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Imaging aerosolized viruses with an X-ray free-electron laser using single-particle rotational invariants

This study demonstrates that rotational invariants derived from XFEL diffraction patterns enable the model-guided and ab initio 3D structure determination of aerosolized bacteriophages, revealing key structural features like capsid asymmetry and internal density variations despite modest experimental resolution.

Original authors: Tim B. Berberich, Johan Bielecki, Jonas A. Sellberg, Benedikt J. Daurer, Carl Nettelblad, Paul Lourdu Xavier, Ivan A. Vartanyants, Garth J. Williams, Luca Gelisio, Richard Bean, Serguei L. Molodtsov

Published 2026-06-23

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Tim B. Berberich, Johan Bielecki, Jonas A. Sellberg, Benedikt J. Daurer, Carl Nettelblad, Paul Lourdu Xavier, Ivan A. Vartanyants, Garth J. Williams, Luca Gelisio, Richard Bean, Serguei L. Molodtsov, Petra Fromme, Andrew Aquila, Adrian P. Mancuso, Ruslan P. Kurta

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine trying to figure out what a tiny, invisible virus looks like. Normally, scientists might try to freeze it and take a picture with an electron microscope, or grow it into a crystal to shoot X-rays at it. But this paper describes a different, high-speed approach: taking a "snapshot" of a virus while it's floating freely in the air, using a super-powerful X-ray laser that destroys the virus in the process.

Here is the simple breakdown of what the scientists did and what they found, using some everyday analogies.

The Challenge: The "Blurry Photo" Problem

Viruses are tiny (about 20 to 300 nanometers). When you shoot X-rays at them, they scatter the light, creating a pattern of dots on a detector.

The Problem: The virus is spinning and tumbling in the air. Every time the laser hits it, the virus is facing a different direction. It's like trying to figure out what a 3D object looks like by taking thousands of photos of it, but every photo is taken from a random angle, and you don't know which angle is which.
The Laser: They used an X-ray Free-Electron Laser (XFEL). Think of this as a camera flash so fast (femtoseconds) that it takes a picture of the virus before the X-rays have time to burn it up. This is called "diffraction-before-destruction."

The Solution: The "Rotational Fingerprint"

Instead of trying to sort out which photo came from which angle (which is very hard), the scientists used a mathematical trick called Rotational Invariants.

The Analogy: Imagine you have a bag of marbles, and you want to know if they are all the same shape without looking at them directly. Instead of looking at each marble, you shake the bag and listen to the sound they make when they collide. Even though you don't know which marble hit which, the pattern of the sounds tells you about the shape of the marbles inside.
How it works: The scientists took thousands of these random X-ray "photos" and mixed them together mathematically. By looking at how the patterns of dots correlate with each other, they could extract a "fingerprint" of the virus's shape that doesn't care about the rotation. This fingerprint contains all the essential 3D information about the virus, stripped of the confusing angles.

The Experiment: Shooting Bacteriophages

They used a specific virus called PR772 (a bacteriophage, which is a virus that infects bacteria). They turned the virus into a fine mist (aerosol) and shot it through the laser beam. They did this in three separate experiments.

What They Found

Even though the "photos" weren't super sharp (the resolution was a bit blurry, like a low-resolution digital image), the mathematical fingerprint allowed them to see some surprising details:

The Virus Isn't a Perfect Ball: They expected the virus to be a perfect 20-sided shape (an icosahedron), like a perfect soccer ball. But their analysis showed it was slightly squashed or distorted. It's more like a soccer ball that someone sat on gently—it's still round, but not perfectly symmetrical.
Inside is Messy: Inside the virus shell, the contents (the genetic material) weren't spread out evenly. In some of the samples, the inside looked lumpy or uneven, like a bag of marbles where some are clumped together.
A Tiny "Nose": In one of the experiments, they spotted a faint little extension sticking out of one corner of the virus.
- Why this matters: This looks like the "nose" of a similar virus (PRD1) that uses to poke a hole in a bacteria to inject its DNA. It suggests these viruses might be in the middle of a "delivery" process, or perhaps they are just naturally a bit wobbly.

Why This Matters (According to the Paper)

The paper emphasizes that this method is powerful because it works even when the images are a bit blurry.

The "Fingerprint" Advantage: By using these rotational invariants, they could see structural details that would have been lost if they just tried to average the blurry photos together.
Real-World Conditions: This method allows scientists to study viruses in a state closer to how they exist in nature (floating in air or liquid) rather than frozen in ice or locked in a crystal.

The Bottom Line

The scientists successfully used a mathematical "fingerprinting" technique to reconstruct the 3D shape of a virus from thousands of random, blurry X-ray snapshots. They discovered that these viruses aren't perfect, rigid geometric shapes; they are slightly squashed, have uneven insides, and sometimes have little protrusions. This proves that this new mathematical approach is a strong tool for understanding the real, messy, and dynamic structure of viruses.

Technical Summary: Imaging Aerosolized Viruses with an X-ray Free-Electron Laser Using Single-Particle Rotational Invariants

Problem Statement
Single-particle imaging (SPI) using X-ray free-electron lasers (XFELs) enables "diffraction-before-destruction" measurements of non-crystalline bioparticles, such as viruses, under near-biologically relevant conditions. However, the lack of translational invariance in non-crystalline targets significantly complicates structure determination. Conventional approaches rely on directly accessible observables like scattered intensities $I(q)$ , requiring the recovery of lost phases to reconstruct real-space electron densities. While iterative phasing algorithms exist, they often struggle with limited experimental resolution and the need for symmetry constraints, which can mask intrinsic structural asymmetries and dynamics. Furthermore, characterizing structural variations within ensembles of aerosolized particles remains challenging due to the complexity of aligning random orientations and the presence of environmental heterogeneity.

Methodology
This work employs rotational invariants derived from X-ray diffraction measurements to facilitate both model-guided and ab initio three-dimensional (3D) structure determination of aerosolized bacteriophage PR772.

Data Acquisition: Diffraction patterns were recorded from PR772 particles aerosolized via an aerodynamic lens stack and probed with femtosecond XFEL pulses (1.6 and 1.7 keV) at the Linac Coherent Light Source (LCLS) across three independent experiments (amo06516, amo86615, amo11416).
Rotational Invariants via XCCA: Instead of relying solely on individual diffraction patterns, the authors utilized Angular X-ray Cross-Correlation Analysis (XCCA). They computed the average difference-pattern two-point angular cross-correlation function (CCF), $C_{diff}(q, q', \Delta)$ , to enhance signal-to-noise ratios and suppress background.
Invariant Extraction: The CCFs were decomposed into Fourier components, $C_n(q, q')$ , which are linear combinations of rotational invariants $B_l(q, q')$ . These invariants, defined as products of spherical harmonic expansion coefficients, encode intrinsic structural information independent of particle orientation.
Structure Determination:
- Ab Initio Reconstruction: The Multi-Tiered Iterative Phasing (MTIP) algorithm, implemented in the xFrame software suite, was used to reconstruct 3D electron densities from the experimentally determined invariants $B_l(q, q')$ . This process solves for unknown unitary matrices (orientation determination) and phases simultaneously without imposing symmetry constraints.
- Model-Guided Analysis: A bead-modeling approach was employed to simulate diffraction from various structural models (e.g., perfect icosahedra, distorted capsids, core-shell structures). These simulations generated theoretical invariants to compare against experimental data, allowing for the verification of specific structural features like density nonuniformities and shape distortions.
Regularization: Advanced regularization techniques, including Ruiz equilibration and low-rank approximation, were applied to the invariants to mitigate noise and numerical errors, optimizing the data for the MTIP algorithm.

Key Results

Structural Asymmetry: Despite modest experimental resolution (ranging from 6 to 13 nm depending on the dataset and metric), the ab initio reconstructions consistently revealed deviations of the PR772 capsid from perfect icosahedral symmetry. These distortions were observed across all three independent experiments, suggesting they are a common structural property rather than an artifact of specific experimental conditions.
Internal Density Variations: The reconstructions and model-guided analysis indicated non-uniform density distributions within the virus particles. Specifically, the amo06516 dataset showed significant internal density heterogeneity compared to the amo86615 dataset, which appeared more uniform.
Vertex Extensions: In the amo06516 subset, faint density extensions emerging from one of the icosahedral vertices were detected. This feature resembles the nanotube protrusion observed in the related PRD1 virus during genome delivery, suggesting potential structural transformations or heterogeneity in the sample.
Invariant Robustness: The rotational invariants $C_n(q, q')$ demonstrated high robustness, showing strong similarity across different experimental runs and particle size subsets, even with varying numbers of diffraction patterns.
Model Validation: Simulations confirmed that perfect icosahedral models failed to reproduce the experimental invariant morphologies. Introducing radial uniaxial compression and composite distortions (radial and tangential) significantly improved the agreement with experimental phase maps, particularly for lower-order invariants ( $n=2, 4$ ). Core-shell models further refined the fit, revealing sensitivity to internal core density.

Significance and Claims
The authors claim that rotational invariants serve as powerful tools for probing the structure and temporal evolution of nano- and bioparticles using XFELs. By removing rotational degrees of freedom, these invariants provide extensive structural information that can be used concurrently in forward modeling and inverse problem solving.

The paper emphasizes that this combined approach of ab initio reconstruction and model-guided analysis enhances the fidelity of structural analysis, particularly when experimental resolution is limited. Crucially, the method allows for the detection of structural features—such as asymmetric capsid distortions and density nonuniformities—that might be obscured by symmetry constraints in traditional crystallographic or cryo-EM analyses. The results suggest that aerosolized viruses may exhibit intrinsic asymmetries and dynamic structural variations (potentially induced by environmental changes during aerosolization or inherent equilibrium dynamics) that are accessible through this correlation-based imaging technique. The work demonstrates that rotational invariants can effectively characterize similarities and structural variations within measured ensembles, offering a pathway to study virus transmission routes and structural dynamics under near-native conditions.