Fibrillar aggregates are ubiquitous in nature and are the structural foundation of materials like bone, tendons, muscles and plant walls.
Fibrils also play a major role in many neurodegenerative disorders like Alzheimer’s and Parkinson’s, where deposits of fibrillar aggregates, also known as amyloids, are one of the hallmarks of disease. Studying the structure of these fibrils is of great interest to understand the mechanisms behind these neuropathies. However, current methods like solid-state NMR-based reconstructions require the isolation of amyloid deposits from brain tissue and a posterior growth of the obtained material using seeding procedures, which may distort the amyloid fibrils’ structure in the process.
In this work we propose a more direct approach to fibril characterization, based on the measurement of the small angle x-ray scattering (SAXS) signature of the amyloid fibrils directly from brain tissue samples using x-ray scanning microdiffraction (XSMD) and reconstruction of the electron density of the fibril’s cross-section combining its SAXS signature with various physical and structural prior constraints. A non-negative matrix factorization (NNMF) approach is developed for the estimation of the amyloid’s SAXS signature, through which the XSMD data is separated into the different components of the experimental sample, include the contribution of the brain tissue, the scattering of air and the sample support and optical artifacts, from which the amyloid component can be isolated.
Using this amyloid SAXS signature, we reconstruct the fibril’s 2D cross-section by solving an inverse problem in which we combine the physical scattering model of the experiment with prior knowledge on the structural characteristics of the cross-section. This process is framed as an optimization problem which we solve using the alternate directions method of multiplier (ADMM) framework, that allows us to exploit the real and reciprocal space structure of the problem in an efficient way. A novel proximal operator is developed for this framework, which has potential application to the wider field of multispectral phase retrieval, and the study of the scattering properties of solid ellipsoids is used to design efficient initialization strategies for the optimization problem. The proposed method is able to recover the structure of fibrils from both computational and experimental data and has the potential to shed light into the impact of fibril polymorphism in neurodegenerative disorders.
- Professor Lee Makowski (Advisor)
- Professor Dana Brooks
- Professor Mario Sznaier