Figure 3. Simulations show that gene expression and capture efficiency influence the observed distribution of splicing.

(a) Simulations of alternative splicing and scRNA-seq under the binary-bimodal model, in which each cell produces one isoform or the other, but rarely both. As in Figure 2b, each row of the histogram shows $\widehat{\mathrm{\Psi }}$ for one intermediate exon across all cells. The observed $\widehat{\mathrm{\Psi }}$ distribution is similar to the true $\mathrm{\Psi }$ distribution, and its shape is largely unaffected by capture efficiency. (b) Simulations with the non-binary, unimodal model, in which most cells present a mixture of the two alternative isoforms. Exons with high expression have a unimodal distribution of true $\mathrm{\Psi }$. Low capture efficiency results in an increase in binary observations (only one isoform observed), leading to a distortion of the observed distribution of $\widehat{\mathrm{\Psi }}$ to look bimodal. Only a handful of the highest expressed exons maintain a unimodal distribution of $\widehat{\mathrm{\Psi }}$. Fewer exons show unimodal splicing as the capture efficiency is reduced. (c) Under the binary-bimodal model, exons with high coverage have slightly fewer binary $\mathrm{\Psi }$ observations, and (d) simulated cells with a high number of total splice junction reads have slightly fewer exons with binary $\widehat{\mathrm{\Psi }}$. (e) Under the unimodal model, exons with intermediate splicing show a strong decrease in binary observations as coverage increases, as seen in real data (Figure 2c). (f) Similarly, simulated cells with high read coverage have a decrease of the proportion of binary $\widehat{\mathrm{\Psi }}$. (g) Effect of capture efficiency on the proportion of binary observations of cassette exons with underlying $\mathrm{\Psi }$ = 0.5. (h) Effect of the initial number of mRNA molecules and underlying $\mathrm{\Psi }$ on the proportion of binary $\widehat{\mathrm{\Psi }}$ observations.

Figure 3—figure supplement 1. Theoretical calculations and simulations of the effect of biological and technical factors in splicing observations.

(a) Theoretical likelihood of capturing only mRNAs representing one isoform of an alternatively spliced gene in a single cell, determined by the total number of mRNAs in the cell, the $\mathrm{\Psi }$ of the isoforms, and a 10% capture efficiency. (b) Probability of observing a binary $\widehat{\mathrm{\Psi }}$ (only one isoform observed) given the number of mRNA molecules of that gene present in the cell, when the underlying $\mathrm{\Psi }$ is fixed at 0.5. (c) Effect of the number of captured mRNA molecules on the uncertainty of $\widehat{\mathrm{\Psi }}$ observations. $\widehat{\mathrm{\Psi }}$ is understood as the maximum likelihood estimate of the underlying $\mathrm{\Psi }$. (d) The posterior probability of having an observed $\widehat{\mathrm{\Psi }}$ within 0.1 of the underlying $\mathrm{\Psi }$. (e) Distribution of the relative error between the average observed $\widehat{\mathrm{\Psi }}$, and the average true $\mathrm{\Psi }$, in our simulations under different capture efficiency rates. The relative error is calculated as the difference between the average $\widehat{\mathrm{\Psi }}$ and the average true $\mathrm{\Psi }$, scaled by the average true $\mathrm{\Psi }$. (f) Distribution of the relative error between the variance in the observed $\widehat{\mathrm{\Psi }}$, and the variance in the true $\mathrm{\Psi }$, in our simulations under different capture efficiency rates.

Figure 3—figure supplement 2. Schematic of scRNA-seq splicing simulator.

Simulator of scRNA-seq splicing data. Green elements represent biological variables; blue elements represent technical processes. The underlying $\mathrm{\Psi }$ is drawn from a Beta distribution with either a bimodal or unimodal shape. Individual gene expression determines the total number of mRNAs, and these mRNAs are spliced stochastically according to $\mathrm{\Psi }$, producing isoforms that splice in or skip the exon. mRNAs are captured with a probability drawn from a normal distribution. Sequencing produces splice junction reads, which determine the observed $\widehat{\mathrm{\Psi }}$.