Aggregative adherence fimbriae form compact structures as seen by SAXS

Bacterial colonization is mediated by fimbriae, which are thin hair-like appendages dispersed from the bacterial surface. The aggregative adherence fimbriae from enteroaggregative E. coli are secreted through the outer membrane and consist of polymerized minor and major pilin subunits. Currently, the understanding of the structural morphology and the role of the minor pilin subunit in the polymerized fimbriae are limited. In this study we use small-angle X-ray scattering to reveal the structural morphology of purified fimbriae in solution. We show that the aggregative fimbriae are compact arrangements of subunit proteins Agg5A + Agg3B which are assembled pairwise on a flexible string rather than extended in relatively straight filaments. Absence of the minor subunit leads to less compact fimbriae, but did not affect the length. The study provides novel insights into the structural morphology and assembly of the aggregative adherence fimbriae. Our study suggests that the minor subunit is not located at the tip of the fimbriae as previously speculated but has a higher importance for the assembled fimbriae by affecting the global structure.


Materials and methods: SAXS data collection:
SAXS experiments were performed at the automated BM29 bioSAXS beamline at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France.

Model free analysis:
The radius of gyration (Rg) of a particle is a well-defined measure of the overall size of a single homogeneous particle of any shape.In the region q ≤ 1/Rg, where distances comparable to Rg are probed, the intensity follows the simple Guinier approximation (Eq.1), This is seen as a characteristic plateau in the curve at low q in a log-log plot.From this relation, radii of gyration can be calculated independently of any structural models or assumptions.For higher angles, the Guinier approximation does not hold.The shape of the scattering pattern I(q) is then given by the structure of the scattering molecules, as encoded in the so-called form factor (P(q)).In terms of mass concentration (cm) and weight (M), the scattering is given by Eq. 2.
() =    (∆  ) 2   () where Δpm is the average excess per-mass scattering length density of proteins compared to water (2.0 × 10 10 cm/g), and NA is Avogadro's number.However, because P(q → 0) = 1, the molecular weight of the scattering molecules can be determined in a model-free way from the value of I0 = I(q → 0).

Structural characterization of subunits:
In many fibers, subunits are linked together by donor strand complementation where an Nterminal donor strand segment from one subunit binds into a hydrophobic binding pocket in the neighboring subunit.Thus, it is theoretically possible to make spherical permutated constructs of them by engineering part of their C-terminal fragment onto the N-terminal side of the molecule 1,2 .Though, this in theory should result in monomer subunits, it is apparent from the SAXS study on dsc-Agg5A, despite donor strand complementation (Fig. S1), that it mainly exists as a dimer in solution (original paper Fig. 1, Table 1).These findings align with previous crystal structure studies illustrating formation of self-complementary dimers of homologous proteins 3 .Then, two subunits are stacked on top of each other in a cylindrical fashion.On the other hand, many other homologous structures contain dimeric asymmetric units which are not self-complimentary.Some of these arrangements are listed in Table S1, complemented with their calculated radii of gyration.
Because of the uncertainty in the experimental gyration radius of dsc-Agg5A, none of the models in Table S1 can be unambiguously chosen.The experimental range of Rg values essentially allows for all the listed dimeric structures.The same is seen when scattering patterns from the models of Table S1 are calculated and compared to experimental data, as in Fig. S2.There, all the models with exception of the monomeric NMR structure lie close to the experimental curve, though clearly no single model describes the data quantitatively.On the other hand, a weighted average of these model curves readily reproduces experimental data, which suggests that the sample is a mixture of both monomeric and dimeric forms of dsc-Agg5A.A Representable PDB structures (Table S1) are used as background for fitting the SAXS.
B By merging the model curves in a linear combination, the model fits perfectly over the experimental curve, after a constant of 4×10 -2 cm 2 /g has been subtracted, to account for the inaccuracies in the buffer subtraction.
An ab initio protein simulation is a computational modeling of protein structure and dynamic using a first principle method, involving protein structure prediction, energy calculations, molecular dynamics simulation, analysis and validation 8 .The shape reconstruction of the subunit A data is shown together with the self-complimentary dimer (2AXW) and the monomeric NMR structure (5LVY) (Fig. S3A).The reconstruction shows a dense part equivalent to a monomeric structure, as well as a less dense part, which corresponds to the second half of a dimer.Such a shape is expected for a solution mixture of monomers and dimers.Taken together, the linear combination in Fig. S2 and the ab initio shape reconstruction in Fig. S3A, point towards a mixture of a self-complimentary dimer (such as 2AXW) and of the NMR subunit structure.The coefficients in the linear combination gives a rough estimate of the proportions of monomers and dimers.These proportions are normally dependent on concentration, but no such dependence was found in the raw data (see original paper Fig. 3).
Possibly, the time scale of equilibration is longer than the few minutes needed to dilute and measure the subunit sample.B Dsc-Agg5AB using balls and space filling.All structures are drawn to scale.All structures are drawn to scale.Molecular representations are generated using VMD version 1.9.3. 9 As discussed above, the dsc-Agg5AB oligomerizes in solution, as seen both in the apparent molecular weight and in the radius of gyration.We have no starting points for describing these assemblies structurally.Thus, an ab initio model is presented and the shape reconstruction is in line with the initial results, demonstrating that dsc-Agg5AB oligomerizes (Fig. S3B).The shape is not unique, and different shapes are identified though they consistently are grouped as large and elongated.

Choice of model
SAXS data can be directly analyzed and compared to idealized structures such as rods, spheres, disks, or random coils, to mention a few.These structures give characteristic slopes in plots of log I vs. log q, which makes validation easy.Fimbriae are expected to adopt rod-like structures, which would correspond to a slope of -1 in such a plot (Fig. S4).However, the fimbriae scattering data demonstrates a slope close to -2, which aligns more with an expected ideal random coil.This is clear evidence that the fimbriae do not form rod-like structures but instead fold into conformations that are more compact.

Figure S4 -Fimbriae data compared to the ideal cases of linear rods and random coils.
The AB data set has been multiplied by a factor of 2 for easier comparison.

Monte Carlo simulation -Model construction
Interpreting the fimbriae as a chain of subunits, these subunits can be monomers or small assemblies, arranged like beads on a string.The chain's parameters can be varied, and the resulting ensemble of the fimbriae structures can be sampled in a simple Monte Carlo simulation, where each set of chain parameters and a number of structures are obtained from the simulation.Subsequently the X-ray scattering pattern of each structure are calculated and the corresponding chain parameters explaining the structure are derived.

Calculating X-ray scattering for chains of proteins
Given a subunit structure and a chain structure (a list of bead coordinates), the total scattering from the fimbria can be written as a general Debye sum (Eq.4.) 6 , where i and run over all atoms, is the scattering factor of atom i, and rij is the distance between atoms i and j.If instead each subunit is approximated as a spherical scatterer with a spherical scattering amplitude F(q), the equation can be written as Eq. 5.

𝐼(𝑞
where the indices a and b now run over the subunits.This expression shows that it is enough to know the conformation of the chain and the intensity form factor F2(q) of the subunits.The former is obtained from Monte Carlo simulations while the latter can be readily calculated from PDB models using programs such as CRYSOL 7 .

Model definition and behavior
The ideal random chain model, which gives the best matching slope in Fig. S4, is not physically reasonable, as an actual chain cannot adopt any random conformation.A real chain cannot overlap with itself and cannot bend at any angle between subunits.In addition, a real chain might attract itself so that non-adjacent subunits tend to stick together.Thus, we constructed a model, which considers these elements, and their parameters are summarized in Table S2 (Fig. S5).

N
The number of beads (subunits) per chain.
The separation between connecting beads.This is a hard-sphere potential with a radius d/2, thus preventing two non-adjacent beads to come closer together than this value.
β Stickiness, defined as β = ε /RT, where ε is the bond energy for the sticky interaction and RT the thermal energy.A Metropolis condition based on exp(-βΔn) is used for each step of the Monte Carlo simulation where Δn bonds are broken.A bond is considered to be formed when the centers of two non-adjacent beads are closer than 1.2d.The result is a square-well potential.
F 2 (q) The intensity form factor of the subunits.Using Monte Carlo simulations, we can simulate three different fimbriae packing models, supplementing the ideal random coil model (Fig. S6A).In the ideal random coil model, chain overlap with itself was allowed (though it is not physically possible).By introducing selfavoidance in the model, the chain swells because of the repulsive interactions between its different segments.If stickiness is introduced (β >0), the chains shrink again because of the added attraction.These effects are also observed from the size of the clouds of blue dots, which represent a large number of independent conformations.An example of an entirely random aggregate of independent spheres is also included for comparison.
Using the assumption that one NMR subunit structure is placed along each link of the chain the four different models will result in different X-ray scattering curves (Fig. S6B).As stickiness is increased, there is a smooth transition from the self-avoiding chain behavior to that of random aggregates of unconnected particles.This means that as stickiness becomes very strong, SAXS cannot distinguish chains of subunits from random aggregates of independent subunits.As expected, the Guinier region moves towards higher q (Rg decreases) as stickiness is increased.At the same time the plateau at intermediate q becomes clearer.Both of these changes are analogous to the difference between the A and A+B fimbriae curves (Fig. S4).

S13
In a similar manner as modeling stickiness, we can also model the filament stiffness (ӨMax).
within the chain structure and predict its effect on the scattering.As the chain is made stiffer, its scattering pattern transitions from that of the flexible and self-avoiding coil to that of an ideal rod, with a slope of -1 in the log-log plot, as expected (Fig. S7).

Figure S5 -
Figure S5 -Illustration of the model, with the NMR subunit structure (from Fig. S1) used

Figure S6 .AF 2 9 B
Figure S6.A Aligned trajectories of simulated ideal random chains, self-avoiding random chains, and