Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

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.
  Article Metrics

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


  • 1. R. C. Lee, R. L. Feinbaum, V. Ambros, The C. elegans heterochronic gene lin-4 encodes small RNAs with antisense complimentarity to lin-14, Cell, 75 (1993), 843-843.
  • 2. G. Ruvkun, Molecular biology: Glimpses of a tiny RNA world, Science, 294 (2001), 797-799.
  • 3. A. M. Denli, B. B. J. Tops, R. H. A. Plasterk, R. F. Ketting, G. J. Hannon, Processing of primary microRNAs by the Microprocessor complex, Nature, 432 (2004), 231-235.
  • 4. G. Meister, M. Landthaler, Y. Dorsett, T. Tuschl, Sequence-specific inhibition of microRNA-and siRNA-induced RNA silencing, RNA, 10 (2004), 544-550.
  • 5. R. F. Place, L. Li, D. Pookot, E. J. Noonan, R. Dahiya, MicroRNA-373 induces expression of genes with complementary promoter sequences, Proc. Natl. Acad. Sci. USA, 105 (2008), 1608-1613.
  • 6. J. C. Carrington, V. Ambros, Role of microRNAs in plant and animal development, Science, 301 (2003), 336-338.
  • 7. J. Lu, G. Getz, E. A. Miska, E. Alvarez-Saavedra, J. Lamb, D. Peck, et al., MicroRNA expression profiles classify human cancers, Nature, 435 (2005), 834-838.
  • 8. H. Hwang, J. T. Mendell, MicroRNAs in cell proliferation, cell death, and tumorigenesis, Br. J. Cancer, 94 (2006), 776-780.
  • 9. G. Martello, L. Zacchigna, M. Inui, M. Montagner, M. Adorno, A. Mamidi, et al., MicroRNA control of Nodal signalling, Nature, 449 (2007), 183-188.
  • 10. M. Kato, T. Paranjape, R. Ullrich, S. Nallur, E. Gillespie, K. Keane, et al., The mir-34 microRNA is required for the DNA damage response in vivo in C. elegans and in vitro in human breast cancer cells, Oncogene, 28 (2009), 2419-2424.
  • 11. G. T. Bommer, I. Gerin, Y. Feng, A. J. Kaczorowski, R. Kuick, R. E. Love, et al., p53-mediated activation of mirna34 candidate tumor-suppressor genes, Curr. Biol., 17 (2007), 1298-1307.
  • 12. T. Chang, E. A. Wentzel, O. A. Kent, K. Ramachandran, M. Mullendore, K. H. Lee, et al., Transactivation of mir-34a by p53 broadlyáinfluences gene expression andpromotesapoptosis, Mol. Cell, 26 (2007), 745-752.
  • 13. L. He, X. He, L. P. Lim, E. De Stanchina, Z. Xuan, Y. Liang, et al., A microrna component of the p53 tumour suppressor network, Nature, 447 (2007), 1130-1134.
  • 14. H. Liu, X. Tian, Y. Li, C. Wu, C. Zheng, Microarray-based analysis of stress-regulated microRNAs in Arabidopsis thaliana, RNA, 14 (2008), 836-843.
  • 15. R. Feinbaum, V. Ambros, The timing of lin-4RNA accumulation controls the timing of postembryonic developmental events in Caenorhabditis elegans, Dev. Biol., 210 (1999), 87-95.
  • 16. V. R. Ambros H. R. Horvitz, The lin-14 locus of Caenorhabditis elegans controls the time of expression of specific postembryonic developmental events, Genes Dev., 1 (1987), 398-414.
  • 17. V. Ambros, A hierarchy of regulatory genes controls a larva-to-adult developmental switch in C. elegans, Cell, 57 (1989), 49-57.
  • 18. M. Haque, Mathematical Modelling of Eukaryotic Stress-Response Gene Networks, PhD thesis, University of Nottingham, 2012.
  • 19. K. Seggerson, L. Tang, E. G. Moss, Two genetic circuits repress the Caenorhabditis elegans heterochronic gene lin-28 after translation initiation, Dev. Biol., 243 (2002), 215-225.
  • 20. P. Arasu, B. Wightman, G. Ruvkun, Temporal regulation of lin-14 by the antagonistic action of two other heterochronic genes, lin-4 and lin-28, Genes Dev., 5 (1991), 1825-1833.
  • 21. M. Lagos-Quintana, R. Rauhut, W. Lendeckel, T. Tuschl, Identification of novel genes coding for small expressed RNAs, Science, 294 (2001), 853-858.
  • 22. N. C. Lau, L. P. Lim, E. G. Weinstein, D. P. Bartel, An abundant class of tiny RNAs with probable regulatory roles in Caenorhabditis elegans, Science, 294 (2001), 858-862.
  • 23. U. Alon, An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC, 2007.
  • 24. J. Sotomayor, Generic bifurcations of dynamical systems, in Dynamical Systems, Academic Press, (1973), 561-582.
  • 25. E. G. Moss, R. C. Lee, V. Ambros, The cold shock domain protein lin-28 controls developmental timing in C. elegans and is regulated by the lin-4 RNA, Cell, 88 (1997), 637-646.
  • 26. J. L. Cherry, F. R. Adler, How to make a biological switch, J. Theor. Biol., 203 (2000), 117-133.
  • 27. M. C. Ow, N. J. Martinez, P. H. Olsen, H. S. Silverman, M. I. Barrasa, B. Conradt, et al., The FLYWCH transcription factors FLH-1, FLH-2, and FLH-3 repress embryonic expression of microRNA genes in C. elegans, Genes Dev., 22 (2008), 2520-2534.
  • 28. W. Rudin, Principles of Mathematical Analysis, 3rd edition, McGraw-Hill, New York, 1976.


Reader Comments

your name: *   your email: *  

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved