Stochastic models are based on simple mathematical models which describe a wide variety of processes. Stochasticity is then added on top of these models. That is to say, we take preexisting mathematical concepts and add a variable of randomness to them. This can be done using stochastic simulations.
Here, we present a cartoon of a stochastic model of transcription, followed by an animation of a stochastic simulation depicting RNA processes, both made by Dr. Thomas Brown, who completed his PhD in Jane Mellor’s lab, where he worked on a stochastic model of transcription, by building on existing models (Raj et al. 2006; Zenklusen et al. 2008; Choubey et al. 2015).
Cartoon of a stochastic model of transcription. Brown et al. 2018.
In this model of transcription, the promoter of a gene of interest is allowed to switch, in a stochastic manner, from an inactive (red) to an active state (green) with rate α and β, respectively. When the promoter is active, transcription initiation is allowed and occurs at a constant rate γ. The RNA polymerase then moves with a constant rate k along the gene of interest. Given gene length N, the total time of transcription is equal to the sum of N exponential distributions with rate k. For simplification, the model assumes that once transcription by the polymerase is over, a mature or cytoplasmic RNA transcript is generated. Finally, all RNAs possess a constant half-life and are subjected to constant degradation δ. RNA distributions were simulated using the Gillespie stochastic simulation algorithm (Gillespie 1977) and the delayed stochastic simulation algorithm (Barrio et al. 2006).
Animation of a stochastic simulation of RNA production and degradation in a population of cells. RNA are transcribed in the nucleus and exported to the cytoplasm before being degraded. At steady state, the number of RNA present in the nucleus and cytoplasm of each cell are counted to create a frequency plot of transcripts.
- Brown T et al. (2018) Antisense transcriptiondependent chromatin signature modulates sense transcript dynamics. Mol Syst Biol. Feb 12;14(2):e8007.
doi: 10.15252/msb.20178007. Pubmed
- Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry 81, 25, 2340–2361.
- Barrio M et al. (2006) Oscillatory regulation of Hes1: Discrete stochastic delay modelling and simulation. PLoS Comput Biol. Sep 8;2(9):e117.
doi: 10.1371/journal.pcbi.0020117. Epub 2006 Jul 25. Pubmed
- Brown T (2019) Study of the dynamics of gene expression by mathematical modelling and systems approaches [PhD thesis]. University of Oxford.
- Raj A et al. (2006) Stochastic mRNA synthesis in mammalian cells. PLoS Biol. Oct;4(10):e309. doi: 10.1371/journal.pbio.0040309. Pubmed
- Zenklusen D et al. (2008) Single-RNA counting reveals alternative modes of gene expression in yeast. Nat Struct Mol Biol. Dec;15(12):1263-71.
doi: 10.1038/nsmb.1514. Epub 2008 Nov 16. Pubmed
- Choubey S et al. (2015) Deciphering Transcriptional Dynamics In Vivo by Counting Nascent RNA Molecules. PLoS Comput Biol. Nov 6;11(11):e1004345.
doi: 10.1371/journal.pcbi.1004345. Pubmed
ArchR: Robust and scaleable analysis of single-cell chromatin accessibility data.https://www.archrproject.com/bookdown/index.html
Software:intrinsic Noise Analyzer
Searching for transcription factor binding sites (TFBSs)
Cell image analysis software
A flexible software sketchbook and a language for learning how to code within the context of the visual arts.
Python package that exploits Approximate Bayesian Computation for parameters interference and model selection.
Python package for stochastic simulations of biochemical systems via Gillespie direct method (SSA), as well as variants such as tau-leaping. Can also perform deterministic simulations by numerical integration of ODEs. https://gillespy2.readthedocs.io/en/latest/index.html
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