Learning the Dynamics of Bursty Transcription and Splicing using Ultra-Fast Parameter Inference and New Analytical Solutions of the Chemical Master Equation

Abstract

Single cell RNA counts data is increasingly available, and can in principle be used to extract mechanistic insight about transcription and splicing dynamics. In order to infer numbers related to processes of biophysical interest---for example, splicing rates, RNA production rates, RNA degradation rates, and the number of splicing steps involved in processing some particular kind of RNA---it is necessary to compare the predictions of quantitative models with counts data. In practice, this involves generating model predictions for an enormous number of parameter sets, and using some measure of goodness of fit to determine reasonable parameter ranges; because this procedure tends to be extremely computationally expensive, one can typically fit only very simple models involving a small state space and small number of parameters. We report on a new approach to fitting the dynamics of bursty transcription and splicing, which uses newly derived analytical solutions to the chemical master equation to greatly speed up parameter inference. The associated speedup, which we have found on simulated counts data to be many orders of magnitude in some cases, comes from not using stochastic simulations or numerical approaches like finite state projection, but the aforementioned closed-form mathematical formulas. Our approach applies to models of splicing involving arbitrarily many splicing steps, introns that can be removed in an arbitrary order, and arbitrarily many downstream alternatively spliced variants. Moreover, it scales extremely well as one's splicing model gets increasingly complicated (e.g. more splicing steps, more alternative splicing branches). We comment on some of the issues associated with using these algorithms to learn parameters from real counts data, including identifiability problems.

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