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Special function methods for bursty models of transcription

Gorin, Gennady and Pachter, Lior (2020) Special function methods for bursty models of transcription. Physical Review E, 102 (2). Art. No. 022409. ISSN 2470-0045. doi:10.1103/physreve.102.022409. https://resolver.caltech.edu/CaltechAUTHORS:20200909-153753998

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Abstract

We explore a Markov model used in the analysis of gene expression, involving the bursty production of pre-mRNA, its conversion to mature mRNA, and its consequent degradation. We demonstrate that the integration used to compute the solution of the stochastic system can be approximated by the evaluation of special functions. Furthermore, the form of the special function solution generalizes to a broader class of burst distributions. In light of the broader goal of biophysical parameter inference from transcriptomics data, we apply the method to simulated data, demonstrating effective control of precision and runtime. Finally, we propose and validate a non-Bayesian approach for parameter estimation based on the characteristic function of the target joint distribution of pre-mRNA and mRNA.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/physreve.102.022409DOIArticle
https://arxiv.org/abs/2003.12919arXivDiscussion Paper
ORCID:
AuthorORCID
Gorin, Gennady0000-0001-6097-2029
Pachter, Lior0000-0002-9164-6231
Additional Information:© 2020 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Received 4 April 2020; accepted 10 August 2020; published 31 August 2020. The DNA, pre-mRNA, and mature mRNA used in Fig. 1(a) are derivatives of the DNA Twemoji by Twitter, Inc., used under CC-BY 4.0. The routine for computing the Taylor approximation coefficient Ω_(j,i) uses a function by Ben Barrowes [80], translated from the FORTRAN original by Zhang and Jin [81]. The routine for computing the Taylor series approximation to the exponential integral E₁ (z) is a heavily modified version of a function by Ben Barrowes [80], translated from the FORTRAN original by Zhang and Jin [81]. The subplots in supplemental Figs. 2–4 [38] were aligned using a function by Pekka Kumpulainen [82]. G.G. and L.P. were partially funded by NIH U19MH114830.
Funders:
Funding AgencyGrant Number
NIHU19MH114830
Issue or Number:2
DOI:10.1103/physreve.102.022409
Record Number:CaltechAUTHORS:20200909-153753998
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200909-153753998
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105305
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:09 Sep 2020 23:09
Last Modified:16 Nov 2021 18:41

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