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

Creators: Gorin, Gennady; Vastola, John J.; Fang, Meichen; Pachter, Lior

Abstract

The question of how cell-to-cell differences in transcription rate affect RNA count distributions is fundamental for understanding biological processes underlying transcription. 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 continuous stochastic transcription rate driving a discrete 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. We introduce a framework for numerically and analytically studying such models, and apply Bayesian model selection to identify candidate genes that show signatures of each model in single-cell transcriptomic data from mouse glutamatergic neurons.

Additional Information

© The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. The DNA, pre-mRNA, and mature mRNA used in Fig. 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. These authors contributed equally: Gennady Gorin and John J. Vastola. Author contributions. 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. G.G. and M.F. fit the single-cell data. L.P. supervised the work. All authors reviewed and edited the manuscript. Data availability. Publicly available data were downloaded from the NeMO archive. The metadata were obtained from http://data.nemoarchive.org/biccn/grant/u19_zeng/zeng/transcriptome/scell/10x_v3/mouse/processed/analysis/10X_cells_v3_AIBS/. Raw FASTQs were obtained from http://data.nemoarchive.org/biccn/grant/u19_zeng/zeng/transcriptome/scell/10x_v3/mouse/raw/MOp/. Pre-built genome references were obtained from the 10× Genomics website, at https://support.10xgenomics.com/single-cell-gene-expression/software/downloads/latest. The FASTQ files were used to generate loom files with spliced and unspliced count matrices. These count matrices are available in the Zenodo package 10.5281/zenodo.7262328. The results of the fits generated with the Monod package, the SDE gradient descent fit, and the MCMC fit are available at https://github.com/pachterlab/GVFP_2021, as well as the Zenodo package 10.5281/zenodo.7262328. All synthetic data, generated using custom stochastic simulation code, as well as the simulation parameters, are deposited in the GitHub and Zenodo repositories. Code availability. Single-cell RNA sequencing data were pseudoaligned using kallisto∣bustools 0.26.0, wrapping kallisto 0.46.2 and bustools 0.40.0. Dataset filtering, reduced model fits, and Akaike information criterion computation were performed using Monod 0.2.4.0. MCMC parameter inference was performed using PyMC3 3.11.4, dependent on Theano-PyMC 1.1.2. Data input/output were performed using loompy 3.0.7. Numerical procedures, such as gradient descent and quadrature, were performed using SciPy 1.4.1 and NumPy 1.21.5. The algorithms were implemented in the framework of Python 3.7.12. All code is available at https://github.com/pachterlab/GVFP_2021 and the associated Zenodo package 10.5281/zenodo.726232892. The GitHub and Zenodo repositories include scripts used to construct a mouse genome reference, pseudoalign datasets, and generate all figures. They are modular: the analysis can be restarted at a set of intermediate steps. The outputs of certain steps, viz. pseudoaligned count matrices, results of the Monod pipeline, the list of genes of interest, results of the gradient descent procedure, and results of the Bayes factor computation procedure can be recomputed, or loaded in based on files available in the repositories. Synthetic data generated by simulation, as well as the routines used to generate the data, are available in the repositories. The CIR simulation is implemented in Python 3.7.12. The Gamma-OU simulation was developed using MATLAB 2020a, and executed in the Python wrapper for Octave, using versions oct2py 5.4.3 and octave-kernel 0.34.1. The authors declare no competing interests.

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