New MATLAB Toolkit Reads Protein Polymerization Directly from Cryo-Electron Tomography Data

Researchers have unveiled an open-source MATLAB script package, tomoPoseLink, that analyzes protein polymerization directly from subtomogram averaging data produced by cryogenic electron tomography. The toolkit, described in BMC Methods, builds chains, fibrils and lattice features from the positions and orientations of individual particles, without requiring prior segmentation, knowledge of the interactions involved, or reference structures. Because the analysis relies on numerical coordinates rather than image classification, it runs quickly on ordinary CPUs and gives users quantifiable control over error rates when distinguishing bound from unbound particles.

Cryogenic electron tomography provides three-dimensional imaging of cells, tissue slices and purified samples. Subtomogram averaging extends the resolution of those tomograms by aligning and averaging subvolumes, allowing protein structures to be determined at angstrom to nanometer resolution. Although structures solved this way are typically lower resolution than those from single-particle cryo-electron microscopy, they carry contextual information that single-particle work cannot, such as cellular localization and interactions with neighboring proteins. That context is exactly where tomoPoseLink operates: it treats the aligned particle dataset not as a stack of isolated structures but as a population whose geometry can be measured.

The analytical gap the toolkit addresses is a practical one. According to the authors, tools for quantifying relationships between particles identified by subtomogram averaging have often been lab- or system-specific, limiting their reuse. Recent efforts have produced more generalizable tools, but many approaches still depend on image-based classification of subtomogram volumes. TomoPoseLink instead works with six numbers per particle: three Euler angles describing orientation and three spatial coordinates. Analyzing that far smaller data volume makes the computation dramatically cheaper than per-pixel density classification and eliminates the need for GPU processing, with full analyses reported to run over minutes on a small number of CPUs thanks to spatial hashing.

The workflow begins with a region of interest, or ROI, containing a group of particles. This region may correspond to a biological boundary such as an intact virus, a microcompartment, a vesicle or a phase-separated condensate, or simply any cluster of particles the analyst wants to examine. The ROI can be defined by segmentation in the Dynamo package or by grouping particles into models with IMOD, and the toolkit accepts Dynamo table format input that can be prepared from the output of any major subtomogram averaging software. Once the ROI is set, a convex hull analysis defines the occupied space, calculating volume by summing polygons formed from three outer particles and the ROI centroid. Particle concentration follows directly as particles per volume.

Because particle coordinates mark particle centers, a naive volume calculation would underestimate the boundary. The toolkit corrects this by computing normal vectors of triangles in the convex hull and expanding the hull outward by the particle radius multiplied by the square root of three, a geometric factor derived from the long diagonal of a cube with side length equal to one particle diameter. A corresponding inward contraction excludes the outermost particles and generates an inner volume. Particles on the hull are flagged as outer and the rest as inner, letting users include or exclude boundary particles in downstream analyses at their discretion.

Linkage detection is the analytical core. Candidate interacting pairs are first restricted to particles in the same ROI within a user-defined search radius, set by default to double the longest dimension of the particle. For each candidate pair the toolkit calculates three parameters: projection distance, radial offset and inter-particle angle. Plotting these values across the whole dataset reveals hot spots that indicate how subunits actually interact. In a polymerizing system, for example, most interactions may cluster along one axis at a step size of roughly one subunit diameter with a small angle between neighbors. Thresholds are then set from the population statistics themselves, typically the mean plus and minus two standard deviations for Gaussian distributions, or the largest mode plus and minus double the full width at half maximum for non-Gaussian data. This data-driven parameterization reduces user bias while making error rates explicit and propagatable, enabling downstream biophysical calculations such as binding affinities and nucleation factors.

Once thresholds are set, particles lying within them are linked; transitively linked particles become chains, and unlinked particles are classified as monomers. Chains are ordered in the original three-dimensional coordinate system of the tomogram, starting from the subunit furthest from the chain’s center of mass, with remaining subunits ordered by Euclidean distance from that start. For particles with D-type symmetry, where a mirror plane creates two identical vector directions, an optional vector flip establishes a common chain direction without altering particle orientations in the averaging itself. Averaging the aligned orientation vectors yields a continuous chain vector describing propagation direction. Where proteins form larger ultrastructures, the toolkit evaluates fibril bundling from inter-chain distances and groups bundles sharing members, with all bundle and linkage parameters derived from the data unless the analyst chooses to impose bounds from outside biochemical or structural knowledge.

To demonstrate the package, the authors applied it to a published, high-accuracy dataset of Rubisco particles polymerizing inside alpha-carboxysomes, bacterial microcompartments available in the EMPIAR archive under accession number 11125. In that dataset, particles were picked by oversampling coordinates inside the carboxysomes, cropped and aligned with Dynamo, classified with RELION 3, and manually reviewed to correct false positive and negative identifications, with alignment sufficient to resolve alpha-helices. Fibril analysis measured a Rubisco-Rubisco bend of 4.1 plus or minus 3.3 degrees and a twist of 2.8 plus or minus 14.9 degrees. The non-zero bending angle combined with the large twist standard deviation suggests that the four symmetric binding sites around the Rubisco-Rubisco interface are not all occupied at any given time, allowing movement between complexes even while they remain bound at one site, a feature the authors attribute to the symmetry mismatch between the six-fold Rubisco pseudolattice and the four-fold symmetry of the subunits.

The demonstration extended beyond individual fibrils. Binding curves showed a strong concentration dependence for Rubisco polymerization. Analyzing bundles of fibrils revealed a pseudolattice in a subset of carboxysomes: rather than the discrete distances of a perfect lattice, the pseudolattice shows elevated propensity at specific distances over a baseline of noise arising from heterogeneity, flexibility and positional uncertainty from the resolution limits of subtomogram averaging. A power spectrum of an orthoslice through the lattice can distinguish the two cases, since a perfect lattice shows periodicity while a pseudolattice does not. Using continuous chain vectors, the team also established for the first time that local Rubisco-Rubisco pairwise angles are dominated by the inter-chain angle produced by fibril bundling, an analysis impossible with earlier particle-based approaches because chains in different registrations produced severe inconsistencies in inter-chain distances and angles. For this application, initial binding parameters were 0.7 to 1.3 subunit diameters projection distance, a radius of 0.5 subunit diameters, and a maximum angle of 25 degrees, chosen from an unbiased overview of all near-neighbor interactions.

The authors caution that the method’s reliability depends on data quality. A subtomogram averaging dataset with accurate particle picking, rigorous correction of false positives and negatives, and resolved alpha-helices is required before advanced biophysical analysis; at lower resolutions, the difference in calculated angle, bend and distance between particles can exceed two standard deviations when moving from 7 angstrom to 2 to 3 nanometer resolution, making conclusions difficult. Within those limits, the toolkit has no intrinsic resolution restrictions, and functions such as concentration calculations remain useful regardless of resolution. The package was designed with head-to-tail polymerization in mind, but other polymerization types may need adjusted fibril parameters, and non-fibril systems such as virus capsids or ribosome clusters near membranes can still benefit from concentration estimates and neighbor-distance and angle plots. Source code is available under a non-commercial, share-and-share-alike MIT license on GitHub, and the modular, object-based structure is intended to let users add their own project-specific analyses as particle picking accuracy improves across the field.

Subject of Research: A computational toolkit for analyzing protein polymerization from cryo-electron tomography subtomogram averaging data

Article Title: A toolkit to characterize protein polymerization from cryo-electron tomography data

Article References: Aguilar, V. M. F., Lee, F., Rochon, K., Lin, S., Lawrence, T., Mancino, P., & Metskas, L. A. (2026). A toolkit to characterize protein polymerization from cryo-electron tomography data. BMC Methods, 3(1), Article 17. https://doi.org/10.1186/s44330-026-00071-w

Image Credits: AI Generated

DOI: 10.1186/s44330-026-00071-w

Keywords: cryo-electron tomography, subtomogram averaging, protein polymerization, MATLAB toolkit, Rubisco, alpha-carboxysomes, fibril bundling, binding analysis, structural biology, open-source software, particle linkage, convex hull volume