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Mean field analysis of a spatial stochastic model of a gene regulatory network

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Sturrock_etal_mean_field_corrected_2.pdf (3.279Mb)
Date
10/2015
Author
Sturrock, M.
Murray, P. J.
Matzavinos, A.
Chaplain, M. A. J.
Keywords
Gene regulatory framework
Feedback loop
Spatial stochastic model
Mean field
Data clustering
QH301 Biology
QA Mathematics
NDAS
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Abstract
A gene regulatory network may be defined as a collection of DNA segments which interact with each other indirectly through their RNA and protein products. Such a network is said to contain a negative feedback loop if its products inhibit gene transcription, and a positive feedback loop if a gene product promotes its own production. Negative feedback loops can create oscillations in mRNA and protein levels while positive feedback loops are primarily responsible for signal amplification. It is often the case in real biological systems that both negative and positive feedback loops operate in parameter regimes that result in low copy numbers of gene products. In this paper we investigate the spatio-temporal dynamics of a single feedback loop in a eukaryotic cell. We first develop a simplified spatial stochastic model of a canonical feedback system (either positive or negative). Using a Gillespie's algorithm, we compute sample trajectories and analyse their corresponding statistics. We then derive a system of equations that describe the spatio-temporal evolution of the stochastic means. Subsequently, we examine the spatially homogeneous case and compare the results of numerical simulations with the spatially explicit case. Finally, using a combination of steady-state analysis and data clustering techniques, we explore model behaviour across a subregion of the parameter space that is difficult to access experimentally and compare the parameter landscape of our spatio-temporal and spatially-homogeneous models.
Citation
Sturrock , M , Murray , P J , Matzavinos , A & Chaplain , M A J 2015 , ' Mean field analysis of a spatial stochastic model of a gene regulatory network ' , Journal of Mathematical Biology , vol. 71 , no. 4 , pp. 921-959 . https://doi.org/10.1007/s00285-014-0837-0
Publication
Journal of Mathematical Biology
Status
Peer reviewed
DOI
https://doi.org/10.1007/s00285-014-0837-0
ISSN
0303-6812
Type
Journal article
Rights
© 2015, Publisher / the Author(s). This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.springer.com / https://dx.doi.org/10.1007/s00285-014-0837-0
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/7709

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