Transcription rate dynamics and RNA copy number noise: General relations and data-driven predictions
Abstract
Stochastic models of gene expression typically begin with a microscopic model of transcription and propagate its statistics to the RNA distribution. Here we develop a doubly stochastic framework in which RNA production is Poisson conditional on a time-varying transcription rate λ(t). For RNA lifetimes drawn independently from an arbitrary finite-mean distribution, we derive the RNA Fano factor in terms of the lifetime survival function and the autocovariance of λ(t). For a Poisson degradation process with rate μ, the survival kernel provides an exponential temporal filter, and the result depends only on the mean, variance, and normalized autocorrelation of λ(t). These quantities may be calculated from an explicit rate model or, under ergodicity and adequate sampling, estimated from a sufficiently long rate trajectory. We validate the data-driven estimator using simulated transcription-rate trajectories, without supplying the known autocorrelation to the estimator. We also obtain exact analytical results for transcription-rate dynamics modeled by a discrete M/M/1 process and by drift-diffusion with reflecting, periodic, or first-passage-reset boundaries, and verify each result by direct simulation of the coupled transcription-rate and RNA copy-number processes.
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BibTeX
@misc{mccune2026transcription,
title = {{Transcription rate dynamics and RNA copy number noise: General relations and data-driven predictions}},
author = {Amara McCune and Ido Golding and Shlomi Reuveni and Sarah Kostinski},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07993},
eprint = {2609.07993},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07993},
}
RIS
TY - UNPB
TI - Transcription rate dynamics and RNA copy number noise: General relations and data-driven predictions
AU - Amara McCune
AU - Ido Golding
AU - Shlomi Reuveni
AU - Sarah Kostinski
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07993
UR - https://arxiv.org/abs/2609.07993
AB - Stochastic models of gene expression typically begin with a microscopic model of transcription and propagate its statistics to the RNA distribution. Here we develop a doubly stochastic framework in which RNA production is Poisson conditional on a time-varying transcription rate λ(t). For RNA lifetimes drawn independently from an arbitrary finite-mean distribution, we derive the RNA Fano factor in terms of the lifetime survival function and the autocovariance of λ(t). For a Poisson degradation process with rate μ, the survival kernel provides an exponential temporal filter, and the result depends only on the mean, variance, and normalized autocorrelation of λ(t). These quantities may be calculated from an explicit rate model or, under ergodicity and adequate sampling, estimated from a sufficiently long rate trajectory. We validate the data-driven estimator using simulated transcription-rate trajectories, without supplying the known autocorrelation to the estimator. We also obtain exact analytical results for transcription-rate dynamics modeled by a discrete M/M/1 process and by drift-diffusion with reflecting, periodic, or first-passage-reset boundaries, and verify each result by direct simulation of the coupled transcription-rate and RNA copy-number processes.
ER -