Skip to main content
Log in

How Salmonella typhimurium measures the length of flagellar filaments

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

Abstract

We present a mathematical model for the growth and length regulation of the filament of the flagellar motor of Salmonella Typhimurium. Under the assumption that the molecular constituents are translocated into the nascent filament by an ATPase and then move by molecular diffusion to the growing end, we find a monotonically decreasing relationship between the speed and the velocity of growth that is inversely proportional to length for a large length. This gives qualitative but not quantitative agreement with data of the velocity of growth. We also propose that the length of filaments is “measured” by the rate of secretion of the σ28-antifactor FlgM, using negative feedback, and present a mathematical model of this regulatory network. The combination of this regulatory network with the length-dependent rate of growth enable the bacterium to detect length shortening and regrow severed flagellar filaments.

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

Access this article

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

  • Chadsey, M.S., Karlinsey, J.E., Hughes, K.T., 1998. The flagellar anti-sigma factor FlgM actively dissociates Salmonella typhimurium σ28 RNA polymerase holoenzyme. Genes Dev. 12, 3123–3136.

    Google Scholar 

  • Chilcott, G.S., Hughes, K.T., 2000. Coupling of flagellar gene expression to flagellar assembly in Salmonella enterica serovar Typhimurium and Escheria coli. Microbiol. Mol. Biol. Rev. 64, 694–708.

    Article  PubMed  CAS  Google Scholar 

  • Dockery, J.D., Keener, J.P., 2001. A mathematical model for quorum sensing in Pseudomonas aeruginosa. Bull. Math. Biol. 63, 95–116.

    Article  PubMed  CAS  Google Scholar 

  • Hughes, K.T., Aldridge, P.D., 2001. Putting a lid on it. Nat. Struct. Biol. 8, 96–97.

    Article  PubMed  CAS  Google Scholar 

  • Iino, T., 1974. Assembly of Salmonella flagellin in vitro and in vivo. J. Supramol. Struct. 2, 372–384.

    Article  PubMed  CAS  Google Scholar 

  • Keener, J.P., 2005. A model for length control of flagellar hooks of Salmonella typhimurium. J. Theor. Biol. 234, 263–275.

    Article  PubMed  CAS  MathSciNet  Google Scholar 

  • Kutsukake, K., Ohya, Y., Iino, T., 1990. Transcriptional analysis of the flagellar regulon of Salmonella typhimurium. J. Bacteriol. 172, 741–747.

    PubMed  CAS  Google Scholar 

  • Macnab, R.M., 2003, How bacteria assemble flagella. Annu. Rev. Microbiol. 57, 77–100.

    Article  PubMed  CAS  Google Scholar 

  • Marshall, W.F., 2004. Cellular length control systems. Annu. Rev. Cell Dev. Biol. 20, 677–693.

    Article  PubMed  CAS  MathSciNet  Google Scholar 

  • Minamino, T., Macnab, R.M., 2000. Interactions among components of the Salmonella flagellar export apparatus and its substrates. Mol. Microbiol. 19, 1–5.

    Article  Google Scholar 

  • Mogilner, A., Rubenstein, B., 2005. The physics of filopodial protrusion. Biophys. J. 89, 1–14.

    Article  Google Scholar 

  • Yonekura, K., Maki-Yonekura, S., Namba, K., 2003. Complete atomic model of the bacterial flagellar filament by electron cryomicroscopy. Nature 424, 643–650.

    Article  PubMed  CAS  ADS  Google Scholar 

  • Zaslaver, A., Mayo, A.E., Rosenberg, R., Bashkiin, P., Sberro, H., Tsalyuk, M., Surette, M.G., Alon, U., 2004. Just-in-time transcription program in metabolic pathways. Nat. Genet. 36(5), 486.

    Article  PubMed  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. P. Keener.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Keener, J.P. How Salmonella typhimurium measures the length of flagellar filaments. Bull. Math. Biol. 68, 1761–1778 (2006). https://doi.org/10.1007/s11538-005-9033-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-005-9033-0

Keywords

Navigation