How Salmonella Typhimurium measures the length of flagellar filaments

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 sigma(28)-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.