Skip to main content
SpringerLink
Log in

On the Long-Term Fitness of Cells in Periodically Switching Environments

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

Because all the cell populations are capable of making switches between different genetic expression states in response to the environmental change, Thattai and van Oudenaarden (Genetics 167, 523–530, 2004) have raised a very interesting question: In a constantly fluctuating environment, which type of cell population (heterogeneous or homogeneous) is fitter in the long term? This problem is very important to development and evolution biology. We thus take an extensive analysis about how the cell population evolves in a periodically switching environment either with symmetrical time-span or asymmetrical time-span. A complete picture of the phase diagrams for both cases is obtained. Furthermore, we find that the systems with time-dependent cellular transitions all collapse to the same set of dynamical equations with the modified parameters. Furthermore, we also explain in detail how the fitness problem bears much resemblance to the phenomenon, stochastic resonance, in physical sciences. Our results could be helpful for the biologists to design artificial evolution experiments and unveil the mystery of development and evolution.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Barkai, N., Leibler, S., 1997. Robustness in simple biochemical networks. Nature 387, 913–917.

    Article  Google Scholar 

  • Becskei, A., Serrano, L., 2000. Engineering stability in gene networks by autoregulation. Nature 405, 590–593.

    Article  Google Scholar 

  • Cherry, J.L., Adler, F.R., 2000. How to make a biological switch. J. Theor. Biol. 203, 117–133.

    Article  Google Scholar 

  • Gammaitoni, L., Hanggi, P., Jung, P., Marchesoni, F., 1998. Stochastic resonance. Rev. Mod. Phys. 70, 223–287.

    Article  Google Scholar 

  • Gardner, T.S., Cantor, C.R., Collins, J.J., 2000. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342.

    Article  Google Scholar 

  • Hernday, A., Krabbe, M., Braaten, B., Low, D., 2002. Self-perpetuating epigenetic pili switches in bacteria. Proc. Natl. Acad. Sci. U.S.A. 99, 16470–16476.

    Article  Google Scholar 

  • Kepler, T.B., Elston, T.C., 2001. Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations. Biophys. J. 81, 3116–3136.

    Article  Google Scholar 

  • Macnab, R.M., 1992. Genetics and biogenesis of bacterial flagella. Annu. Rev. Genet. 26, 129–156.

    Article  Google Scholar 

  • Moss, F., 1994. Stochastic resonance: from the ice ages to the monkey’s ear. In: Weiss, G.H. (Ed.), Contemporary Problems in Statistical Physics. SIAM, Philadelphia.

    Google Scholar 

  • Murray, J.D., 2002. Mathematical Biology. Springer, Berlin.

    MATH  Google Scholar 

  • Paulsson, J., 2004. Summing up the noise in gene networks. Nature 427, 415–418.

    Article  Google Scholar 

  • Rao, C.V., Wolf, D.M., Arkin, A.P., 2002. Control, exploitation and tolerance of intracellular noise. Nature 420, 231–237.

    Article  Google Scholar 

  • Rosenberg, S.M., 2001. Evolving responsively: adaptive mutations. Nat. Rev. Genet. 2, 504–515.

    Article  Google Scholar 

  • Schlax, P.J., Capp, M.W., Record, M.T. Jr., 1995. Inhibition of transcription initiation by lac repressor. J. Mol. Biol. 245, 331–350.

    Article  Google Scholar 

  • Spudich, J.L., Koshland, D.E., 1976. Non-genetic individuality: chance in the single cell. Nature 262, 467–471.

    Article  Google Scholar 

  • Tanaka, M.M., Bergstrom, C.T., Levin, B.R., 2003. The evolution of mutator genes in bacterial populations: the role of environmental changes and timing. Genetics 164, 843–854.

    Google Scholar 

  • Thattai, M., van Oudenaarden, A., 2004. Stochastic gene expression in fluctuating environments. Genetics 167, 523–530.

    Article  Google Scholar 

  • Unden, G., Becker, S., Bongaerts, J., Holighaus, G., Schirawski, J., Six, S., 1995. O 2-sensing and O 2-dependent gene regulation in facultatively anaerobic bateria. Arch. Microbiol. 164, 81–90.

    Google Scholar 

  • Vilar, J.M.G., Kueh, H.Y., Barkai, N., Leibler, S., 2002. Mechanisms of noise-resistance in genetic oscillators. Proc. Natl. Acad. Sci. U.S.A. 99, 5988–5992.

    Article  Google Scholar 

  • Warren, P.B., ten Wolde, P.R., 2004. Enhancement of the stability of genetic switches by overlapping upstream regulatory domains. Phys. Rev. Lett. 92, 128101-∼14.

    Article  Google Scholar 

  • Wolf, D.M., Arkin, A.P., 2002. Fifteen minutes of fim: control of type 1 pili expression in E. coli. OMICS 6, 91–114.

    Article  Google Scholar 

  • Wolf, D.M., Arkin, A.P., 2003. Motifs, modules and games in bacteria. Curr. Opin. Microbiol. 6, 125–134.

    Article  Google Scholar 

  • Wolf, D.M., Eeckman, F.H., 1998. On the relationship between genomic regulatory element organization and gene regulatory dynamics. J. Theor. Biol. 195, 167–186.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, National Taiwan University, Taipei, Taiwan, ROC

    Ning-Ning Pang

  2. Department of Physics, Tamkang University, Tamsui, Taipei, Taiwan, ROC

    Wen-Jer Tzeng

Authors
  1. Ning-Ning Pang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wen-Jer Tzeng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Ning-Ning Pang or Wen-Jer Tzeng.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pang, NN., Tzeng, WJ. On the Long-Term Fitness of Cells in Periodically Switching Environments. Bull. Math. Biol. 70, 210–235 (2008). https://doi.org/10.1007/s11538-007-9250-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-007-9250-9

Keywords

Search

Navigation