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Inside mammalian cells, single genes are known to be transcribed in stochastic bursts leading to the synthesis of nuclear RNAs that are subsequently exported to the cytoplasm to create mRNAs. We systematically characterize the role of export processes in shaping the extent of random fluctuations (i.e. noise) in the mRNA level of a given gene. Using the method of Partitioning of Poisson arrivals, we derive an exact analytical expression for the noise in mRNA level assuming that the nuclear retention time of each RNA is an independent and identically distributed random variable following an arbitrary distribution. These results confirm recent experimental/theoretical findings that decreasing the nuclear export rate buffers the noise in mRNA level, and counterintuitively, decreasing the noise in the nuclear retention time enhances the noise in the mRNA level. Next, we further generalize the model to consider a dynamic extrinsic disturbance that affects the nuclear-to-cytoplasm export. Our results show that noise in the mRNA level varies non-monotonically with the disturbance timescale. More specifically, high- and low-frequency external disturbances have little impact on the mRNA noise level, while noise is amplified at intermediate frequencies. In summary, our results systematically uncover how the coupling of bursty transcription with nuclear export can both attenuate or amplify noise in mRNA levels depending on the nuclear retention time distribution and the presence of extrinsic fluctuations.
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This content will become publicly available on April 1, 2026
Incorporating spatial diffusion into models of bursty stochastic transcription
The dynamics of gene expression are stochastic and spatial at the molecular scale, with messenger RNA (mRNA) transcribed at specific nuclear locations and then transported to the nuclear boundary for export. Consequently, the spatial distributions of these molecules encode their underlying dynamics. While mechanistic models for molecular counts have revealed numerous insights into gene expression, they have largely neglected now-available subcellular spatial resolution down to individual molecules. Owing to the technical challenges inherent in spatial stochastic processes, tools for studying these subcellular spatial patterns are still limited. Here, we introduce a spatial stochastic model of nuclear mRNA with two-state (telegraph) transcriptional dynamics. Observations of the model can be concisely described as following a spatial Cox process driven by a stochastically switching partial differential equation. We derive analytical solutions for spatial and demographic moments and validate them with simulations. We show that the distribution of mRNA counts can be accurately approximated by a Poisson-beta distribution with tractable parameters, even with complex spatial dynamics. This observation allows for efficient parameter inference demonstrated on synthetic data. Altogether, our work adds progress towards a new frontier of subcellular spatial resolution in inferring the dynamics of gene expression from static snapshot data.
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- Award ID(s):
- 2339241
- PAR ID:
- 10593077
- Publisher / Repository:
- Royal Society Publishing
- Date Published:
- Journal Name:
- Journal of The Royal Society Interface
- Volume:
- 22
- Issue:
- 225
- ISSN:
- 1742-5662
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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