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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

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.
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Keywords 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. Mathematical Biosciences and Engineering, 2020, 17(4): 2881-2904. doi: 10.3934/mbe.2020162

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