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.
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.
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.
Dockery, J.D., Keener, J.P., 2001. A mathematical model for quorum sensing in Pseudomonas aeruginosa. Bull. Math. Biol. 63, 95–116.
Hughes, K.T., Aldridge, P.D., 2001. Putting a lid on it. Nat. Struct. Biol. 8, 96–97.
Iino, T., 1974. Assembly of Salmonella flagellin in vitro and in vivo. J. Supramol. Struct. 2, 372–384.
Keener, J.P., 2005. A model for length control of flagellar hooks of Salmonella typhimurium. J. Theor. Biol. 234, 263–275.
Kutsukake, K., Ohya, Y., Iino, T., 1990. Transcriptional analysis of the flagellar regulon of Salmonella typhimurium. J. Bacteriol. 172, 741–747.
Macnab, R.M., 2003, How bacteria assemble flagella. Annu. Rev. Microbiol. 57, 77–100.
Marshall, W.F., 2004. Cellular length control systems. Annu. Rev. Cell Dev. Biol. 20, 677–693.
Minamino, T., Macnab, R.M., 2000. Interactions among components of the Salmonella flagellar export apparatus and its substrates. Mol. Microbiol. 19, 1–5.
Mogilner, A., Rubenstein, B., 2005. The physics of filopodial protrusion. Biophys. J. 89, 1–14.
Yonekura, K., Maki-Yonekura, S., Namba, K., 2003. Complete atomic model of the bacterial flagellar filament by electron cryomicroscopy. Nature 424, 643–650.
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.
Author information
Authors and Affiliations
Corresponding author
Rights 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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11538-005-9033-0