Mesoscale structures in amorphous silks from a spider’s orb-web

Of the 7–8 silk fibers making up an orb-web only the hierarchical structural organization of semicrystalline radial fibers -composed of major ampullate silk- has been studied in detail, given its fascinating mechanical features. While major ampullate silk’s nanofibrillar morphology is well established, knowhow on mesoscale (> 50–100 nm) assembly and its contribution to mechanical performance is limited. Much less is known on the hierarchical structural organization of other, generally less crystalline fibers contributing to an orb-webs’ function. Here we show by scanning X-ray micro&nanodiffraction that two fully amorphous, fine silk fibers from the center of an orb-web have different mesoscale features. One of the fibers has a fibrillar composite structure resembling stiff egg case silk. The other fiber has a skin–core structure based on a nanofibrillar ribbon wound around a disordered core. A fraction of nanofibrils appears to have assembled into mesoscale fibrils. This fiber becomes readily attached to the coat of major ampullate silk fibers. We observe that a detached fiber has ripped out the glycoprotein skin-layer containing polyglycine II nanocrystallites. The anchoring of the fiber in the coat suggests that it could serve for strengthening the tension and cohesion of major ampullate silk fibers.

Orb-webs built by Araneoidea spiders are composed of seven to eight functional silk fibers ( Fig. 1A) 1,2 . Of these, the hierarchical structural organization of load-bearing radial or dragline fibers, composed principally of major ampullate gland silk (MaS) proteins, has been studied in most detail by scattering, imaging and spectroscopy techniques. Although its blend of strength, extensibility and toughness shows phylogenetic variability attributed to silk protein evolution 3,4 , the hierarchical structural organisation of MaS fibers derived by scattering techniques is highly conserved 5,6 . Indeed, atomic-scale, wide-angle X-ray and neutron scattering (WAXS/WANS) suggest a two-phase system with 10-15% crystalline, alanine-rich β-sheet nanodomains of a few nm diameters 7-10 , randomly dispersed in a disordered, polypeptidic matrix. Diffuse short-range order (SRO) X-ray scattering peaks 8 from the amorphous phase do not allow differentiating specific (e.g. helical 11 ) hydrogen-bonding motifs. Microscopic models for mechanical performance of dry fibers assume that the nanodomains act as reinforcement-nodes of an amorphous network with hydrogen-bonding interactions 12,13 . Nanoscale, small-angle X-ray scattering (SAXS) and related techniques agree to self-assembly of nanodomains with less-ordered chain segments into lamellar stacks of nanofibrils of 5-7 nm diameters 8,10,14,15 , backed by bottom-up molecular modelling 16 . Scanning nanobeam X-ray diffraction (nanoXRD) with down to ~ 40 nm focal spots suggest a homogeneous nanofibrillar morphology as volume fractions of nanofibrils and nanodomains appear to be correlated 17 . We note, however, variability of nanofibrillar dimensions and volume concentrations when comparing XRD to atomic force microscopy (AFM) and transmission/scanning electron microscopy (TEM/SEM) results, implying that the nature and contribution of nanofibrils to mechanical properties are not fully resolved 18 . A notable exception are ultrathin MaS ribbons of the genus Loxosceles whose mechanical properties can be directly related to individual nanofibrils 19,20 . There is, however, a lack of scattering or imaging evidence of higher-order (mesoscale: > 50-100 nm) assembly of nanofibrils in MaS fibers although hierarchical network models based on nanofibrillar domains allow simulating mechanical data such as strain-hardening 21 . Indirect evidence for nanofibrillar bundles of ~ 150 nm diameter was obtained by X-ray particle size analysis for more crystalline (44%) bagworm silk while a smaller diameter of ~ 40 nm was proposed for MaS fibers 15 . The assumption of a homogeneous hierarchical structural organisation assumed in most experimental and modelling approaches is, however, biased by fiberspecific mesoscale heterogeneities. Indeed, a skin-core structure has been observed by TEM for N. clavipes 22 and nanoXRD for A. bruennichi's MaS fibers but is absent for B. mori fibers 8,17 . Biochemical analysis of N. clavipes fibers suggests a sequence of (from outside) lipidic, glycoprotein and proteneous layers and a core with a heterogeneous distribution of MaSp1 and MaSp2 proteins 23 . Various functions have been attributed to the (mesofibrillar 8,24 ) proteneous skin-layer such as providing plasticity and confinement for the core 23  www.nature.com/scientificreports/ generated by the nanofibrils in the core 25 . It is, however, fair to say that the phylogenetic origin of the skin-core structure and its contribution to MaS fibers mechanical properties 4 are currently not understood. As compared to MaS fibers, the hierarchical structural organization of less crystalline or amorphous orb-web fibers, such as flagelliform silk (flag) fibers forming the cores of the capture-spiral thread 1,2 , is less well explored. Flag fibers appear also to be structurally more diverse, as N. clavipes and A. bruennichi's flag fibers are amorphous showing strong SRO scattering 26,27 while A. trifasciata, E. fuliginea and C. sexcuspidata flag fibers contain a fraction of crystalline polyglycine II (PG-II) nanodomains 26,28 of unknown distribution in the matrix. In the absence of network-reinforcing nodes discussed for MaS fibers 12,13 , molecular or super-molecular reinforcement motifs (e.g. β-springs 29 ) have been proposed contributing to the blend of toughness and extensibility of flag fibers 30 . Enhancing these functional properties by mesoscale features could provide an evolutionary advantage for stopping larger preys impacting an orb-web while limiting the metabolic cost of making larger diameter fibers. Indeed, a possible enhancement mechanism could be the incorporation of skin-core structures used for improving mechanical performance of synthetic polymers and biomaterials 31 . Silk fiber composites with mesoscale features are, however, not well documented for Araneoidea, as also for other types of spider silks although we note the fibrillar composite structure of A. aurentatia's cylindrical gland fibers used for constructing egg cases 32 .
Probing bulk fibrillar features by TEM 32,33 or atomic force microscopy (AFM) 34 requires ultra-thin sections and embedding techniques which are prone to artefacts. In the exceptional case of ultra-thin L. laeta ribbons, single nanofibrils could, however, be directly visualized by AFM 19 . While not reaching the resolution of TEM and AFM, scanning nanoXRD can reveal fibrils down to the 100 nm scale and below as shown for the skin-layer of whole A. bruennichi's MaS fibers 8,17 . Indeed, nanoXRD has confirmed the amorphous nature of A. bruennichi's flag fibers while A. marmoreus flag fibers show an amorphous core and a mesofibrillar skin-layer containing crystalline PG-II nanodomains 27 . A possible relation of the skin-core structure to the nature of prey caught in the web has been suggested 27 but more flag fibers have to be studied across Araneoidea to establish a trend.
Here we explore by scanning nanoXRD whether highly amorphous silk fibers with weak chain interactions can contain specific mesoscale features suggesting functional differences. Our aim was detecting such fibers insitu in the natural environment of orb-web fibers. We focused principally on silks from the hub of A. bruennichi spiders orb-web serving as central foraging site (Fig. 1A,B). As compared to the geometrically well-defined mesh of the capture-section composed of fibers with known functions such as load-bearing, stiff radial threads and the flexible, sticky capture-spiral, fibers in the centre of the hub are more irregularly arranged (Fig. 1B) 1,2 and functionally less well understood or even differentiated. Indeed, the function of decorating fibers from the stabilimentum attached to the hub is controversial 35 and the nature of fibers used for adjusting the final tensioning of radial fibers in the hub 2 remains to be identified. www.nature.com/scientificreports/ We used two approaches for analysing nano&mesoscale fiber features: (i) modelling based on microXRD patterns and (ii) imaging by density projections based on scanning nanoXRD combined with modelling. In view of the levels of structural organization (see above) we will assume that single silk fibers are externally homogeneous with diameters down to approximately the micron-range. "Filament" is used for a detached part of a fiber and "fibril" for a fiber sub-structure with an unspecified diameter. The term "nanofibril" is used for diameters up to about 50 nm and "mesofibril" for diameters up to the micron-scale.

Results and discussion
Hub-area density projections. Optical images of the hub fragment reveal a conglomerate of multiple fibers (Fig. 1C,D). We generated composite images (CIs) of the hub fragment by scanning microXRD, corresponding to density projections based on X-ray scattering contrast (see Methods). We identify in the WAXS CI ( Fig. 2A) several orb-web features 1 such as two bunches of four radial threads and the hub-spiral (contrast provided in both cases by Bragg peaks and SRO 8 ) as well as the mesh of decorating silk fibers (contrast provided principally by SRO 17 ). We observe the same features in the SAXS CI (Fig. 2B). The contrast is provided in this case by fibrillar correlations and shape-transforms 8 . Further microstructural data supporting these identifications are presented in the Supplementary Material. We observe, however, only in the SAXS-CI several fine fibers (Fig. 2B). The absence or weakness of Bragg peaks and SRO scattering suggests their highly amorphous nature. The scattering contrast for the amorphous fibers is provided by equatorial SAXS streaks, oriented normal to the fiber axis. We identify two different types of amorphous fibers distinguished by narrow (am 1 ) and more diffuse streaks (am 2 ) (Fig. 2C,D). In the following we will analyse the hierarchical structural organization of am 1 fibers based on a microXRD pattern derived from the SAXS-CI. The mechanically particularly stable support provided by a MaS bridge-thread section for an am 2 -type fiber enabled scanning nanoXRD with subµm step increments. This allowed analysing the am 2 fibers hierarchical structural organization based on real space SAXS&WAXS-CIs and reciprocal space nanoXRD patterns. Fibrillar composite structure of am 1 fiber. The diameter of the projected am 1 fiber was derived from the spatial distribution of equatorial streaks in the SAXS-CI as 2.0 ± 0.4 µm (SM Fig. 2H,I). The streaks can be related to the transform of fibrillar shapes which can be approximated by cylinders with diameter d c (see Methods). Indeed, the modulated intensity decay of the streak in Fig. 2D was modeled by cylinders of d c ~ 115 nm diameter where the matrix of (assumed) lower density provides the scattering contrast ( Fig. 2E; SM Eq. 4). The azimuthal width of the streak translates into an orientation distribution of f c = 0.998(1) corresponding to quasiparallel mesofibrils (SM Fig. 3C; SM Eq. 1). The homogeneous distribution of streaks across the line-scans of the fiber (SM Fig. 2I) suggest the model of parallel, cylindrical mesofibrils distributed randomly in the matrix with an undefined volume density (Fig. 2F,G). The presence of meridional diffuse scattering, which cannot be resolved from the beamstop (Fig. 2C), suggests that the model of infinite, homogeneous cylinders is an idealization. The model resembles the structure of egg case silk fibers from A. aurantia cylindrical glands 32 , showing stiffness and extensibility comparable to MaS fibers 30,36,37 . The mesoscale features of am 1 fibers suggest therefore also enhanced stiffness. The lack of an important SRO fraction suggests that molecular contributions to extensibility (e.g. helical motifs) can be excluded. However, while am 1 fibers have a hierarchical structural organization resembling egg case silk it is not established that they are also produced by cylindrical glands.
Skin-core structure of am 2 fiber. The association of am 2 -type with MaS fibers suggests a functional relation. Indeed, the SAXS-CI obtained by scanning microXRD reveals a crimped am 2 fiber emanating from the upper bunch of radial threads (Fig. 2B). The separation of a crimped fiber from a MaS thread is also visible in a SEM image (Fig. 3A). A spectrum of crimped and elongated, flexible fibers with ribbon-like features is covering bridge-thread fibers (Fig. 3B,C). Partial fusion of crimped fibers with the MaS skin reveals about 300 nm diameter substructures -limited by the SEM resolution-implying surface interactions (Fig. 3D). The crimped morphology is particularly well visible when the overall am 2 fiber direction is along the MaS fiber axis (Fig. 3C). The fiber becomes extended when bridging the two fibers of the MaS thread. We generated SAXS&WAXS-CIs based on scanning nanoXRD of an am 2 fiber attached to a bridge-thread section with a gap between the two fibers (Fig. 4A). The straight, bridging part of the am 2 fiber has remained connected to one of the MaS fibers by a thin filament (Fig. 4A). This geometry provides stability for scanning nanoXRD and allows observing weak scattering from the am 2 fiber without scattering from the bridge-thread. Indeed, the WAXS-CI reveals the projection of the am 2 fiber and the filament by faint diffuse scattering (Fig. 4B,C). The fiber is tilted by 7° ± 1° from the horizontal scan axis, corresponding also to the fiber axis direction of the MaS fibers, revealed by the contrast provided by β-sheet peaks and SRO scattering 8 (Fig. 4B,D). The am 2 fiber density projection is, however, not completely homogeneous as we observe within its contours a several µm long domain defined by two Bragg peaks of 0.418 ± 0.001 nm and 0.378 ± 0.004 nm lattice spacings (Fig. 4C,E,F). The nature of this domain will be discussed below. The diameter of the am 2 fiber was determined from the intensity distribution of a horizontal scan-line (Fig. 4C,E) as for the am 1 fiber (SM Fig. 2I), assuming that the diffuse scattering at each scan-point (Fig. 4G) is proportional to the amount of protein probed by the nanobeam. Although we masked the strongest (0.418 nm) Bragg peak visible in several patterns (Fig. 4I) we find a slight asymmetry of the profile suggesting enhanced diffuse scattering from an 2nd, unknown component (Fig. 4G). We simulated the profile by a sine function with a width of 10 µm fwb (full-width-at-base) (Fig. 4G) corresponding to a fiber diameter of 1.2 ± 0.2 µm (10 µmxsin7° ± 1°). A sine function is appropriate for the continuous shape-change of a cylindrical cross-section; a hollow cylinder is excluded as the diffuse scattering would increase when probing from the outer skin and decrease towards the center of the cylinder (SM Fig. 4A www.nature.com/scientificreports/ The SAXS-CI is based on the contrast provided by the equatorial streaks (Fig. 4D). The contours of the bridgethread are revealed by an enhanced contrast of the skin-layer mesofibrils 8 (Fig. 5A). The banded structure on the bridge-thread will be discussed below. The am 2 fiber is revealed by horizontal groups of streaks defining a skin-core structure (Fig. 5A,B). The azimuthal width of the strongest streak in a group (e.g. streak 1 in Fig. 6A) corresponds to a spread in fibrillar orientations of about 8° fwhm or about 15° fwhm for an averaged streak of a whole scan-line (SM Fig. 3A,B). Averaging across a larger fiber volume is at the origin of the diffuse streak observed by microXRD (Fig. 2D). Similar groups of streaks define three further fibrous features which are partially overlapping in the am 2 fibers density projection (SM Fig. 6B). We identify one of these features in the optical micrograph as the filament connecting the am 2 fiber to the lower MaS fibers surface (Fig. 4A). The other fibrous features in the projection image are optically out of focus. The absence of an equatorial Bragg peak implies the absence of inter-fibrillar correlations. The angular deviation of the fibrillar axis from the direction of the am 2 fiber axis by ~ 8° is attributed to a wound ribbon of fibrils. The intensity variation in a group of streaks (Figs. 6A, SM Fig. 6B,C) is due to the geometry of the skin-layer probed. Indeed, for a cylindrical cross-section, the nanobeam will probe more fibrils through the skin-layer at the edge than at the center of the fiber (SM Fig. 4A,B). The projection of the fiber diameter derived from the spatial extension of the two groups of streaks in a single horizontal line is 1.2 µm ± 0.2 µm as also derived from the diffuse scattering data (Fig. 4G). The thickness of the skin-layer determined from the extension of the group of streaks is ~ 200 nm. The filament shows also streaks expected for fibrillar morphology (SM Fig. 7A). Albeit the low counting statistics we start seeing a modulation of the intensity profile as for the am 2 fiber profile suggesting mesofibrils (SM Fig. 7B). We assume therefore that the filament and probably the other fibrous features visible in the SAXS-CI (SM Fig. 6B) have become detached during rupture of the am 2 fiber from the MaS skin-coat. A cylinder diameter of d c = 4.4 ± 0.3 nm diameter was determined by Guinier's approach (Supplementary Materials) for the strongest streak showing a continuous intensity decay (Fig. 5C). This diameter corresponds to the scale of nanofibrillar diameters obtained by different techniques. Indeed, diameters of 6-7 nm were obtained Guinier's approach for nanofibrils in the cores Nephila and Argiope MaS fibers 8,14 . A diameter of 4.7 nm was derived from the equatorial SAXS correlation peak for bagworm silk nanofibrils 15 while single nanofibrils with 20 nm × 7 nm cross-section were imaged by AFM for recluse spider silk ribbons 19 . The diffuse scattering profile (Fig. 4G) suggests that am 2 fiber cores contain disordered protein. For the projection of ribbon-like skin-layer one would expect observing towards the center of the fiber fibrillar scattering at different crossing-angles. Indeed, we observe patterns with multiple weak streaks which we attribute to fibrils at discrete angles (SM Fig. 7C,D). The weakness of these streaks does, however, not provide information on the homogeneity of the skin-layer which might have become locally degraded during the rupturing process. Preliminary evidence suggests at least partial assembly of nano-into mesofibrils in the skin-layer. Indeed, a modulation of the equatorial streak profile is observed for the weaker streaks at the inside of the skin-layer (Figs. 6B, SM Fig. 8A). We determined the peak positions by fitting Gaussians to the profile (SM Banded pattern on bridge-thread. The banded pattern on the surface of the bridge-thread SAXS-CI ( Fig. 5A) is generated by streaks with enhanced intensity along the direction of the bands, overlapping with the equatorial streaks from the core nanofibrils 8 . We exclude scattering from "ordered regions" of a few µm size derived from Raman studies for Nephila and B. mori fibers 39 as no evidence for bulk crystalline domains of this size was obtained by scanning nanoXRD of A. bruennichi's bridge-threads 8 . We rather attribute the banded pattern to scattering from the mesh of filaments wound around the bridge-thread fibers (Figs. 3B). The density of these filaments appears to fluctuate locally along the threads or even disappear. We have selected a single band by its enhanced scattering (Fig. 6E). Selected streaks from the band show the modulated intensity decay of mesofibrils suggesting equatorial-type scattering (SM Fig. 5A,B). We therefore propose as model layers of mesofibrils which are aligned normal to the axis of the filaments (Fig. 6F). Given the close association of these band-like features and the am 2 -fibers with the MaS-surface (see also below) we put forward the hypothesis of a common glandular origin. Indeed, the proximal region of the MaS gland has been proposed to be at the origin of the MaS fibers core while protein secreted by the distal region was proposed to be at the origin of Nephila's proteneous skin-layer 22 ; also assumed for A. bruennichi's MaS fibers 8 . The different fibrous morphologies could therefore be due to different levels of assembly.

Interaction of am 2 fiber with MaS fibers coat.
We discuss here the nature of the domain observed within the contours of the am 2 fiber projection, which is defined by Bragg peaks (Fig. 4C,E,F). The peaks show an azimuthal spread which can be separated into several Gaussians suggesting a cluster of nanocrystallites (SM Fig. 9A-D). Slight changes in the texture of the peaks suggest clusters differing slightly in orientation along the am 2 fiber. The same peaks corresponding to 60-100 nm nanocrystallites were observed for MaS bridge-threads 8 while we derive 30-40 nm nanocrystallites for the am 2 fiber domain (Supplementary Material). These nanocrystallites, observed initially only together with MaS diffraction patterns (called S,S* peaks), were explained by the non-periodic lattice (NPL) model based on peptide chain side-group ordering of the β-sheet nanocrystalline fraction 40,41 . A recent model attributes these peaks, however, to the PG-II lattice as they are also observed for the MaS glycoprotein skin-layer 23 lacking poly(L-alanine) peaks 17 . Peak positions and intensities of the Bragg peaks in the am 2 domain agree also to PG-II (100)/(101) reflections 42 . We assume therefore that a fragment of the glycoprotein shell containing PG-II nanocrystallites has been ruptured together with the am 2 -fiber section from the MaS coat. Indeed, glycoprotein is revealed by its SRO scattering (Fig. 4H) contributing to the asymmetry of the diffuse scattering profile (Fig. 4G). The SAXS-CI reveals two rupture zones on the MaS thread and the filament connecting the am 2 fiber to one of the rupture zones (Fig. 5A, SM Fig. 10A-E). Streaks from the MaS proteneous skin-layer with about 15° azimuthal fwhm (similar to the skin of pristine MaS fibers 8 ) are observed next to the lower rupture zone (SM Fig. 10D) while random SAXS due is observed within the rupture zone (SM Fig. 10E). We attribute the random SAXS to randomly orientated mesofibrils in the proteneous skin-layer below the ruptured glycoprotein layer. Indeed, the radial profile of the streaks shows the modulated intensity decay of the streaks of the MaS mesofibrillar skin-layer 8 . The scattering data support therefore the biochemical analysis of the MaS coat 23 .

Conclusions
Our results suggest that even highly amorphous spider silk fibers can contain specific mesoscale features suggesting functional differences. Indeed, we have identified two types of amorphous, fine silk fibers by their mesoscale organizations. The fibrillar composite structure of am 1 fibers derived from modeling reciprocal space features in microXRD patterns appears providing enhanced stiffness as for egg case silk fibers although we do not have evidence that both types of fibers have the same glandular origin. The ribbon of weakly interacting nanofibrils wound around a core of disordered protein of am 2 fibers observed in real space by scanning nanoXRD resembles www.nature.com/scientificreports/ the skin-core structure of MaS fibers 8 suggesting a blend of toughness and flexibility. The results suggest that am 2 fibers can be anchored in the glycoprotein skin-layer of MaS fibers enabling functions related to fine-tuning the tension of the radial threads or increasing the lateral cohesion of bridge-thread fibers. It is probable that am 2 -type fibers and other fibrous surface features have the same glandular origin as MaS fibers protein skinlayer suggesting that care is required when interpreting surface-sensitive spectroscopy and imaging techniques. The evolution of nanoXRD towards sub-100 nm focal spots and enhanced reciprocal space resolution enabled by the upgraded ESRF source 17,43 should allow refining the am 1 fiber model by imaging mesofibrils in real space and resolving a possible meridional correlation peak. Probing of fiber sections with smaller focal spots should allow refining the proposed partial assembly of nanofibrils in the am 2 fibers skin-layer into mesofibrils. It will also be necessary developing protocols for transferring delicate orb-web structures on sample supports while maintaining their architecture in order to reduce background scattering and provide a mechanically stable support for scanning nanoXRD. This would allow generating coarse density projections of larger areas followed by high-resolution scanning of specific features. A general conclusion emerging from this work is that practically any orb-web silk fiber has become accessible to scanning nanoXRD.

Materials and methods
Silk fibers. The fibers were obtained from the orb-webs of two adult Argiope bruennichi (Araneidae) spiders living in their natural habitat (Fig. 1B) and transferred onto Si 3 N 4 membranes for X-ray scattering analysis 8 . We collected a fragment from the central hub including part of the stabilimentum 1 and a piece from a bridge-thread supporting the orb-web with an attached crimped fiber of unknown glandular origin, also found in the hub-area. X-ray scattering. Scanning microXRD was performed in transmission geometry on the hub-silk sample using a monochromatic SR beam of λ = 0.0940 nm wavelength, focused to an about 1.5(h) µm × 1.5(v) µm fullwidth-half-maximum (fwhm) spot. Scanning nanoXRD was performed in the same geometry on the bridgethread sample using a monochromatic SR beam of λ = 0.0835 nm, focused to an about 190(h) nm × 170(v) nm (fwhm) spot 8 . A selected area of each sample was mesh-scanned through the focus. Radiation damage by propagating radicals was limited by a step-width of ≥ 500 nm (hxv) 8 . XRD patterns covering lattice spacings from the SAXS to WAXS range were recorded at each mesh-point by an ultrasensitive Si pixel detector.
Composite X-ray diffraction images. The sequence of patterns from a mesh-scan was transformed into a so-called "composite image" (Abbr.: CI) corresponding to a density projection with a lateral resolution determined by the step-scan increments. "WAXS-CIs" were based on pixels covering the reciprocal space from Q ~ 2 nm −1 (d ~ 3.1 nm) to Q ~ 25 nm −1 (d ~ 0.25 nm) where: Q = 2π/d scale; d: lattice spacing. "SAXS-CIs" were based on pixels covering reciprocal space from the edge of the beamstop (Supplementary Materials) to ~ 3.3 nm −1 (d ~ 1.9 nm). The contrast in SAXS&WAXS-CIs is provided by Bragg peaks, SRO, molecular shapes or nanoscale aggregates 8,17 . Specific features can be localized in CIs based on pixels limited to the corresponding part of reciprocal space such as Bragg peaks or SAXS streaks. SAXS/WAXS analysis. Real space information was obtained from patterns by comparison with known patterns or by modelling based on lattices and shapes. Information on extracting atomic-scale information such as lattice metrics, crystallinity, particle size and orientation distribution from Bragg peaks in the WAXS range is provided in the Supplementary Materials. Here we will indicate briefly the approach used for analyzing SAXS features; details are provided in Supplementary Materials. Indeed, SAXS patterns of MaS fibers show generally up to two meridional Bragg peaks due to density modulations along the nanofibrils 8,14 and an equatorial streak attributed to the nanofibrillar shape transform 10,44 . For amorphous fibers with fibrillar morphology only the equatorial streak is observed. The modulated intensity decay observed for mesofibrils was approximated by uncorrelated cylinders of diameter d c and modelled by a Bessel function (SM Eq. 4, 5). The micro-and nanobeam instrumental resolution provides access to d c ~ 100 nm while the modulation period becomes too extended for d c ≤ 10 nm, i.e. in the range nanofibrils. An approximate d c value was in such a case determined from the slope of the streaks intensity decay by Guinier's approach 8,10,14 . The equatorial interface scattering streak 45,46 at the edge of fibers in SAXS-CIs is weak or not observable. We exclude scattering from the interface of cavities which have an irregular distribution in the bulk of MaS fibers 22 while equatorial SAXS streaks show a regular distribution down to at least the 50 nm scale 17 .