Modeling bursty transcription and splicing with the chemical master equation

RNA velocity unraveled

“…Splicing rate data are more challenging to obtain, but targeted experiments [76], genome-wide imaging [77], and our preliminary mechanistic investigations [78] suggest that selection and removal of individual introns is stochastic, but the overall splicing process has rather complex kinetics, not reducible to a single step.…”

“…Only genes with spliced–unspliced Pearson correlation above 0.05 are used for fitting parameters (as on p. 4 of SN2 in [1]); if the correlation is below this threshold, the gene is removed from procedure and presumed stationary. This is valid for the constitutive model, but inappropriate for broader model classes: for example, bursty transcription yields strictly positive correlations, making this statistic ineffective for identifying dynamics [78, 104].…”

“…As an illustration of what this means, we consider the simplest, univariate model of transcription, a classical birth-death process: where α is a constant transcription rate and β is a constant efflux rate. Depending on the system, β may have various biophysical interpretations, such as splicing, degradation, or export from the nucleus [78, 104].…”

“…Extending the solution to multiple species merely requires defining the correct multivariate G ( z, t ). This is tractable for all directed acyclic graphs of splicing [78]. However, the broader set of models does not have an analytical solution, even in terms of the exponential integral, because it requires integrals of the following intractable form: Extending the solution to piecewise constant transcription rates, as in Figure 3, or to any piecewise constant parameter values, only requires computing the appropriate y ( t ).…”

“…We have described a preliminary method that can partially bypass these problems [78]. Sequencing "long" reads, which at this time is possible with technologies such as Oxford Nanopore [69], or sequencing of "full-length" libraries produced with methods such as Smart-seq3 [127], enhances identifiability and facilitates the construction of new annotations based on presence or absence of intron sequences.…”