Bulletin of Mathematical Biology

, Volume 68, Issue 7, pp 1761–1778

How Salmonella typhimurium measures the length of flagellar filaments

Original Paper

DOI: 10.1007/s11538-005-9033-0

Cite this article as:
Keener, J.P. Bull. Math. Biol. (2006) 68: 1761. doi:10.1007/s11538-005-9033-0


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.


Flagellar Filament Length 

Copyright information

© Society for Mathematical Biology 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA