Mathematical modelling of a microRNA-regulated gene network in <i>Caenorhabditis elegans</i>

Mainul Haque; John R. King; Simon Preston; Matthew Loose; David de Pomerai; Mainul Haque; John R. King; Simon Preston; Matthew Loose; David de Pomerai

doi:10.3934/mbe.2020162

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 4: 2881-2904. doi: 10.3934/mbe.2020162

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Research article

Mathematical modelling of a microRNA-regulated gene network in Caenorhabditis elegans

1.
Department of Mathematics and Physics, University of Portsmouth, Portsmouth PO1 2UP, UK
2.
Institute of Genetics, School of Biology, University of Nottingham, Nottingham NG7 2RD, UK
3.
SRBC Nottingham, University of Nottingham, Nottingham NG7 2RD, UK

Received: 17 December 2019 Accepted: 24 February 2020 Published: 30 March 2020

MicroRNAs are known to regulate gene expression either by repressing translation or by directing sequence-specific degradation of target mRNAs, and are therefore considered to be key regulators of gene expression. A gene-regulatory pathway involving heterochronic genes controls the temporal pattern of Caenorhabditis elegans postembryonic cell lineages. Based on experimental data, we propose and analyze a mathematical model of a gene-regulatory module in this nematode involving two heterochronic genes, lin-14 and lin-28, which are both regulated by lin-4, encoding a microRNA. The conditions under which the model experiences bifurcations are investigated. We determine the parameter regimes for which the system exhibits monostability and bistability, the latter associated with a biological switch. We observe in particular that bistability occurs without co-operativity, in keeping with knowledge about the regulatory behaviour of lin-14 and lin-28. The analytical results are confirmed by numerical simulations that illustrate how the microRNA lin-4 plays a crucial role in determining of the qualitative dynamics of the model.
- microRNA lin-4,
- heterochronic genes (lin-14 and lin-28),
- mathematical modelling,
- biological switches
Citation: Mainul Haque, John R. King, Simon Preston, Matthew Loose, David de Pomerai. Mathematical modelling of a microRNA-regulated gene network in Caenorhabditis elegans[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 2881-2904. doi: 10.3934/mbe.2020162

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Abstract

MicroRNAs are known to regulate gene expression either by repressing translation or by directing sequence-specific degradation of target mRNAs, and are therefore considered to be key regulators of gene expression. A gene-regulatory pathway involving heterochronic genes controls the temporal pattern of Caenorhabditis elegans postembryonic cell lineages. Based on experimental data, we propose and analyze a mathematical model of a gene-regulatory module in this nematode involving two heterochronic genes, lin-14 and lin-28, which are both regulated by lin-4, encoding a microRNA. The conditions under which the model experiences bifurcations are investigated. We determine the parameter regimes for which the system exhibits monostability and bistability, the latter associated with a biological switch. We observe in particular that bistability occurs without co-operativity, in keeping with knowledge about the regulatory behaviour of lin-14 and lin-28. The analytical results are confirmed by numerical simulations that illustrate how the microRNA lin-4 plays a crucial role in determining of the qualitative dynamics of the model.

References

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