Investigating beta-sheet nanocrystal ordering and correlation with small-angle X-ray scattering

In disordered soft matter system, amorphous and crystalline components might be coexisted. The interaction between the two distinct structures and the correlation within the crystalline components are crucial to the macroscopic property of the such material. The spider dragline silk biopolymer, is one of such soft matter material that exhibits exceptional mechanical strength though its mass density is considerably small compare to structural metal. Through wide-angle X-ray scattering (WAXS), the research community learned that the silk fiber is mainly composed of amorphous backbone and $\beta$-sheet nano-crystals. However, the morphology of the crystalline system within the fiber is still not clear. Therefore, a combination of small-angle X-ray scattering experiments and stochastic simulation is designed here to reveal the nano-crystalline ordering in spider silk biopolymer. In addition, several density functional theory (DFT) calculations were performed to help understanding the interaction between amorphous backbone and the crystalline $\beta$-sheets.

By taking advantage of the prior information obtained from WAXS, a rather crude nano-crystalline model was initialized for further numerical reconstruction. Using Markov-Chain stochastic method, a hundreds of nanometer size $\beta$-sheet distribution model was reconstructed from experimental SAXS data, including silk fiber sampled from \textit{Latrodectus hesperus}, \textit{Nephila clavipes}, \textit{Argiope aurantia} and \textit{Araneus gemmoides}. The reconstruction method was implemented using MATLAB and C++ programming language and can be extended to study a broad range of disordered material systems.