shows the fraction unique kmers at each TSL. Again TSL1-4 show a trend with TSL5 looking more similar to TSL1 & 2. Interestingly the trend is actually in the opposite direction to what I had expected, although this comes with the caveat that I’m not controlling for any differences in the genome-wide distribution of the different TSLs so I’d take this with a pinch of salt.

Why TSL5 transcripts are more similar to TSL1-2 transcripts I’m not sure, perhaps this scale shouldn’t be considered as ordinal after-all. I think I’d better get in contact with Ensembl for some more information about the TSL. If anyone has any thoughts, please do comment below.

Of course this doesn’t take away from the central premise that the higher TSL transcript models are more likely to be “real” and accurate quantification over these transcripts should be a priority over quantifying as many transcript models as possible, given some of these models will be wrong.

Thanks to Ian for the suggestion, it turned out an unexpected result!

kallisto_geneset_random_filter_kmers

Figure 6. Impact of filtering on fraction unique 31-mers

kallisto_geneset_random_filter_cor

Figure 7. Impact of filtering on correlation coefficient. X-axis trimmed to [0.7-1]

transcript_support_kmers

Figure 8. Fraction unique 31-mers for transcripts split by Transcript Support Level (TSL)

transcript_support_length

Figure 9. Transcript length (log10) split by Transcript Support Level (TSL)

Road-testing Kallisto

In this blog post I’m going to discuss some testing I’ve been doing with Kallisto, a lightning-fast tool for RNA-Seq transcript expression quantification. First though, I’ll discuss very briefly how Kallisto works (skip to “Testing Kallisto” if you don’t want my very simplified explanation of Kallisto).

Alignment-free quantification in RNA-Seq

RNA-Seq bioinformatics can take many forms but typically involves alignment of sequence reads to a reference genome, in order to establish where the reads originate from, followed by estimation of transcript abundance using a reference gene set. These steps are computationally heavy and can be very time-consuming even with multi-threading. Last year, Rob Patro et al released Sailfish which demonstrated that it was not necessary to actually align each read to the genome in order to obtain accurate transcript abundance estimates, all you actually need to do is establish the most likely transcript for each read. They achieved this by shredding the transcriptome and reads into kmers (short overlapping sequences; see Fig. 1), and then matching the transcriptome and read kmers which is a very fast and has a low memory usage. We discussed this paper in our journal club last year and I think most of us took a bit of time to accept that this was actually a viable approach, it just felt like you were losing too much information by shredding the reads into kmers. The results were very convincing though and the Sailfish paper was quickly followed by further “alignment-free” tools including a modified method using only a subset of the read kmers called RNASkim, an update to Sailfish called Salmon, and most recently Kallisto. Kallisto is actually a slight deviation from the kmer shredding method as it forms a de Bruijn graph from the transcript kmers and then aligns the read kmers to the transcriptome de Bruijn graph to form what they describe as “pseudoalignments” (Fig.2). The accuracy of Kallisto is equivalent to the best in class methods whilst being >100 x faster! In fact Kallisto is so quick, it’s perfectly feasible to bootstrap the quantification estimates 100 times to obtain an estimate of the technical variance which is very useful when testing for differentially expressed transcripts (utilised by Sleuth).

kmers

Figure 1. Kmers. Sequences can be split into overlapping (k)mers where k is less than the length of the sequence. Typically for assembly purposes, a single nucleotide overlap is used and the kmers are transformed into a de Bruijn graph which links overlapping kmers. Figure from http://homes.cs.washington.edu/~dcjones/assembly-primer/index.html.

kallisto method schematic

Figure 2. Schematic representation of pseudoalignment. a. Transcripts (shown in colours) are shredded into kmers and then used to form coloured de Bruijn graph (c) in which each transcript corresponds to a path through the graph and each node is a kmer. A read (shown in black at top) is aligned to the graph by matching kmers to find the compatibility of the read to the transcripts. In this case, the read could have originated from either the pink or blue transcripts. Figure adapted from Kallisto publication.


Testing Kallisto

As I mentioned briefly in a previous blog post, Highlights from Genome Science 2015,  Mick Watson gave a very engaging presentation of his recent paper with Christelle Robert at Genome Science 2015 in which they identified human genes that cannot be accurately quantified in isolation using standard RNA-Seq analyses. He explained that for some genes, many of the reads which originate from the gene will align to multiple places in the genome so the quantification of these genes is very inaccurate with many methods. Their proposal is to use the multi-mapping reads to define “multi-map groups” (MMGs) which can treated as a meta-gene for the downstream differential expression testing. Mick presented an example where this analysis of MMGs leads to an interesting finding which would be missed by standard analyses.

After Mick’s talk, I got thinking about a similar analysis for Kallisto to flag transcripts which it cannot accurately quantify. There’s been lots of excitement about the speed to the alignment-free methods, and with the introduction of Sleuth, a pipeline from sequence reads to differentially expressed transcripts can now easily analyse dozens of samples on a small cluster within just a few hours. However, I wanted to get a feel for the accuracy of Kallisto before I jumped in with any real data. My assumption was that transcripts with little unique sequence would be very difficult to quantify by Kallisto (or any other tool for that matter). Originally I followed the methodology from Robert and Watson and simulated 1000 reads per transcript – I quickly realised this was inappropriate. Because each transcript has the same number of reads assigned to it, the simulation wasn’t properly testing whether the expectation–maximization (EM) algorithm used by Kallisto is able to correctly resolve the number of reads per transcript. I therefore took a slightly different approach and simulated 1-100 reads at random from each gene in my reference gene set (hg38 Ensembl v.80 filtered to retain transcripts from protein-coding genes only) with 30 repeat simulations (x30). The two metrics I was interested in were the difference between the sum of ground truths and the sum of Kallisto estimated counts, and the correlation between the ground truth and the estimated counts per simulation. The first metric describes how accurately Kallisto quantifies the true abundance of a transcript within the transcriptome and the second metric described how accurate the Kallisto estimate is for differential expression purposes. N.B It’s possible that a transcript may show a very good correlation but the estimated counts are systematically over- or under-estimated. For the purposes of differential expression analysis this may not be so much of an issue so long as the fold changes in expression are accurately captured.

Figure 3 shows the relationship between the number of unique kmers (here shown as the fraction of all kmers across the transcript) and the fold difference between the sum of ground truths and the sum of Kallisto estimates. As expected, transcripts with a higher fraction of unique kmers are quantified more accurately by Kallisto. However, I was surprised to see Kallisto still seems to accurately quantify many of the transcripts which don’t have a single unique kmer(!). I’m not sure whether this might be an artefact of the simulation somehow?

Kallisto simulation accuracy fold difference

Figure 3. Increased fraction of unique kmers is associated with lower fold differences between Kallisto estimated counts and ground truth. Transcripts were binned by the fraction of kmers which are unique to the transcript. The log2-fold difference between the sum of ground truths and Kallisto estimated counts is shown, along with a boxplot per bin to show the distribution within each bin. Transcripts with absolute differences > 2-fold are shown in red at 1 or -1 respectively.

Figure 4 shows the overall correlation between the sum of ground truths and the sum of estimated counts. Transcripts where the estimated counts were 1.5-fold higher or lower than the ground truths are flagged as “Poor” accuracy. In total, just 701/182510 (0.46%) transcripts failed this threshold. With a even-tighter threshold of 1.2-fold, still only 2.8% of transcripts fail. There were a few transcripts which are considerably overestimated in each individual simulation, the most extreme of which is ENST00000449947, a transcripts of the Azoospermia factor DAZ2 which is ~9-fold overestimated on average across the simulations. When we look at the transcript table and model for DAZ2, (Fig. 5 & Fig. 6) we can see that there are 9 transcripts within this locus, and they appear to vary only in the inclusion/exclusion of particular exons so their sequences will be very similar. In fact, of the 9 transcripts, only ENST0000382440 contains any unique kmers (13/3223; 0.4%), whereas the rest contain 1784-3232 non-unique kmers. It’s no surprise then that Kallisto struggles to accurately quantify the abundance of all 9 transcripts (Fig. 7) with three of the transcripts having zero estimated counts across all simulated data sets. When we look back at the Ensembl table, we can see that a number of the transcripts are annotated with the flag TSL:5 (Transcript Support Level 5) which indicates that there are no mRNAs or ESTs which support this transcript, i.e it’s highly suspect. If all these TSL:5 transcripts were removed from the gene set, every transcript would have some unique kmers which would certainly improve the Kallisto quantification for the transcripts of this gene. Since these transcripts are likely to be miss-assembly artefacts, it seems sensible to suggest they should be removed from the gene set to allow accurate quantification at the other transcripts of this gene.

Kallisto simulation accuracy correlation

Figure 4. Correlation between sum of ground truths and estimated counts from Kallisto across all simulation (n=30). The number of reads per transcript per simulation was randomly sampled from a uniform distribution [0-100], hence the sum of ground truths is not the same for each transcript. Transcripts for which the Kallisto estimates are >1.5-fold higher or lower are flagged as “Poor” quality

Ensembl transcripts

Figure 5. ENSG00000205944 Transcript table from Ensembl.

Ensembl transcript models

Figure 6. ENSG00000205944 Transcript models from Ensembl.

Kallisto accuracy DAZ2

Figure 7. As per Figure 4 except transcripts from gene DAZ2 (ENSG00000205944) are highlighted.

So far, so good for most (99.54%) transcripts with regards to accurate overall quantification. The next thing I wanted to look at was the Pearson product-moment correlation coefficient (r) between the ground truth and estimated counts. Most of the time I’m interested in doing differential expression testing with RNA-Seq. I know with a real data set the estimates themselves will be systematically biased by all sorts of things, chiefly amplification biases and illumina sequencing biases, but I need to know the Kallisto estimates correlate well with the transcript abundance. Figures 8 & 9 shows the relationship between the fraction of unique kmers and the correlation between ground truth and estimted counts. Again as expected, Kallisto performs much better when the transcript contains a high fraction of unique kmers, with a clear drop off in performance below 5% unique kmers. Yet again, Kallisto is still performing very well for some transcripts which don’t have a single unique kmer. In fact, it does slightly better for transcripts with 0-1% unique kmers than those with 1-2% unique kmers(!), which I’m at a complete loss to explain. Perhaps someone from Lior Pachter’s group can explain how this is possible?

In this case it’s slightly more difficult to define a threshold to flag transcripts with a low correlation as the range of ground truths for each transcript will be different so the comparison between transcripts wouldn’t be on the same basis. For my purposes, I’ve just flagged any transcript with less than 5% kmers as being difficult to quantify for now.

If we were to set a correlation coefficient threshold of 0.75, then 10.3% of transcripts would be flagged as failing the threshold. We can see in Figure 10 that transcripts from loci with a larger number of transcripts show much worse correlation. Returning to the example of ENSG00000205944 from earlier, all the transcripts fail to meet this threshold, with ENST00000382440 (the only transcript with unique kmers) showing the highest correlation (0.729).

Kallisto accuracy unique kmers

Figure 8. Transcripts with more unique kmers have a better correlation between ground truth and Kallisto estimates. Transcripts were binned by the fraction of kmers which are unique to the transcript. The boxplot shows the distribution of correlation coefficients per bin.

Kallisto accuracy unique kmers zoom

Figure 9. As per Fig.8 except x-axis restricted to [0-0.1].

Kallisto accuracy correlation transcripts per gene

Figure 10. Transcripts from loci with more transcripts have lower correlations between ground truth and Kallisto estimates. Transcripts were binned by the number of transcripts for the gene which they are annotated to. Boxplots show the distribution of correlation values per bin


Summary

Kallisto appears to be highly accurate for the majority of transcripts, with estimated counts for 99.54% of transcripts within 1.5-fold of the true counts and 97.2% within 1.2-fold. This seems pretty fantastic to me. Most of the transcripts show a good correlation between the simulated read counts and the Kallisto estimates (~90% coefficient > 0.75) which seems pretty good to me for a transcript level analysis with a very complex simulated transcriptome. Right now, I’ve not got anything to compare this to but I’m happy Kallisto’s performing very well. I’m going to add Sailfish and Salmon to the pipeline soon for comparison and then compare to some alignment-based methods.

Finally, this simulation has reminded me of the importance of properly considering the gene set. Inclusion of the poorly supported transcripts here looks likely to have reduced the accuracy of well supported transcripts from the same locus. Before I go onto quantify expression in my samples, I clearly need to define a high confidence set of transcripts. One of the fantastic things about the speed of Kallisto is that it’s so quick that I can include this simulation with every run of the pipeline and retest my new geneset at run-time. This also means anyone else using it within the group will get a report on the suitability of their gene set and transcripts which can’t be accurately quantified will be flagged in the final results.


With thanks:

There have been a number of really informative blog posts on alignment-free quantification, including from the authors of the tools. The Kallisto team have also been very quick at responding helpfully to questions on their google groups forum which is fantastic to see. Any misunderstanding or misrepresentation of how these methods work is, however, entirely my fault!

Rob Patro – Salmon and Kallisto http://robpatro.com/blog/?p=248

Lior Pachter – Kallisto https://liorpachter.wordpress.com/2015/05/10/near-optimal-rna-seq-quantification-with-kallisto/

Nextgenseek – Kallisto http://nextgenseek.com/2015/05/kallisto-a-new-ultra-fast-rna-seq-quantitation-method/