Dissection of Pilus Tip Assembly by the FimD Usher Monomer

Type 1 pili are representative of a class of bacterial surface structures assembled by the conserved chaperone/usher pathway and used by uropathogenic Escherichia coli to attach to bladder cells during infection. The outer membrane assembly platform—the usher—is critical for the formation of pili, catalysing the polymerisation of pilus subunits and enabling the secretion of the nascent pilus. Despite extensive structural characterisation of the usher, a number of questions about its mechanism remain, notably its oligomerisation state, and how it orchestrates the ordered assembly of pilus subunits. We demonstrate here that the FimD usher is able to catalyse in vitro pilus assembly effectively in its monomeric form. Furthermore, by establishing the kinetics of usher-catalysed reactions between various pilus subunits, we establish a complete kinetic model of tip fibrillum assembly, able to account for the order of subunits in native type 1 pili.


SI1. Effects of bound detergent on apparent protein molecular weight
The molecular weight of a protein can be calculated from sedimentation velocity data using the Svedberg equation: (eq. S1) where s and D are the sedimentation coefficient and diffusion constant, respectively, extracted from the experimental data; R is the gas constant; T is the temperature; M is the molecular weight of the protein; € ν is the partial specific volume of the protein; and ρ is the buffer density. The presence of detergent bound to the protein will affect its apparent molecular weight such that: (eq. S2) where M tot , M p and M d signify the total molecular weight of the complex and those of protein and detergent, respectively. The partial specific volume of the complex ( € ν tot ) will be a weighted average of the protein € ν p and the detergent € ν d : (eq. S3) By rearranging equation 1, and substituting in equations 2 and 3, we find that: (eq. S4) In all our experiments, we have calculated an apparent molecular mass (M app ), using € ν p : (eq. S5) Combining equations 4 and 5, then rearranging, we can therefore show how M app will be affected by differing amounts of detergent bound to the protein: Given that € ν p = 0.7249 cm 3 .g -1 , € ν d = 0.814 cm 3 .g -1 and ρ = 1.00718 g.cm -3 , we can calculate the exact impact of any given quantity of detergent bound to the protein: Thus, the presence of any detergent will lead us to overestimate the mass of protein by 0.67 times the mass of detergent, and any numbers we derive for the mass of complexes can be considered overestimates.

SI2. Derivation of expected kinetics of DSE
According to classical kinetics (see e.g. Fersht, 1985 1 for details) product formation for the general reaction: should have a double exponential form. When k +1 and k -1 are fast compared to k +2 and k -2 , as is known to be the case for the donor strand exchange reaction, and when FimC:FimG is in large excess over FimD:FimC:FimH, these two exponentials have the rates: (eq. S8) and (eq. S9) where K D = k −1 k +1 and [CG] is the concentration of FimC:FimG added.
Because k +1 and k -1 are known to be 5.7 x 10 6 M -1 .s -1 and 197 s -1 , respectively at 4 ˚C 2 , we can evaluate λ 1 directly. Regardless of FimC:FimG concentration this phase will have reached equilibrium within the dead time of mixing (~1 s), and will be unmeasurable over our timescale of experiment (15 s -30 min). Thus, formation of product will take place with a single rate equal to k +2 [CG] [CG]+ K D . Note that k -2 = 0, because donor strand exchange is irreversible. The amplitude of this phase will be equal to the total amount of product formed at completion, i.e. the concentration of FimD:FimC:FimH provided. As the observed rate of product formation follows double exponential kinetics (see main text), but a simple binding followed by DSE model only predicts a single exponential, an additional reaction step is required to account for the data.

SI3. Surface plasmon resonance measurements
In order to confirm that the affinity of the NTD of FimD for chaperone:subunit complexes is not affected by the detergent used to keep the entire usher soluble, we carried out SPR experiments using a Biacore 3000 instrument (GE healthcare). The SPR results are shown in Table S1. As can be seen, the presence of DDM at 0.05 % has a negligible effect on the affinity of the FimD NTD for either chaperone:subunit complex measured. Furthermore, our results are consistent with those determined previously by the Glockshüber group 2 . We are therefore confident that our use for data fitting of the numbers in ref 2 -determined at multiple temperatures and using multiple techniques -is appropriate.

Production of FimC:FimF Q99C[A647]
The mutation FimF Q99C was introduced into FimF by site-directed mutagenesis where P is the concentration of product formed, S 0 is the initial concentration of the limiting substrate (FimD:FimC:FimH:FimG), I p and I s are the intensities of the product and substrate bands, respectively, and c is a correction factor equal to I p I s + I p for FimD:FimC:FimH:FimG complex alone (i.e. with no FimC:FimF added). This correction factor was required to account for the fact that a small band is present at the position of product in the usher complex samples (corresponding to FimD:FimC:FimH:FimG 2 and arising from the protein production). The above analysis corrects for differences in intensity between the lanes and for small quantities of contaminants at the position of the product band. However it should be noted that due to difficulty in determining background and the assumption that stain intensity is proportional to amount of protein, this method is less accurate and quantitative than fluorescence.    labelled FimG or FimF fit best to double exponentials while the non-fluorescent data set appears to fit better to a single exponential. However, it should be borne in mind that densitometry from silver-stained gels is much less precise and sensitive than quantitation of fluorescence, so the second phase could be present but undetectable. Double exponential fits to the data are also shown. The concentrations of FimC:FimF are coloured by rainbow from lowest to highest and are: 1 µM (red), 2 µM (yellow), 5 µM (green), 10 µM (cyan) and 20 µM (blue). After fitting all five data sets to the model in Fig. 2a (see text for details), the best fit value for k DSE is 2.1 ± 0.9 min -1 .