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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 (Unpublished)

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To what extent do cell-to-cell differences in transcription rate affect RNA copy number distributions, and what can this variation tell us about biological processes underlying transcription? We argue that successfully answering such questions requires quantitative models that are both interpretable (describing concrete biophysical phenomena) and tractable (amenable to mathematical analysis); in particular, such models enable 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 (governed by a stochastic differential equation) coupled to a discrete stochastic RNA transcription and splicing process, and compare and contrast two biologically plausible hypotheses about observed transcription rate variation. One hypothesis assumes transcription rate variation is due to DNA experiencing mechanical strain and relaxation, while the other assumes that variation is due to fluctuations in the number of an abundant regulator. Through a thorough mathematical analysis, we show that these two models are challenging to distinguish: properties like first- and second-order moments, autocorrelations, and several limiting distributions are shared. However, our analysis also points to the experiments which best discriminate between them. Our work illustrates the importance of theory-guided data collection in general, and multimodal single-molecule data in particular for distinguishing between competing hypotheses. We use this theoretical case study to introduce and motivate a general framework for constructing and solving such nontrivial continuous-discrete models.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper ItemData/Code
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. This version posted September 6, 2021. The DNA, pre-mRNA, and mature mRNA images used in Figure 3 are derivatives of the DNA Twemoji by Twitter, Inc., used under CC-BY 4.0. Color palettes used in all figures are partially derived from dutchmasters by EdwinTh, used under the MIT license. 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. Code Availability: Python code that can be used to reproduce the figures is available at
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Record Number:CaltechAUTHORS:20210907-221001270
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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:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110753
Deposited By: Tony Diaz
Deposited On:08 Sep 2021 15:42
Last Modified:16 Nov 2021 19:42

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