Why the “perfect rings” in herpesvirus EM images are geometrically extraordinary
This repository contains pure-Python tools that let anyone reproduce the simple but shocking geometric calculation that can be done to investigate images b and c from: https://pmc.ncbi.nlm.nih.gov/articles/PMC6146708/figure/F8/ (copied versions also in repo for reference). See ref [1] for source publication.
In a random 3D distribution of ~120 nm spherical capsids imaged in an 80 nm thin section, the probability that 25 capsids all show near-perfect 100+ nm rings with no obvious small arcs is approximately 1 in 6 million (and both Figure 8b + 8c together ≈ 1 in a trillion).
This calculation does not need to reference any publications in virology for vlidation, it stands on it's own. Justthe images, geometry and scale bars are needed.
| File | What it does |
|---|---|
capsid_section_probability.py |
Analytic (exact) calculation of the 1-in-millions result used in the final answer |
capsid_section_monte_carlo.py |
Monte-Carlo version + histogram of expected chord diameters |
visualize_random_vs_planar.py |
3-D matplotlib visualisation: random distribution (expected) vs perfectly planar (observed) |
projected_tem_view_simulation.py |
Generates fake “TEM micrographs” showing what each scenario actually looks like in 2-D projection |
All scripts are heavily commented, require only numpy and matplotlib, and run with a single python scriptname.py.
python capsid_section_probability.pyOutput (as of 2025 parameters):
Capsid diameter : 120.0 nm
Section thickness : 80.0 nm
Threshold diameter : 100.0 nm
Probability one capsid looks >= 100 nm : 0.53513
Figure 8b (~25 capsids) → P(all full) = 1.70e-07 (1 in 5,891,657)
Figure 8c (~20 capsids) → P(all full) = 1.29e-05 (1 in 77,529)
Run the other scripts to see the histograms and pictures — the visualisations make the statistical claim instantly obvious to anyone.
Classic thin-section TEM images of herpesviruses (and many other large viruses) routinely show fields of dozens of nearly identical ~100–120 nm rings.
Under the standard assumptions (spherical particles, random 3-D positions, honest ~70–100 nm sections), this is many-sigma impossible without extreme ordering or selection.
These scripts let anyone verify that claim in < 10 seconds, change the numbers (capsid size, section thickness, threshold), and see for themselves.
[1] Mariamé B, Kappler-Gratias S, Kappler M, Balor S, Gallardo F, Bystricky K. Real-Time Visualization and Quantification of Human Cytomegalovirus Replication in Living Cells Using the ANCHOR DNA Labeling Technology. J Virol. 2018 Aug 29;92(18):e00571-18. doi: 10.1128/JVI.00571-18. PMID: 29950406; PMCID: PMC6146708. (https://pmc.ncbi.nlm.nih.gov/articles/PMC6146708/)
MIT License – do whatever you want with the code (commercial use, modification, sale, etc.). See LICENSE for the full text.
Feel free to cite or link this repo when you need to show — with actual math — why those “textbook perfect” viral capsid micrographs are geometrically astonishing.
— November 2025