betAS: intuitive analysis and visualization of differential alternative splicing using beta distributions

Beta distributions model PSI levels and associated confidence

Profiling AS from an RNA-seq-derived transcriptome relies on sampling the mRNA molecules present in the studied tissue at a given moment. RNA-seq reads that map to annotated exon–exon or exon–intron junctions are typically used as supporting evidence for either the inclusion or exclusion of alternative sequences in transcripts. The relative inclusion level of a known alternative sequence in a biological sample can be conveniently modeled by the beta distribution, with shape parameters given by the number of inclusion and exclusion reads (Fig. 1; Supplemental Fig. S1; see Materials and Methods; Katz et al. 2010; Shen et al. 2014; Vaquero-Garcia et al. 2016; Han et al. 2017; Sterne-Weiler et al. 2018), with the precision of the inclusion level estimate being therefore proportional to the number of supporting reads.

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FIGURE 1.

Beta distributions model PSI levels and associated confidence. Explanatory diagram of the estimation of the PSI with the beta distribution for an alternative transcript sequence (exon) of interest (green) from the RNA-seq junction read counts supporting the sequence's inclusion (inc) or exclusion (exc). The ability of the beta distribution to incorporate the mean value and the confidence of the PSI is further illustrated for two discrepant scenarios of read coverage: lower, with 10 reads (blue), and higher, with 1000 reads (salmon). PSIs randomly generated from the respective beta distributions (500 colored vertically “jittered” points per distribution and associated solid density lines) are dispersed around mean values, being less dispersed as coverage (i.e., confidence associated with supporting evidence) increases. Colored 95% confidence intervals for a proportion's test with P (in this case, PSI) equal to 0.8, with 10 (blue) or 1000 (salmon) trials. Colored (green/blue/salmon) squircles: alternative exons; gray squircles: constitutive exons; junction read depictions colored according to their exon coverage.

As shown in Figure 1, for a particular AS event the PSI quantification alone provides no information on the total number of supporting RNA-seq reads but only on the proportion of them providing evidence for inclusion. The two depicted AS events have contrasting numbers of reads supporting inclusion/exclusion (8/2 for the lower coverage example in blue, 800/200 for the higher-coverage case in salmon) but show the same PSI value. However, the stronger evidence provided by higher coverage (salmon) confers more confidence to its PSI estimate than to that of a case with lower coverage (blue), as illustrated by their confidence intervals (Fig. 1).

betAS pipeline enables intuitive visualization of the magnitude and significance of alternative splicing changes

To provide a decision-support tool for the analysis of AS differences between conditions, allowing subsequent interpretation of their biological implications, betAS implements intuitive visuals that incorporate the estimated inclusion levels and their precision.

AS is more prevalent and more conserved, across vertebrates, in nervous system tissues (Barbosa-Morais et al. 2012; Merkin et al. 2012). Moreover, neuronal-specific RNA-binding proteins that regulate AS in neurons contribute to the functional complexity of neurodevelopmental processes (Licatalosi and Darnell 2006; Raj and Blencowe 2015). Given this relevance of AS in neuronal specification, as a case study, betAS was applied to the analysis of AS changes during the transition from pluripotency to mature neuronal function in mouse by comparing the transcriptomes of samples in the extremes of the publicly available murine neuronal differentiation time line (Hubbard et al. 2013): embryonic stem cells (ESCs) and mature neurons (28 d in vitro).

Volcano plots illustrating the effect size/significance relationship for PSI differences across AS events are shown in Figure 2C,D. In this example, the selection of events differentially spliced between the two conditions aims to maximize both the probability of their PSI values being greater in one of the conditions and the actual difference in PSI between the two conditions. Thus, higher values of P_diff and lower values of FPR highlight more robust separations between the estimated distributions of PSI (Supplemental Figs. S2 and S3), while greater effect sizes (ΔPSI) suggest stronger impacts on sequence inclusion of the biological differences between conditions.

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FIGURE 2.

betAS pipeline enables intuitive visualization of AS changes. (A,B) Beta distributions (vertical “jitter” and density plots of the emitted values) illustrating PSI dispersion for each sample (A) and per phenotypic group (B), with the vertical dashed lines indicating the median PSI for each group, PSI_neurons (dark red) and PSI_ESC (green). (C,D) Volcano plots illustrating the effect size (ΔPSI) as the difference between the median group PSIs and their significance assessed by the estimated probability of differential AS, based on the proportion of differences between ESC and neurons beta distribution randomly emitted values that are >0 (P_diff) (C), and by the false positive rate (FPR) (D). Events are colored by the F-statistic, that is, the ratio of between- to within-group PSI variations (see Materials and Methods). Both y-axis scales are log-transformed to facilitate visualization. Upper row of trimmed points represents P_diff > 0.9995 and FPR < 0.0001. (E–H) Beta distributions (density plots of the emitted values) and vast-tools’ PSIs (bottom, colored ticks) for selected events illustrative of different combinations of effect size and significance of AS differences, identified by vast-tools’ IDs (VAST-DB annotation for the mouse mm10 genome assembly): (E) MmuEX0003638 (gene Actn4, chr7:28895121–28895180), (F) MmuEX0001385 (gene 4833439L19Rik, chr13:54564515–54564621), (G) MmuEX0012381 (gene Commd6, chr14:101640288–101640299), and (H) MmuINT0085965 (gene Kctd17, chr15:78436995–78438486). (ESCs) Embryonic stem cells.

betAS allows the interpretation of ΔPSI values associated with different PSI/coverage scenarios. For instance, while the selected Gon4l exon (Fig. 2A,B) is barely more included in neurons than in ESCs, the volcano plot illustrates some stronger and more robust AS changes (Fig. 2C,D), with several AS events showing switch-like behaviors, as seen by extreme differences (i.e., close to absolute values of 1) in PSI between neurons and ESCs (Fig. 2C,D). Some of these AS changes are illustrated in Figure 2E–H, where the visualization of the beta distributions that model sample-wise inclusion levels elucidates on the differences at the PSI levels and their precision across samples. Among them, the two most extreme examples in significance and effect size, with absolute ΔPSI values >0.50, are exon MmuEX0003638 in gene Actn4, rarely included (PSI ≈ 0) in ESC but typically included (PSI ≈ 0.70) in mature neurons (Fig. 2E) and in neuronal tissues (https://vastdb.crg.eu/event/MmuEX0003638@mm10), and intron MmuINT0085965 in Kctd17, that shows high retention levels in ESC (PSI ≈ 0.75) and is spliced out (PSI ≈ 0) in neurons (Fig. 2H). In both cases, there are coverage differences (associated with differences in gene expression) between the two conditions, reflected by the different widths of the respective beta distributions (Fig. 2E,H). Visualization of inclusion levels through density plots of the respective beta distributions together with the usage of associated significance metrics such as the P_diff also allows the user to spot outlier replicates, as for exon MmuEX0012381 in Commd6 (Fig. 2G), nearly constitutively included (PSI ≈ 1) in all ESC samples except one (PSI ≈ 0.2). Although showing an average ΔPSI similar to that of the intron retention event in Figure 2H, its P_diff significance is penalized due to that inconsistency between replicates (Fig. 2C).

Assessment of betAS ability to estimate differential AS on simulated RNA-seq splice junction read counts from empirically derived PSI and coverage values

In order to benchmark betAS’ accuracy in quantifying differential AS, it should be tested on simulated RNA-seq junction read counts, such that the ability of the ΔPSI values estimated with betAS from the simulated reads could be compared with “ground truth,” reference ΔPSI values. Therefore, the biological and technical variability in PSI and read count distributions and their association with the sequencing sampling, together with the features of beta and Poisson distributions, were explored to simulate RNA-seq spliced junction read counts inspired in a real biological data set (see Supplemental Methods).

Large-scale AS quantifications available from GTEx (Lonsdale et al. 2013) were used to simulate “biology-inspired” PSI values (Fig. 3A; see Materials and Methods). To simulate PSIs reflecting the natural inclusion patterns of highly regulated AS events, the focus was on (i) tissues with prevalent and functionally relevant AS (muscle and brain); and (ii) AS events with typical inclusion levels that are lowly variable in samples of the same tissue, properties that find a proxy in the mathematical concept of unimodality of a distribution. For each representative tissue-unimodal AS event, junction read counts were simulated for a set of N replicates from PSI/coverage pairs.

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FIGURE 3.

betAS accuracy in measuring PSI differences from simulated read counts. (A) Explanatory diagram of the implemented approach to simulate empirically inspired RNA-seq junction read counts. Reference PSI (PSI_REF) and coverage (cov_REF) values for 563 muscle (red) and 309 cerebellum (blue) samples in GTEx version 7 are used to generate N (number of replicates) pairs of randomly emitted low-variance PSI and coverage values per event, used to simulate RNA-seq junction read counts on which betAS accuracy in measuring PSI differences can be evaluated. (B,C) Examples of the simulation approach applied over a low coverage, cov_REF in [8,20] junction read counts, and low number of replicates, N = 5, event (B) and over a high coverage, cov_REF in [100,500] junction read counts, high number of replicates, N = 100, event (C). (Top panels) Density and bottom rug plot showing the original distribution of PSI values for all samples; top rug plot showing the randomly emitted (simulated) low-variance PSIs. Vertical lines indicate PSI_REF values for muscle and cerebellum. (Middle panels) Histogram and bottom rug plot showing the original distribution of coverage values for all samples; top rug plot showing the randomly emitted coverage values. Vertical lines indicate cov_REF values for muscle and cerebellum. (Bottom panels) “betAS on simulated read counts”: density plots representing PSI estimation as done in betAS, with values randomly emitted from a beta distribution with the shape associated with the simulated junction read counts per sample. Solid vertical lines indicate PSI_REF values for muscle and cerebellum, while dashed vertical lines indicate the median PSI values estimated by betAS for muscle and cerebellum.

Differences in inclusion between cerebellum and muscle estimated with betAS from the simulated junction read counts (ΔPSI_estimated) were compared with those found for the reference tissue PSIs per event in GTEx (ΔPSI_REF) (Fig. 3A; Supplemental Figs. S4 and S5). As expected, betAS accuracy in estimating the “real” ΔPSI increases with the simulated number of replicates (N) and coverage (Supplemental Fig. S5), as illustrated by the selected illustrative examples in Figure 3B,C. Moreover, discrepancies found between ΔPSI_simulation and ΔPSI_REF are more pronounced for median PSI values in the alternative region in the middle of the [0,1] range, that is, around 0.5 (in green in Supplemental Fig. S5). This is expected due to the “scaling effect” (Baeza-Centurion et al. 2020), that is, alternatively spliced sequences with intermediate PSI levels are more likely to undergo larger ΔPSIs as a response to perturbations than those nearly constitutively included or excluded.

In any case, even considering low replication level and coverage (Fig. 3B; Supplemental Fig. S5), betAS accurately estimates real ΔPSI values, being therefore a suitable tool for differential AS analysis.

Differential AS significance metrics P_diff and FPR introduced by betAS will naturally depend on coverage and ΔPSI values. In a simulated typical scenario of differential AS analysis between two groups of three biological replicates each, an arbitrary P_diff cutoff of 0.95 will allow significant detection of events with |ΔPSI| values higher than ∼0.3, ∼0.2, and ∼0.1 for coverages of 10, 100, and 1000 reads, respectively (Supplemental Fig. S6A). Similarly, an arbitrary FPR cutoff of 0.05 will allow significant detection of events with |ΔPSI| values higher than ∼0.2, ∼0.15, and ∼0.05 for those coverages (Supplemental Fig. S6B). Despite the proportionality between P_diff and FPR (Supplemental Figs. S3A and S6C), that discrepancy between the two metrics in the minimum effect size detectable with a typical significance cutoff of 5% is explained by them representing different meanings of significance (see Materials and Methods), therefore providing complementary information to support users’ decisions on differential AS. The observed variability in the minimum |ΔPSI| values detectable for fixed P_diff/FPR cutoff and coverage is due to the aforementioned “scaling effect,” that is, the precision of quantification of ΔPSI values depends on the actual range of PSI values involved.

Visual comparison of betAS with other tools for differential AS analyses

The probability of differential AS P_diff and FPR introduced by betAS were compared to significance metrics from other well-established methods for differential splicing analysis with matching AS event annotation (see Supplemental Methods): SUPPA2 (Trincado et al. 2018), rMATS (Shen et al. 2014), and Whippet (Supplemental Fig. S7; Sterne-Weiler et al. 2018). As in betAS applied on junction read counts, both SUPPA2's and rMATS' effect size and significance metrics allow the visualization of the differential AS results through a volcano plot. However, neither SUPPA2 nor rMATS are oriented toward allowing visual inspection of how each replicate contributes to its estimated group PSI and that contribution reflects on the differential AS estimates, something particularly relevant when dealing with few samples. Thus, using betAS visualization infrastructure on differential AS metrics obtained with those tools contributes to make their metrics directly comparable and interpretable. Results of differential AS in mouse neuronal development obtained with each tool were compared for the same set of alternative exons.

SUPPA2's differential AS approach relies on monitoring the uncertainty in PSI estimates as a proxy of biological variability. Since low coverage is associated with higher variability, SUPPA2's assumption is that the significance of each observed ΔPSI between conditions depends on where in the distribution of coverage/uncertainty that difference is (Trincado et al. 2018). Thus, the same ΔPSI can be considered significant if falling in a low uncertainty (high coverage) region while that might not be the case if it falls in the high uncertainty (low coverage) region. Likewise, each ΔPSI obtained is evaluated as more or less extreme for its cognate transcript average coverage level. SUPPA2's estimates of the significance of AS differences are supported by showing ΔPSI values between replicates as a function of the average transcript abundance (Supplemental Fig. S8D,E).

The significance cutoff suggested by SUPPA2 (see Supplemental Methods) and a P_diff > 0.95 were considered to study differences in differential AS calls identified by betAS and SUPPA2. Inspection of events that are selected as differentially spliced by both, one or none of the approaches, that is, cases in each “quadrant” of the scatter plot comparing the respective significance metrics (Fig. 4A), elucidates on the estimates underlying the significance calls for AS differences made by SUPPA2 and betAS. For instance, exon MmuEX0051014 in Usp4 (Fig. 4F), considered significantly differentially spliced by betAS based on an estimated P_diff > 0.95, has PSI estimates per sample such that, even showing a small ΔPSI, their group probability distributions are separated enough between ESC and neurons to be considered different under the P_diff cutoff considered. For SUPPA2, however, such a small ΔPSI is not sufficient to be considered significant at that average coverage (Supplemental Fig. S8D). On the other hand, exon MmuEX0024526 in Isca2 (Fig. 4G) is considered significantly differentially spliced by SUPPA2, as its ΔPSI is among the most extreme in its range of coverage (Supplemental Fig. S8D), but not by betAS based on P_diff, due to the relatively high interreplicate variability illustrated by the overlap of PSI distributions between ESC and neurons (Fig. 4G, bottom).

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FIGURE 4.

Comparison of the significance of differential AS between betAS, SUPPA, and rMATS. (A) Scatterplot comparing betAS’ and SUPPA's differential AS significance metrics. betAS’ estimated probability of differential AS, based on the proportion of differences between the beta distributed randomly emitted values per group that are >0 (P_diff) and SUPPA's P-value, with dashed lines defining quadrants indicating the significance cutoffs considered (P_diff > 0.95 for betAS, P-value <0.05 for SUPPA). Points are colored based on the differential AS calls by both tools: events considered differentially spliced by both betAS and SUPPA (red), by betAS (blue), or SUPPA (green) alone or by none of the tools (gray). Selected example events for each quadrant as larger outlined dots. (B) Scatterplot comparing betAS’ and SUPPA's differential AS effect size (ΔPSI). Red diagonal solid line indicates identity: ΔPSI_SUPPA = ΔPSI_betAS. (C) Scatterplot comparing betAS’ and rMATS' differential AS significance metrics. betAS’ P_diff and rMATS' FDR, with dashed lines defining quadrants indicating the significance cutoffs considered (P_diff > 0.95 for betAS, FDR < 0.05 for rMATS). Points are colored based on the differential AS calls by both tools: events considered differentially spliced by both betAS and rMATS (red), by betAS (blue), or rMATS (yellow) alone or by none of the tools (gray). Selected example events for each quadrant as larger outlined dots. (D) Scatterplot comparing betAS’ and rMATS' differential AS effect size (ΔPSI). Red diagonal solid line indicates identity: ΔPSI_rMATS = ΔPSI_betAS. (E) Receiving operating characteristic (ROC) curves betAS’ differential AS calls with P_diff (solid lines) and FPR (dashed lines), considering as ground truth the differential calls from SUPPA (yellow, P-value <0.05) or rMATS (green, FDR < 0.05). (F–H) SUPPA and vast-tools’ PSIs (top) and densities of emitted beta distributed values for individual samples (middle) and their merging per sample group (bottom, with dashed lines signing median values) for selected events illustrative of different combinations of effect size and significance of AS differences, identified by vast-tools’ IDs (VAST-DB annotation for the mouse mm10 genome assembly): (F) MmuEX0051014 (gene Usp4, chr9:108388277–108388380), (G) MmuEX0024526 (gene Isca2, chr12:84773793–84773908), (H) MmuEX0018137 (gene Fam179b, chr12:64990941–64991090). (ESCs) Embryonic stem cells.

rMATS' differential AS statistical approach relies on modeling inclusion levels by both accounting for the PSI uncertainty in individual replicates, dependent on the total number of supporting RNA-seq reads, and the (biological) variability of PSI values across replicates (Shen et al. 2014). betAS’ ΔPSI values are generally more consistent with those obtained by rMATS (Fig. 4D) than with those obtained by SUPPA2 (Fig. 4B), reflecting the consistency between vast-tools and rMATS PSI quantification. Although rMATS’ FDR is more sensitive than betAS’ P_diff at the selected cutoff (Fig. 4C,E; Supplemental Fig. S9A–C), the significance assessment by betAS and rMATS is also more consistent than between betAS and SUPPA2. One example illustrative of the difference in sensitivity is exon MmuEX0018137 in Fam179b, whose lower inclusion in mature neurons compared to ESC (Fig. 4H) is considered significant by rMATS, but betAS P_diff is <0.95. Visual inspection of the inclusion levels summarized with beta distributions again uncovers high interreplicate variability illustrated by the overlap of PSI distributions between ESCs and neurons, that penalizes the P_diff (Fig. 4H), in contrast with the MmuEX0011507 exon in Clasp1, considered significantly differentially spliced between ESCs and neurons by both tools (Supplemental Fig. S9F), consistently with its known increased inclusion levels in neural tissues (https://vastdb.crg.eu/event/MmuEX0011507@mm10). Similar observations are made when choosing FPR as the significance metric for betAS (Supplemental Figs. S8C and S9C).

The comparison of differential AS between betAS and Whippet (Supplemental Fig. S10) leads to similar observations as that between betAS and rMATS.

betAS applied to differential AS between multiple groups

The differential AS approach implemented by betAS can be applied to multiple (i.e., more than two) groups in a novel ANOVA-inspired way that extends the P_diff definition to the comparison of the differences between samples belonging to different biological conditions to those found between replicates. Statistics for multigroup differential AS are, to our knowledge, absent from the aforementioned established tools and therefore a unique feature of betAS, applicable to the study of splicing in a variety of biological contexts.

To illustrate this, we applied multiple-group betAS to the analysis of AS differences in a subset of human transcriptomes of the forebrain, hindbrain, heart, kidney, liver, and testis (Fig. 5; Cardoso-Moreira et al. 2019). By comparing the medians of differences “between” and “within” groups, both through their difference and their ratio (Fig. 5A,B), while visually inspecting their distributions (Fig. 5C–F, panels on the left), tissue-specific AS can be identified (Fig. 5C–F). While the increased number of samples renders the individual beta distributions less relevant in terms of visualization, the probability that |between|>|within| is, in this case, useful to identify AS events with differences between tissues. The selected exon HsaEX0021044 in DST, for instance, is more commonly skipped in kidney, liver, and testis, whether its inclusion is higher and more variable in brain and heart tissues (Fig. 5C). On the contrary, exon HsaEX0051256 in PTS is more excluded in brain and heart but less so in kidney, liver, and testis (Fig. 5E).

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FIGURE 5.

Beta distributions model inclusion level differences across multiple groups. (A) Scatterplot comparing betAS’ difference of the median of absolute differences between and within groups and the estimated probability that absolute differences between groups are greater than those within groups. Points are colored based on the estimated F-statistic as the median of absolute differences between groups divided by the median of absolute differences within groups. Highlighted points are associated with the selected example AS events in panels C–F. (B) Scatterplot comparing betAS’ difference of the median of absolute differences between and within groups and the estimated F-statistic as the median of absolute differences between groups divided by the median of absolute differences within groups. Points are colored based on the estimated probability that absolute differences between groups are greater than those within groups. Highlighted points are associated with the selected examples in panels C–F. (C–F, left) density plots of the absolute differences between (red) and within (gray), with dashed vertical lines indicative of the median values of each distribution. (Right) Beta distributions (violin plots of the emitted values) for selected events, identified by vast-tools’ IDs (VAST-DB annotation for the human hg19 genome assembly): (C) HsaEX0021044 (gene DST, chr6:56329483–56329554), (D) HsaEX0015811 (gene CLTB, chr5:175823480–175823533), (E) HsaEX0051256 (gene PTS, chr11:112100931–112100953), (F) HsaEX0055568 (gene RPS24, chr10:79799962–79799983).

In order to explore the tissue specificity of AS events or more general questions about AS differences across groups, betAS allows flagging the more variable events across groups (Fig. 5A,B), while inspection of the underlying beta distributions (Fig. 5C–F) can inform on which conditions are driving the differences. Moreover, applying the F-statistic to differential AS quantifications allows ranking events based on how robust the differences between groups are when compared to the differences between samples in the same phenotypical group (Fig. 5A,B; Supplemental Fig. S3).

betAS can also be used to study differential AS across groups with a sequential association, for example, the mouse neuronal differentiation time line data set (Fig. 6; Hubbard et al. 2013). In this case, differences between sequential groups inform on the “steps,” or the monotonicity of the variation of inclusion levels (Fig. 6A,B). Thus, “sequential” differences between groups together with their number of modes may clarify the monotonicity of transitions in inclusion levels, such as those illustrated by event MmuEX0045617 in Stxbp1, whose PSI decreases from ESC to nearly full skipping around 0 d in vitro and then progressively increases as neurons differentiate (Fig. 6C). The number of modes (or “step heights”) of the “sequential” differences and of the “generalized” differences (the median of differences found between groups in the extremes of the time line) can be useful to interpret the progression of PSI along a sequence. For instance, the inclusion of exon MmuEX0024060 in Ilf3 (Fig. 6E) decreases monotonically (from 0 until 16 d in vitro) with multiple “steps” of the same size (PSI difference), thus showing one sequential mode that is different from 0. Exon MmuEX0016666 in Elavl2 (Fig. 6F) shows a PSI increasing in the early differentiation time points (from −4 to 0 and then to 1 d in vitro), consistent with its function in safeguarding loss of neuronal ELAV function in Drosophila (Carrasco et al. 2020) with a PSI “step” that is represented by the positive sequential mode identified.

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FIGURE 6.

Beta distributions model inclusion level differences across sequential groups. (A) Scatterplot comparing betAS’ median “generalized” differences between groups, that is, the median of differences found between groups and the effect size (ΔPSI_betAS) between the extremes of the time line (development days 28—neurons—to −8—ESC). Points are colored based on the estimated monotonicity coefficient (see Supplemental Methods) and shaped based on the F-statistic as the median of absolute differences between groups divided by the median of absolute differences within groups. Highlighted points are associated with the selected example AS events in panels C–F. (B) Volcano plot comparing betAS’ median “generalized” differences between groups and the estimated probability that absolute differences between groups are greater than those within groups. Points are colored based on the estimated F-statistic as the median of absolute differences between groups divided by the median of absolute differences within groups. Highlighted points are associated with the selected examples in panels C–F. (C–F, left) Density plots of the PSI differences between sequential groups (orange) in the time line with rug plots (top) indicating the identified modes, with dashed vertical black line indicative of 0. (Middle) Density plots of the absolute “generalized” (red), sequential (orange), and within (gray) groups differences in PSIs, with vertical lines indicative of the median values of each distribution. (Right) Beta distributions (violin plots of the emitted values, with point indicating the mean of each distribution) for selected events, identified by vast-tools’ IDs (VAST-DB annotation for the mouse mm10 genome assembly): (C) MmuEX0045617 (gene Stxbp1, chr2:32794588–32794713), (D) MmuEX0026784 (gene Lrch2, chrX:147484754–147484804), (E) MmuEX0024060 (gene Ilf3, chr9:21388112–21388150), (F) MmuEX0016666 (gene Elavl2, chr4:91254141–91254179).