A Model for Length Control of Flagellar Hooks of {\it Salmonella} Typhimurium


We present a mathematical model for the growth and length regulation of the hook component of the flagellar motor of {\it Salmonella} Typhimurium. Under the assumption that the molecular constituents are translocated into the nascent filament by an ATP-ase and then move by molecular diffusion to the growing end, where they polymerize into the growing tube, we find that there is a detectable transition from secretion limited growth to diffusion limited growth. We propose that this transition can be detected by the secretant FliK, allowing FliK to interact with FlhB thereby changing the secretion target of the type III secretion machinery and terminating the growth of the hook. The growth of biofilm is a major problem in many industrial and health related settings, as it is the major cause of hospital infections and manufacturing production disruptions, for example.