Transient power-law behaviour in stochastic gene expression models

Data and code for the paper 'Transient power-law behaviour following induction distinguishes between competing models of stochastic gene expression', now published in Nature Communications. Preprint available here.

Please direct any questions regarding the paper to the authors. For any questions regarding the code please raise an issue or contact Andrew.

The following table contains a description of the uploaded data and relevant code used in the analysis and figures in the paper, as well as a description of the data format.

Name	Type	Description
Experimental data	Folder	Contains the experimental data from [1] and [2] that was used in the nonlinear regression and estimation of short-time exponents for Fig. 5, Supplementary Fig. 14, and Supplementary Fig. 16.
Synthetic Data for Regression	Folder	Contains the synthetic data generated for Fig. 4 and Supplementary Figs. 3-12 to validate the estimation of the short-time exponent from mean mRNA count measurements.
Steady-state data	Folder	Contains the data from sampling the steady-state mRNA count distributions of various $N$ = 3,4,5 state models and comparing with the corresponding effective telegraph model distribution, investigated in Fig. 2, and Supplementary Figs. 1-2.
Powerlaw_calc.ipynb	Jupyter notebook (Julia)	Code for Fig. 3 - solving moment equations to investigate power-law behaviour in the mRNA count statistics.
Example_DataRegression.ipynb	Jupyter notebook (Julia)	Code for performing the non-linear regression and estimation of model parameters applied to the yeast data in Fig. 5 and Supplementary Fig. 14 and the mouse data in Supplementary Fig. 16.
mRNA_dist_FSP.ipynb	Jupyter notebook (Julia)	Code for Fig. 2 - solving the chemical master equation for the steady-state mRNA count distribution of the 5-state model and effective telegraph model and subsequent calculation of the Wasserstein distance.

Package dependencies

All Julia calculations were performed in v1.8.5. To execute the code included here the following Julia packages are required:

• Catalyst.jl
• FiniteStateProjection.jl
• MomentClosure.jl
• DifferentialEquations.jl
• Sundials.jl
• LinearAlgebra.jl
• Plots.jl
• Latexify.jl
• Colors.jl
• CairoMakie.jl
• LsqFit.jl
• GLM.jl
• BlackBoxOptim.jl
• SpecialFunctions.jl
• StatsBase.jl
• DataFrames.jl
• CSV.jl
• XLSX.jl

Citation

Our paper can be cited in the following way:

Nicoll, A. G., Szavits-Nossan, J., Evans, M. R., & Grima, R. (2025). Transient power-law behaviour following induction distinguishes between competing models of stochastic gene expression. Nature Communications, 16(1), 2833. doi:10.1038/s41467-025-58127-4

@article{nicoll_transient_2025,
	title = {Transient power-law behaviour following induction distinguishes between competing models of stochastic gene expression},
	volume = {16},
	copyright = {2025 The Author(s)},
	issn = {2041-1723},
	url = {https://www.nature.com/articles/s41467-025-58127-4},
	doi = {10.1038/s41467-025-58127-4},
	language = {en},
	number = {1},
	urldate = {2025-03-24},
	journal = {Nature Communications},
	author = {Nicoll, Andrew G. and Szavits-Nossan, Juraj and Evans, Martin R. and Grima, Ramon},
	month = mar,
	year = {2025},
	note = {Publisher: Nature Publishing Group},
	keywords = {Bioinformatics, Computational models, Transcription},
	pages = {2833},
}

This repository can be cited in the following way:

Andrew Nicoll. (2024). agnflame/PowerLaw: Pre-release (v0.1.0). Zenodo. https://doi.org/10.5281/zenodo.14245774

@misc{nicoll_agnflamepowerlaw_2024,
	title = {agnflame/{PowerLaw}: {Pre}-release},
	url = {https://doi.org/10.5281/zenodo.14245774},
	publisher = {Zenodo},
	author = {Nicoll, Andrew},
	month = nov,
	year = {2024},
	doi = {10.5281/zenodo.14245774},
}

References

[1] Li, G., Neuert, G. Multiplex RNA single molecule FISH of inducible mRNAs in single yeast cells. Sci Data 6, 94 (2019). https://doi.org/10.1038/s41597-019-0106-6

[2] S. Hao and D. Baltimore, RNA splicing regulates the temporal order of TNF-induced gene expression, Proceedings of the National Academy of Sciences 110, 11934 (2013). https://doi.org/10.1073/pnas.1309990110