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The Exodus Project Group

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Melthucelha Smith
Melthucelha Smith

Sample Modeling Ms Sax S



Small-angle X-ray scattering (SAXS) is a relatively simple experimental technique that provides information on the global conformation of macromolecules in solution, be they fully structured, partially, or extensively unfolded. Size exclusion chromatography in line with a SAXS measuring cell considerably improves the monodispersity and ideality of solutions, the two main requirements of a "good" SAXS sample. Hydrogen/deuterium exchange monitored by mass spectrometry (HDX-MS) offers a wealth of information regarding the solvent accessibility at the local (peptide) level. It constitutes a sensitive probe of local flexibility and, more generally, of structural dynamics. The combination of both approaches presented here is very powerful, as illustrated by the case of RD, a calcium-binding protein that is part of a bacterial virulence factor.




Sample Modeling Ms Sax S



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A simulation method was developed for modelling SAXS data recorded on cellulose rich pulps. The modelling method is independent of the establishment of separate form factors and structure factors and was used to model SAXS data recorded on dense samples. An advantage of the modelling method is that it made it possible to connect experimental SAXS data to apparent average sizes of particles and cavities at different sample solid contents. Experimental SAXS data could be modelled as a superposition of a limited number of simulated intensity components and gave results in qualitative agreement with CP/MAS 13C-NMR data recorded on the same samples. For the water swollen samples, results obtained by the SAXS modelling method and results obtained from CP/MAS 13C-NMR measurements, agreed on the ranking of particle sizes in the different samples. The SAXS modelling method is dependent on simulations of autocorrelation functions and the time needed for simulations could be reduced by rescaling of simulated correlation functions due to their independence of the choice of step size in real space. In this way an autocorrelation function simulated for a specific sample could be used to generate SAXS intensity profiles corresponding to all length scales for that sample and used for efficient modelling of the experimental data recorded on that sample.


Small Angle X-ray Scattering (SAXS) is a versatile technique that can be used to obtain quantitative measurements of the nanostructure in cellulose containing samples (Jakob et al. 1994, 1996; Fratzl 2003; Keckes et al. 2003; Penttilä et al. 2019). The character of cellulose containing samples can span a great variety (Foster et al. 2018), be it cellulose nanocrystals (CNCs), cellulose nano fibrils (CNFs) or cellulose rich pulps, which are used for the preparation of CNCs and CNFs (Foster et al. 2018). In the former case cellulose rich pulps are subjected to acid hydrolysis, normally by use of concentrated sulfuric acid, breaking down the anatomy of the pulp fibre, yielding dispersions of charged cellulose nano-particles (Elazzouzi-Hafraoui et al. 2008; Foster et al. 2018). CNFs are made by mechanical homogenization of cellulose rich pulps or chemically modified cellulose rich pulps (Pääkkö et al. 2007; Saito et al 2007). Water-based dispersions of CNCs and CNFs have been the target of some recently published studies illustrating the capacity of the SAXS technique (Håkansson et al. 2014; Su et al 2015; Phan-Xuan et al. (2016); Geng et al. 2017; Mao et al. 2017; Rosén et al. 2018; Brett et al. 2020).


Pores resulting from the removal of components during pulping can range in size from fractions of a nanometre to several tens of nanometres. Dimensionally, the widths of cellulose fibrils, cellulose fibril aggregates and pores are in the size range addressable by SAXS measurements. SAXS measurements can be performed on both dry and water swollen fibre samples, where the dry and swollen states of the same material show large structural differences, Fig. 2.


Scattering intensity \(I\left(q\right)\) as a function of the scattering vector \(q\) obtained from SAXS data recorded on a cellulose-rich pulp (sample HWP, see Experimental) in the water swollen and the dry state


The sample materials used were pre-hydrolysed bleached softwood soda pulp (SWP), eucalyptus sulphite dissolving pulp, 96α (HWP) and cotton linters (Lint). All sample materials were initially dry. Dry samples were used after being exposed to ambient conditions for several days. Water swollen samples were placed in an excess of deionized water overnight before sample preparation and measurement.


For each sample the identity, relative glucose content, fibre saturation point (FSP) and the corresponding volumetric fill factor is given in Table 1. For the water swollen samples the FSP measurements were used to determine the volumetric fill factor, a necessary input for the simulation of relevant SAXS intensity profiles.


For comparison purposes, CP/MAS 13C-NMR spectra were recorded on the water swollen samples. Estimates of the average lateral fibril dimension (LFD) and the average lateral fibril aggregate dimension (LFAD) from CP/MAS 13C-NMR spectra, based on the method by Larsson and Wickholm (Larsson et al. 1997; Wickholm et al 1998) are given in Table 2.


Small angle X-ray data was recorded on dry and water swollen samples and the recorded SAXS data was modelled using a simulation model described in detail in the Supplementary Information (SI). Here only a brief account of the main features of the simulation model are given.


The advantage of the simulation method is that it makes it possible to associate each simulated intensity profile with an apparent average particle size (AAPS) and an apparent average cavity size (AACS), connecting each intensity profile to a length scale characteristic of the structures in the sample material. Here, the concept of cavity was used to describe interstitial spaces between solid particles whether filled with water or evacuated. For all samples used in this study, three intensity components (six adjustable model parameters plus one background intensity) were used to model the experimental SAXS data.


Figure 4 shows the results from modelling SAXS data recorded on dry samples and Fig. 5 shows the results from modelling SAXS data recorded on the corresponding water swollen samples. Modelling parameters are shown in Table 3 (dry samples) and Table 4 (water swollen samples).


Modelling results for the dry samples. Solid lines (red) represent the modelled intensity, circles represent experimental intensity. Error bars for the experimental intensity are plotted, in most cases error bars are covered by the markers. The scattering intensity has been arbitrarily scaled to minimize overlap of the curves. Top: SWP, middle: HWP, bottom Lint


The values of the weights for the three simulated superposition components (I1, I2, and I3 in Tables 3 and 4) used to model the recorded SAXS data are shown in Fig. 6. Although the length scales (Δxk in Tables 3 and 4) are not identical between samples, the three superposition components are coarsely viewed as representing the abundance of larger (I1), intermediate (I2) and smaller (I3) structural features in the samples.


The values of the relative weights for the three simulated superposition components (I1, I2, and I3 in Tables 3 and 4) used to model the recorded SAXS data. From top to bottom the samples are SWP, HWP and Lint. The inset in the upper right of each panel gives the sample name. The three superposition components were viewed as representing the abundance of larger (I1, light grey bars), intermediate (I2, grey bars), and smaller (I3, black bars) structural features in the samples


As illustrated in Fig. 7 the presence of both cellulose fibrils and fibril aggregates forms the basis of obtaining multiple components when fitting the SAXS data. For the samples the fitting components I2 and I3 (Table 4) were interpreted as corresponding to the length scales between fibril aggregates and cellulose fibrils (A and F in Fig. 7), respectively. Simulating the intensity components used for modelling experimental data, the volumetric fill factor was a necessary input. For the water swollen samples the volumetric fill factor was determined from FSP measurements. For the dry samples, the volumetric fill factor cannot be determined by FSP measurements since it implies swelling of the sample, thus the volumetric fill factor was arbitrarily set to a value of 0.9, representing a dense but not a completely cavity free sample material.


In Fig. 6, the three dry samples SWP, HWP and Lint all showed large dominating structures, as modelled by the I1 components, that gave a considerable signal intensity contribution in the observable q-range. In all the investigated dry samples the largest relative component weight (wk) was observed for the I1 components. This agreed with expectations, as cellulose fibrils aggregate into larger structures as a consequence of drying, contributing to hornification (Krässig 1993).


Less abundant smaller structures were observed when modelling experimental SAXS intensities of the dry samples. The AAPS corresponding to the intensity component I2 were found to be in a size range similar to the size range of the LFAD measured by CP/MAS 13C-NMR on water swollen samples, Table 2, though no direct correlation between samples was found.


The AAPS related to the intensity component I3 showed the presence of particles larger than the LFD measured by CP/MAS 13C-NMR on water swollen samples. One possible reason for this is illustrated in Fig. 8. During drying intimate local aggregation of fibrils could lead to local removal of cavities (electron density contrast) between fibrils, yielding SAXS AAPS representing partial fibril aggregates. One interesting finding is that all modelling results of the SAXS data of dry samples contained an I3 component, associated with AAPS, significantly smaller than the LFAD (CP/MAS 13C-NMR, water swollen samples) and AACS values in the range of 1 nm. The I3 component predicted by the modelling was interpreted as the existence of small-scale porosity of the cellulose structure also in the dry state, consistent with the materials known ability to rapidly re-swell. Further, the lack of correlation between the I3 AAPS for the dry samples and LFD obtained by CP/MAS 13C-NMR measurements on water swollen samples, could be explained by a larger compliance during drying of thinner fibrils. In the SWP and HWP samples, fibrils may make more intimate fibril-to-fibril contacts than the thicker, more rigid, Lint fibrils. The Lint samples showed more similar AAPS I3-values in both the dry and the water swollen samples.


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