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Analytical solutions of the chemical master equation with bursty production and isomerization reactions

Gorin, Gennady and Pachter, Lior (2021) Analytical solutions of the chemical master equation with bursty production and isomerization reactions. . (Unpublished)

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Splicing cascades that alter gene products post-transcriptionally also affect expression dynamics. We study a class of processes and associated distributions that emerge from a bursty promoter model coupled to a path graph of downstream mRNA splicing, and more generally examine the behavior of finite-activity jump drivers coupled to a directed acyclic graph of splicing with one or more roots. These solutions provide full time-dependent joint distributions for an arbitrary number of species, offering qualitative and quantitative insights about how splicing can regulate expression dynamics. Finally, we derive a set of quantitative constraints on the minimum complexity necessary to reproduce gene co-expression patterns using synchronized burst models. We validate these findings by analyzing long-read sequencing data, where we find evidence of expression patterns largely consistent with these constraints.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper ItemCode ItemIPython Parallel reference documentation
Gorin, Gennady0000-0001-6097-2029
Pachter, Lior0000-0002-9164-6231
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. Version 1 - March 24, 2021; Version 2 - June 30, 2021. The DNA illustration used in Figures 1 and 4, modified from [44], is a derivative of the DNA Twemoji by Twitter, Inc., used under CC-BY 4.0. The directed acyclic graph generation code was adapted from the IPython Parallel reference documentation: The yellow and gray colors used in Figures 1, 3, and 4 are the Pantone Colors of the Year 2021, PANTONE 17-5104 Ultimate Gray and PANTONE 13-0647 Illuminating. G.G. and L.P. were partially funded by NIH U19MH114830. Code availability: Python notebooks that can be used to reproduce Figures 5 and 6 are available at
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Record Number:CaltechAUTHORS:20210325-075042340
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Official Citation:Analytical solutions of the chemical master equation with bursty production and isomerization reactions. Gennady Gorin, Lior Pachter. bioRxiv 2021.03.24.436847; doi:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108549
Deposited By: Tony Diaz
Deposited On:25 Mar 2021 23:07
Last Modified:16 Nov 2021 19:12

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