Diffraction pattern simulation of cellulose fibrils using distributed and quantized pair distances

Nanoscale Mechanism of Moisture-Induced Swelling in Wood Microfibril Bundles

Understanding nanoscale moisture interactions is fundamental to most applications of wood, including cellulosic nanomaterials with tailored properties. By combining X-ray scattering experiments with molecular simulations and taking advantage of computed scattering, we studied the moisture-induced changes in cellulose microfibril bundles of softwood secondary cell walls. Our models reproduced the most important experimentally observed changes in diffraction peak locations and widths and gave new insights into their interpretation. We found that changes in the packing of microfibrils dominate at moisture contents above 10-15%, whereas deformations in cellulose crystallites take place closer to the dry state. Fibrillar aggregation is a significant source of drying-related changes in the interior of the microfibrils. Our results corroborate the fundamental role of nanoscale phenomena in the swelling behavior and properties of wood-based materials and promote their utilization in nanomaterials development. Simulation-assisted scattering analysis proved an efficient tool for advancing the nanoscale characterization of cellulosic materials.

Combining computational and experimental studies for a better understanding of cellulose and its analogs

Over the last decade, the structural refinement of cellulose allomorphs and their analogs has been advanced using high-resolution fiber diffraction. This also includes structures of crystals complexed with small molecules, which can inherently involve disorders. Computational methods, including density functional theory, in combination with molecular modeling are leading to improved structural analyses. Spectroscopic techniques such as vibrational spectroscopy give quantitative and robust data directly related to structural insights on cellulose. These data will benefit from improved molecular modeling's capacity for interpretation and will also serve as a gauge to measure the capacity of molecular modeling as an aid in structural determinations. Improvement in the capacity to directly simulate experimental data such as that from scattering, diffraction, and spectra will be the key for further integration of modeling and experimental approaches.

Combining scattering analysis and atomistic simulation of wood-water interactions

Molecular-scale interactions between water and cellulose microfibril bundles in plant cell walls are not fully understood, despite their crucial role for many applications of plant biomass. Recent advances in X-ray and neutron scattering analysis allow more accurate interpretation of experimental data from wood cell walls. At the same time, microfibril bundles including hemicelluloses and water can be modelled at atomistic resolution. Computing scattering patterns from atomistic models enables a new, complementary approach to decipher some of the most fundamental questions at this level of the hierarchical cell wall structure. This article introduces studies related to moisture behavior of wood with small/wide-angle X-ray/neutron scattering and atomistic simulations, recent attempts to combine these two approaches, and perspectives and open questions for future research using this powerful combination. Finally, we discuss the opportunities of the combined method in relation to applications of lignocellulosic materials.

Extending the Debye scattering equation for diffraction from a cylindrically averaged group of atoms: detecting molecular orientation at an interface

The Debye scattering equation is now over 100 years old and has been widely used to interpret diffraction patterns from randomly oriented groups of atoms. The present work develops and applies a related equation that calculates diffraction intensity from groups of atoms randomly oriented about a fixed axis, a scenario that occurs when molecules are oriented at an interface by the presentation of a binding motif as in antibody binding. Using an example biomolecule, the high level of sensitivity of the diffraction pattern to the orientation of the molecule and to the direction of the incident beam is shown. The use of the method is proposed not only for determining the orientation of molecules in biosensors and at membrane interfaces, but also for determining molecular conformation without the need for crystallization.

FiXR: a framework to reconstruct fiber cross-sections from X-ray fiber diffraction experiments

Ab initio reconstruction methods have revolutionized the capabilities of small-angle X-ray scattering (SAXS), allowing the data-driven discovery of previously unknown molecular conformations, exploiting optimization heuristics and assumptions behind the composition of globular molecules. While these methods have been successful for the analysis of small particles, their impact on fibrillar assemblies has been more limited. The micrometre-range size of these assemblies and the complex interaction of their periodicities in their scattering profiles indicate that the discovery of fibril structures from SAXS measurements requires novel approaches beyond extending existing tools for molecular discovery. In this work, it is proposed to use SAXS measurements, together with diffraction theory, to infer the electron distribution of the average cross-section of a fiber. This cross-section is modeled as a discrete electron density with continuous support, allowing representations beyond binary distributions. Additional constraints, such as non-negativity or smoothness/connectedness, can also be added to the framework. The proposed approach is tested using simulated SAXS data from amyloid β fibril models and using measured data of Tobacco mosaic virus from SAXS experiments, recovering the geometry and density of the cross-sections in all cases. The approach is further tested by analyzing SAXS data from different amyloid β fibril assemblies, with results that are in agreement with previously proposed models from cryo-EM measurements. The limitations of the proposed method, together with an analysis of the robustness of the method and the combination with different experimental sources, are also discussed.

Calculation of the cross-sectional shape of a fibril from equatorial scattering

An alternate formulation of helical diffraction theory is used to generate cross-sectional shapes of fibrous structures from equatorial scattering. We demonstrate this approach with computationally generated scattering intensities and then apply it to scattering data from Tobacco Mosaic Virus (TMV) and in vitro assembled fibrils of Aβ₄₀ peptides. Refining the cross-sectional shape of TMV from SAXS data collected on a 26mg/ml solution resulted in a circular shape with outer diameter of ∼180Å and inner diameter of ∼40Å consistent with the known structure of TMV. We also utilized this method to analyze the equatorial scattering from TMV collected by Don Caspar from a concentrated (24% ∼295mg/ml) gel of TMV as reported in his Ph.D. thesis in 1955. This data differs from the SAXS data in having a sharp interference peak at ∼250Å spacing, indicative of strong interparticle interactions in the gel. Analysis of this data required consideration of interatomic vectors as long as 2000Å and resulted in generation of images that were interpreted as representative of local organization of TMV particles in the sample. Peaks in the images were separated, on average by about 250Å with a density consistent with Caspar's original measurements. Analysis of SAXS data from Aβ fibrils resulted in a cross-sectional shape that could be interpreted in terms of structural models that have been constructed from ssNMR and cryoEM. These results demonstrate an unexpected use of the small-angle region of fiber diffraction patterns to derive fundamental structural properties of scattering objects.