(a) Top: Experimental design. Carbonyl cyanide m-chlorophenyl hydrazone (CCCP) reduces the proton motive force (pmf) and was present during growth of the second fragment (60 min) and removed during growth of the third fragment, which allowed the pmf to regenerate. TB: tryptone broth without dye, AnTc: anhydrotetracyline induction of flagella genes. Bottom: Fragment lengths represented as basal/apical (F1/F2) coordinates (n = 255 for 0 µM CCCP, n = 395 for 10 µM CCCP, n = 371 for 20 µM CCCP, n = 353 for 30 µM CCCP). The fits represent the injection-diffusion model with parameters D ≈ 5.25 × 10−13 m2 ⋅ s−1, and kon ≈ 26.10, 3.19, 1.19, 0.70 s−1 for 0 µM, 10, 20, 30 µM CCCP respectively. Representative fluorescent microscopy images of labelled flagella and matching coordinates are highlighted by coloured frames and arrows. Scale bar 2 µm. (b) Filament length as a function of time for decreasing values of kon. For small values of kon, the injection rate but not flagellin transport is rate-limiting, which results in a quasi-linear growth. (c) Growth curves for the CCCP raw data of panel a determined by fitting the data to the injection-diffusion model with a fixed parameter a. The values for kon decrease by a factor of 8 (10 µM CCCP), 22 (20 µM CCCP), and 38 (30 µM CCCP), compared to the untreated control. (d) Equation and biophysical parameters of the injection-diffusion model.