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Interpretable and tractable models of transcriptional noise for the rational design of single-molecule quantification experiments

Gorin, Gennady and Vastola, John J. and Fang, Meichen and Pachter, Lior (2021) Interpretable and tractable models of transcriptional noise for the rational design of single-molecule quantification experiments. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210907-221001270

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Abstract

The question of how cell-to-cell differences in transcription rate affect RNA count distributions is fundamental for understanding biological processes underlying transcription. We argue that answering this question requires quantitative models that are both interpretable (describing concrete biophysical phenomena) and tractable (amenable to mathematical analysis). This enables the identification of experiments which best discriminate between competing hypotheses. As a proof of principle, we introduce a simple but flexible class of models involving a stochastic transcription rate coupled to a discrete stochastic RNA transcription and splicing process, and compare and contrast two biologically plausible hypotheses about transcription rate variation. One assumes variation is due to DNA experiencing mechanical strain, while the other assumes it is due to regulator number fluctuations. Although biophysically distinct, these models are mathematically similar, and we show they are hard to distinguish without comparing whole predicted probability distributions. Our work illustrates the importance of theory-guided data collection, and introduces a general framework for constructing and solving mathematically nontrivial continuous–discrete stochastic models.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://doi.org/10.1101/2021.09.06.459173DOIDiscussion Paper
https://github.com/pachterlab/GVFP_2021Related ItemData/Code
ORCID:
AuthorORCID
Gorin, Gennady0000-0001-6097-2029
Vastola, John J.0000-0002-5625-2106
Fang, Meichen0000-0002-8217-0710
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 - September 6, 2021; Version 2 - December 24, 2021; Version 3 - December 25, 2021; Version 4 - December 26, 2021. The DNA, pre-mRNA, and mature mRNA used in Figure 1 are derivatives of the DNA Twemoji by Twitter, Inc., used under CC-BY 4.0. G.G. acknowledges the help of Victor Rohde in exploration of the stochastic process literature. G.G., M.F. and L.P. were partially funded by NIH U19MH114830. J.J.V. was supported by NSF Grant # DMS 1562078. Availability: The simulated data, algorithms, and Python notebooks used to generate the figures are available at https://github.com/pachterlab/GVFP_2021. G.G. and J.J.V. contributed equally to this work. J.J.V. and G.G. conceived of the work, derived the mathematical results, and drafted the manuscript. G.G, M.F., and J.J.V. worked on simulating the models and numerically implementing their analytic solutions. L.P. supervised the work. All authors reviewed and edited the manuscript. The authors have declared no competing interest.
Funders:
Funding AgencyGrant Number
NIHU19MH114830
NSFDMS-1562078
Subject Keywords:Chemical master equation; Markov modeling; mRNA transcription; Stochastic differential equations; Extrinsic noise
DOI:10.1101/2021.09.06.459173
Record Number:CaltechAUTHORS:20210907-221001270
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210907-221001270
Official Citation:Interpretable and tractable models of transcriptional noise for the rational design of single-molecule quantification experiments. Gennady Gorin, John J. Vastola, Meichen Fang, Lior Pachter. bioRxiv 2021.09.06.459173; doi: https://doi.org/10.1101/2021.09.06.459173
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110753
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:08 Sep 2021 15:42
Last Modified:03 Jan 2022 23:44

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