Partial Orientation Retrieval of Proteins From Coulomb Explosions

TL;DR

The paper addresses the challenge of unknown protein orientation in Single Particle Imaging by proposing a method to extract partial orientation information from Coulomb explosion footprints. It employs a hybrid Monte Carlo/Molecular Dynamics framework to simulate explosions for 45 proteins (100–4000 atoms) and uses virtual detectors to generate explosion footprints; relative orientation between two orientations is described by a rotation angle $\theta$. The authors show that partial orientation information can be retrieved, with a practical L2-distance cutoff near $1$ rad that scales roughly linearly with the number of atoms, and that larger proteins yield more orientation matches. This approach has the potential to augment EMC-based reconstructions, reducing the number of high-quality diffraction patterns required and enabling noisier data to contribute to SPI reconstructions, thereby advancing protein imaging at XFELs.

Abstract

Single Particle Imaging techniques at X-ray lasers have made significant strides, yet the challenge of determining the orientation of freely rotating molecules during delivery remains. In this study, we propose a novel method to partially retrieve the relative orientation of proteins exposed to ultrafast X-ray pulses by analyzing the fragmentation patterns resulting from Coulomb explosions. We simulate these explosions for 45 proteins in the size range 100 -- 4000 atoms using a hybrid Monte Carlo/Molecular Dynamics approach and capture the resulting ion ejection patterns with virtual detectors. Our goal is to exploit information from the explosion to infer orientations of proteins at the time of X-ray exposure. Our results demonstrate that partial orientation information can be extracted, particularly for larger proteins. Our findings can be integrated into existing reconstruction algorithms such as Expand-Maximize-Compress, to improve their efficiency and reduce the need for high-quality diffraction patterns. This method offers a promising avenue for enhancing Single Particle Imaging by leveraging measurable data from the Coulomb explosion to provide valuable insights about orientation.

Figures (4)

• Figure 1: Geometry and setup of the simulated experiment. Detectors are placed on each side of the incoming particle at the XFEL interaction point. The detectors capture the ejected ions from the exploding sample. Perspective along X-ray beam.
• Figure 2: Panel a) Relative orientation between molecules against L2 distance (Eq.\ref{['eq:L2']}) between pairs of images from 10000 images from lysozyme. There is no global correlation but there is a trend for in the regime of lower L2 distance. We see from the distribution of points that the regime we are interested in contains a very small part of the data. Note that each point is a pair of images. Panel b) Zoomed in on the highlighted area of interest.
• Figure 3: Panel a) The average relative orientation (colormap) of pairs under a given threshold (x-axis) for the set of 45 proteins simulated ordered by size from the bottom in ascending order. Note that the y-axis is not linear. Evaluated on 8000 images per protein. Where average relative orientation is 0 there is no data. Panel b) A linear regression on where the threshold is located plotted against the size of protein.
• Figure 4: Average number matches (pairs under L2 threshold) per image as number of starting images increases. We expect more matches per image as the number of images is increased since we sample the space more finely and thus expect sampled orientations to be closer together on average.