Probing the Nanostructure and Arrangement of Bacterial Magnetosomes by Small-Angle X-Ray Scattering

This study explores lab-based small-angle X-ray scattering (SAXS) as a novel quantitative stand-alone technique to monitor the size, shape, and arrangement of magnetosomes during different stages of particle biogenesis in the model organism Magnetospirillum gryphiswaldense. The SAXS data sets contain volume-averaged, statistically accurate information on both the diameter of the inorganic nanocrystal and the enveloping protein-rich magnetosome membrane. As a robust and nondestructive in situ technique, SAXS can provide new insights into the physicochemical steps involved in the biosynthesis of magnetosome nanoparticles as well as their assembly into well-ordered chains. The proposed fit model can easily be adapted to account for different particle shapes and arrangements produced by other strains of magnetotactic bacteria, thus rendering SAXS a highly versatile method.


Introduction
In contrast, transmission electron microscopy (TEM) allows the precise determination 85 of particle numbers, sizes, and shapes as well as their chain assemblies. 86 Nonetheless, gathering statistically significant datasets from time-resolved 87 experiments on cultures is very laborious and time consuming. Furthermore, the 88 analysis is often hindered by preparation or drying artefacts. X-ray radiation based 89 techniques such as extended X-ray absorption fine structure (EXAFS) and X-ray 90 absorption near edge structure (XANES) were already applied for characterization of 91 magnetite biomineralization, however, quantitative TEM measurements were still 92 necessary to address magnetosome size distribution (18,19). 93 As an alternative, small-angle X-ray scattering (SAXS) has been used to assess the  techniques such as TEM, electron tomography or SANS rather than as a stand-alone 135 analytical method. 136 In this study, SAXS is explored as a quantitative stand-alone bulk measurement 137 technique allowing time-efficient particle size analysis (in contrast to well-138 established, but laborious methods such as TEM). Despite the detailed structural 139 resolution of magnetosomes, which can be achieved by highly brilliant X-ray beams  Structural characterization of magnetosome nanoparticles 163 Transmission electron microscopy (TEM). 164 For TEM analysis of whole cells, specimens were directly deposited onto carbon-165 coated copper grids. TEM imaging was performed on a Jeol Jem 1400+ (Freising,166 Germany) operated at an acceleration voltage of 80 kV. Images were recorded with a 167 Gatan Erlangshen ES500W CCD camera. Average particle sizes were measured by 168 data processing using the ImageJ software package v1.52i. Corporation, Japan). All data sets were recorded with a position-sensitive detector 176 (PILATUS 300K, Dectris) placed at different distances from the sample to cover a 177 wide range of scattering vectors q with 0.002 Å -1 < q < 0.5 Å -1 , where q is given as  Therefore, an alternative model is proposed, which contains all structural parameters 209 of interest to the here presented study: the magnetosome particle radius (R), the 210 degree of polydispersity and the distance between neighbouring particles (l). For 211 simplification, no indirect Fourier transformation was included in the evaluation.

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Based on the model presented in Fig. 2b, it can be assumed that the x-ray contrast of

216
In this model, the magnetite crystal was regarded as a sphere (rather than a facetted 217 object) decorated densely, but randomly with smaller spheres simulating the protein-  The intensity I(q) is determined by the square of the amplitude of the scattered wave, 259 which, in turn, is given by equation 1 in case of a particle with the volume V p and an 260 excess electron density distribution Δ(r).
For a system of monodisperse spheres with radius R, eq. 1 can be expressed as a 263 function of the particle radius according to equation 2.
In order to calculate the intensity for polydisperse systems composed of different The scattering intensity I(q) originating from non-interacting small and large spheres 271 is given by the corresponding amplitudes A(q) according to equation 3 (29): where d denotes the distance between the centres of gravity of the large and the 274 small spheres whereas d ij represents the mutual distances between small spheres.

275
The first two terms are equal to the intensities of non-interacting spheres of the 276 corresponding size (cf. eq. 2). In the case of large spheres, the first term decays 277 rapidly with I(q) ~q -4 , and therefore does not contribute significantly to the scattering 278 intensity at high values of q (cf. Fig. S1), whereas the second term associated with the small spheres (high amount) plays the dominant role. Due to polydispersity in 280 real-world systems, the factor   qd qd sin cancels out the third term at high q. 281 Concomitantly, the average over the fourth term vanishes as the distance d ij varies 282 randomly.

283
As discussed above, SAXS represents a low-resolution method at low scattering  and R g the radius of gyration. For the subsequent analysis it is important to note that 299 I small (q) mainly contributes to the scattering intensity for q > 0.05 Å -1 (Fig. 3)  anaerobically grown, magnetosome-producing cells were analysed by TEM and 304 SAXS (Fig. 3). In this experiment, the radius of the magnetosome is derived from the  However, while there were no phenotypical differences between the two specimens 334 of magnetite-free bacteria identified by TEM (Fig. 3c,d), their corresponding SAXS 335 profiles clearly showed a deviation, particularly in the regime of high q (Fig. 3e, blue 336 and green curves), which indicates a substantial biological variability in these 337 systems, and thus complicates the identification of a suitable background curve.

338
The assembly of the magnetosomes into ordered chains is the major reason for the

359
According to the decoupling approximation, the total scattering intensity is 360 proportional to the product of the scattering originating from one particle (form factor) 361 and the scattering due to inter-particle interactions (structure factor). The structure 362 factor S(q) is related to the probability distribution function of inter-particle distances 363 g(r) and can be expressed according to equation 7 for isotropic systems. Next, magnetosome biomineralization and chain formation during cell growth were 375 investigated. Therefore, samples were drawn at different production time points and 376 subsequently analysed by TEM and SAXS (Fig. 4). Using the scattering data 377 obtained at time zero as background (Fig. 4a, black  with TEM results (Fig. 4b), which clearly demonstrate the 1D crystalline order of 384 magnetosomes after 23 h.

385
Such an ordered chain-like nanoparticle array resembles a chain as described by a 386 linear pearl model (36), which is based on the form factor for N S spheres with radius 387 R linearly joined by short strings of length l (cf. Fig. 2; the thickness of the strings is 388 not taken into account). The scattering intensity I(q) for such an assembly is given by

631
Sketch of a single magnetosome (as shown in Fig. 1) and the corresponding x-ray contrast model.

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Additionally, the calculated scattering profile of the small particles is given for comparison (grey line).