Kinetic Analysis of the Growth Rate of the Flagellar Hook in Salmonella typhimurium by the Population Balance Method

Abstract

The growth rate of flagellar hooks in Salmonella typhimurium was analyzed by computer-aided simulation of the length distributions of mutant hooks of uncontrolled length (polyhooks). The wild-type hook has a relatively well-controlled length, with an average of 55 nm and a standard deviation of 6 nm. Mutations in the fliK gene give rise to polyhooks. A histogram of the lengths of polyhooks from a fliK mutant shows a peak at 55 nm with a long monotonic tail extending out to 1 μm. To analyze the growth rate, we employed the population balance method. Regression analysis showed that the histogram could fit a combination of two theoretical curves. In the first phase of growth, the hook starts with a very fast growth rate (40 nm/min), and then the rate exponentially slows until the length reaches 55 nm. In the second phase of growth, where the hook length is over 55 nm, the hook grows at a constant rate of 8 nm/min. Second mutations in either the fliK or flhB genes, as found in pseudorevertants from fliK mutants, give rise to polyhook filaments (phf). The ratio between the numbers of hooks with and without filament was 6:4. The calculated probability of filament attachment to polyhooks was low so that the proportion of hooks that start filament growth was only 2% per minute. The lengths of polyhooks with and without filaments were measured. A histogram of hook length in phf's was the same as that for polyhooks in single-site fliK mutants, against the expectation that the distribution would shift to a shorter average. The role of FliK in hook length control is discussed.