Physics Colloquium – Adam Opperman

Manifold-based Machine Learning for Scattering Data

Adam Opperman, PhD Candidate
University of Wisconsin-Milwaukee Department of Physics & Astronomy

Small Angle X-ray Scattering (SAXS) is a technique used to capture X-ray diffraction images of proteins in solution, mimicking biological conditions. These images provide insight into the overall shape and structure of the protein. By imaging the protein system at various times during a reaction, dubbed time-resolved SAXS (TR-SAXS), the evolution of the protein structure is observed. These measurements are commonly taken at X-ray Free Electron Laser (XFEL) facilities which generate X-rays with precision and high flux. The Compact X-ray Light Source (CXLS) and accompanying Compact X-ray Free Electron Laser (CXFEL) are under construction at Arizona State University. Due to the compact nature of the source in combination with the yet incomplete development, CXFEL has a reduced level of photon flux available compared to other XFELs. Due to this constraint, new analytical methods are needed to process TR-SAXS data.

We propose an application of a manifold-based machine learning technique called Non-linear Laplacian Spectral Analysis (NLSA) to address this issue. This graph-theoretic algorithm maps data into an intrinsic subspace in which dynamic information can be extracted with high fidelity. To verify the applicability of NLSA, we simulated TR-SAXS data from two different protein systems: Calmodulin and Photoactive Yellow Protein. The simulations were done within the bounds of the expected capabilities of the CXFEL. Then, we applied NLSA to each dataset to extract kinetic and spatial information. We compared the results to those from Singular Value Decomposition (SVD), the current standard method of analysis. We find that NLSA provides significantly more accurate and consistent structural kinetics information compared to that of SVD. Further, NLSA is more capable of identifying temporal trends in cases of extreme timing uncertainty.