Transient and delay chemical master equations

Creators: Gorin, Gennady; Yoshida, Shawn; Pachter, Lior

Abstract

The serial nature of reactions involved in the RNA life-cycle motivates the incorporation of delays in models of transcriptional dynamics. The models couple a bursty or switching promoter to a fairly general set of Markovian or deterministically delayed monomolecular RNA interconversion reactions with no feedback. We provide numerical solutions for the RNA copy number distributions the models induce, and solve several systems with splicing and degradation. An analysis of single-cell and single-nucleus RNA sequencing data using these models reveals that the kinetics of nuclear export do not appear to require invocation of a non-Markovian waiting time.

Additional Information

The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY 4.0 International license. G.G. thanks Dr. John J. Vastola and Catherine Felce for valuable discussions. G.G. and L.P. were partially funded by the National Institutes of Health grant U19MH114830. A part of the reported results were obtained during a Data Sciences Co-op with Celsius Therapeutics, Inc. The DNA and RNA illustrations are derived from the DNA Twemoji by Twitter, Inc., used under CC-BY 4.0. Code availability All scripts used to process data and generate the figures are located at https://github.com/pachterlab/GYP_2022. The raw count matrices, as well as the outputs of the Monod pipeline, are available on Zenodo (Gorin, 2022). The authors have declared no competing interest.

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Submitted - 2022.10.17.512599v2.full.pdf

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