The measured neuron

Every picture of a neuron you have seen is schematic. So, in a different place, is every reconstruction in the public archive. Computed for all 298,339 of them.

A neuron in a textbook has a round body, a few branches at the top and a tail that leaves the frame. It is a diagram, and everyone knows it is a diagram. The interesting question is what the honest version would look like, and the answer is that nobody can draw one — not because the data is secret but because no single file contains it.

There is a public archive of reconstructed neurons¹: 298,339 morphologies traced by hand from real tissue. This page counts every one of them, and opens the files themselves from 22 of the contributing archives. The archive records, for each reconstruction, which parts of the cell it contains, whether its widths were measured, whether it is three-dimensional, whether its axon was followed to the end, and whether anyone corrected for the tissue shrinking under the microscope. Requiring all five leaves 104 files out of 298,339, which is 0.03% of them.

Why the diagram is schematic

Start with the reason the textbook picture exists, which is not laziness. A whole-brain reconstruction of a single neuron reaches about 4.4 mm from end to end. The thinnest process such a cell carries is about 0.17 µm, a figure from electron microscopy², because visible light cannot resolve anything that small³. Drawing both at once means holding a range of 25,607 to one in a single picture: 4.4 orders of magnitude.

Every scale one cell holds at once. The band is about what a figure can render between its largest and smallest mark, which is assumed rather than measured: three orders of magnitude. The cell needs 4.4.

A figure printed at a thousand pixels across would render that thinnest process 0.039 of a pixel wide. Showing it as a single pixel would take a canvas 25,607 pixels across. The schematic is not a casual lie about a neuron; it is what is left when a shape that spans 4.4 orders of magnitude is forced onto something that holds three.

The two neurons nobody can combine

So a reconstruction has to choose, and the choice is made by how the tissue was prepared rather than by anyone's preference. A cell recorded in a slice sits in a piece of brain a third of a millimetre thick; its widths can be measured, and its axon is cut off by the blade. A cell traced through a whole brain keeps its axon⁴, and nobody measured its widths.

Two real files. Left: Allen Cell Types, 2.8 mm of dendrite and 58 µm of axon, drawn at 1,084 distinct widths because that is how many the file records. Right: MouseLight, 59.8 mm of axon reaching 4.7 mm from the soma, drawn at one width because the file contains one.

The cell on the right carries 59.8 mm of axon. The cell on the left carries 58 µm, and it is the kind of picture that a search for a cortical neuron returns. Neither is wrong. Each is missing the half the other has, and the halves cannot be added, because they come from different animals prepared in different ways.

What the archive contains

Each line adds one requirement to the line above it. The order matters, and the interactive lets you change it.

22,491 reconstructions contain a soma, a dendrite and an axon together, which is 7.5% of the archive. 70.1% record no varying width anywhere. 22.1% are flat — traced as a projection, with no depth at all. 2.7% are marked as corrected for shrinkage. Requiring all five at once leaves 104.

The shortage is structural rather than unlucky. Of the 36,582 reconstructions whose axon its depositor marked complete, 5,420 also carry a measured width: 14.8%. Measured on the files rather than on the archive's own labels, the same split appears. The 120 whole-brain reconstructions sampled here reach a median 4.4 mm from the soma and hold a median of 1 distinct widths across the entire arbor. The 1,261 slice and culture reconstructions reach 192 µm and hold 121.

Is it a gradient?

The obvious next claim is that the further an arbor reaches, the coarser its recorded thickness becomes — a smooth trade rather than two camps. Pooled across every sampled cell, the rank correlation between reach and coarseness is 0.28, which looks like strong support. It is not, because reach and method are the same variable in that sample: almost every far-reaching cell is whole-brain and almost every near one is a slice, so the correlation measures which archive a file came from.

The test that separates them is to run it inside each archive, where the method is held constant. An archive qualifies with at least 20 sampled cells and a 3-fold spread in reach, because a set of cells that all reach the same distance cannot show a gradient either way. A gradient counts as surviving if the median within-archive correlation exceeds 0.20 and at least 60% of qualifying archives exceed it. That rule was fixed before the answer was known.

1,381 sampled reconstructions from 20 archives. The verdict: no gradient survives inside archives. Median within-archive correlation -0.00 across 19 qualifying archives, against a pooled figure of 0.28.

no gradient survives inside archives. What the data supports is the weaker and more specific statement: two ways of preparing tissue, each of which destroys what the other keeps.

Who corrects

The 104 reconstructions that meet every requirement come from 6 laboratories. 65 rat, 24 Xenopus laevis, 15 mouse. 48 of them — 46% — carry a single DOI, 10.1093/cercor/bhx352, which is the paper that states the shrinkage correction⁵ those files were corrected with. The corrected corner of the archive is not a slow accumulation of good practice across the field. It is a few groups that correct as a matter of protocol, and their cells.

That is what the question on this page looks like when it is made concrete. Not whether a picture is accurate, but how far you have to go before the number under it was measured by someone, on purpose, and written down.

The same thing happens to numbers

A figure loses its provenance in the same way a picture does. Two examples turned up in the course of checking the sources for this page, and neither is about neuroscience going wrong; both are about a number outliving the measurement it came from.

The membrane area of a dendrite is roughly double what its traced skeleton suggests, because spines carry much of it. The factor is often attributed to a 2001 paper on hippocampal synapse counts, which contains no such factor⁶: it is the source for where spines are, not how much membrane they hold. The measured factor is 1.78 to 2.39, from a 2016 study of human cortical cells⁷, and it applies only beyond sixty micrometres from the soma, because the dendrite is nearly bare closer in. So the familiar shortcut — double it — is wrong twice: wrong in its source, and wrong to apply it uniformly.

The synaptic delay everyone quotes as half a millisecond comes from a 1965 paper on the frog neuromuscular junction⁸. That paper reports a minimum of 0.4 to 0.5 ms, at twenty degrees, in a low-calcium solution chosen to make single events visible; the typical delay in the same preparation is about 0.75 ms. A fast central synapse at body temperature releases in about a hundred and fifty microseconds⁹. Three different quantities, routinely quoted as one.

Limits

The five requirements are read from the archive's own metadata, which means they are the depositors' claims about their files rather than measurements of them. That distinction is not decorative: a reconstruction is flagged as having a measured width if its widths are not all identical, and that test passes a file holding three values. Every width statement on this page is therefore computed from the files, using a stricter rule that is stated in the code and labelled assumed in the payload.

Nor can you always tell what a file's numbers mean. An SWC file has seven columns and none of them is a unit: the convention is micrometres, and there is no field in which a file could say otherwise. Of the 22 archives sampled here, 20 can be confirmed to be in micrometres and 2 cannot: Helmstaedter and Siegert. One of them describes an arbor reaching 163,313 µm from its soma, which is further than the brain it came from; the other gives its cells a soma about the width of a mitochondrion. Neither file is corrupt. They are almost certainly written in nanometres or in voxels, correctly, by people who knew what they meant. The test used here is the only yardstick inside a file: a soma is between 3 and 60 µm across in essentially every neuron, so an archive whose somata are not somata is not in micrometres. That leaves 1,381 of 1,501 sampled reconstructions to measure from, and the 120 dropped are counted and named rather than quietly discarded.

A measured width is not the same as a reliable one. When the same eight cells were reconstructed by two competent light-microscopy pipelines, the widths differed by about a factor of two on visually matched segments¹⁰: 1.80 ± 0.15 µm against 0.91 ± 0.09 µm. The field's own tracing benchmark excluded diameter¹¹ altogether, as too subjective at the resolutions used for whole-arbor reconstruction. And three experts tracing one dendrite¹² agreed on 0.470 ± 0.071 of it by area, while one person re-tracing after a fortnight agreed with themselves on 87.5%. There is no single true morphology to draw, and this page's widths inherit all of that.

Every count here is a snapshot. The census was taken on 2026-09-05, and the archive grows continuously: it passed 298,339 reconstructions that day, and the figure on the day you read this is larger. Re-running fetch_data.py takes a fresh census and every number on the page moves with it.

The sample of files is drawn from 22 archives with a fixed seed, taking up to a fixed number of cells from each archive's first page of records. It is not a uniform random sample of the archive, and archives differ in what they contain, so the medians here describe the sample rather than the whole.

This page does not claim that textbook diagrams have been audited for accuracy. No such study was found. What is shown instead is arithmetic: the range a true-proportion drawing must span, against the range a figure can render.

Nor is the contrast between the two cells in the second figure a measurement of how much axon slicing removes. They are different cells from different animals. The published figure for that is¹³ 48–49% of intracortical axon lost in a 300 µm slice; 15–17% of dendrite, and it covers local axon only; a long-range projection is lost entirely.

Depth is the one thing no figure here uses. Reconstructions made in slices are distributed without a shrinkage correction, and tissue prepared this way loses roughly half its thickness¹⁴ — 63 ± 10% in the preparation these files come from¹⁵. The archive that supplies the widths handled this by leaving depth-derived measurements out of its own analysis¹⁶ rather than by correcting the coordinates¹⁷. So both drawings on this page are flat projections, and the code that reads them returns two columns rather than three.

The code

Two public sources, no key: the NeuroMorpho.Org API and the Allen Institute API. fetch_data.py takes the census and the sample and records a hash of each; swclib.py parses the reconstructions and holds the rule about depth; build_neuron.py computes the payload and builds the interactive; fig_neuron.py draws the four figures; update_page.py writes this page from the payload; test_neuron.py checks the failure modes, including the parser against a fixture whose every quantity was worked out by hand. The archive holds the scripts, the frozen census and the two reconstructions the second figure draws; it does not hold the fifteen hundred files the sample was computed from, which the fetch script will pull again.

Download source · 1.5 MB All code

Sources

Numbered markers in the text above point here. Emission factors, cost ranges and lifespan figures are representative values from these sources, not measurements made for this project.

1. Ascoli, Donohue & Halavi, The Journal of Neuroscience 27(35):9247-9251, 2007, doi:10.1523/JNEUROSCI.2055-07.2007; Tecuatl, Ljungquist & Ascoli, FASEB BioAdvances 6(7):207-221, 2024, doi:10.1096/fba.2024-00048.NeuroMorpho.Org, the archive every count on this page is computed from; CC BY 4.0.
2. Shepherd & Harris, The Journal of Neuroscience 18(20):8300-8310, 1998, doi:10.1523/JNEUROSCI.18-20-08300.1998.The 0.17 um calibre of a CA3-to-CA1 axon shaft, the thinnest structure a drawing at true proportions would have to render.
3. Huang, Bates & Zhuang, Annual Review of Biochemistry 78:993-1016, 2009, doi:10.1146/annurev.biochem.77.061906.092014.The diffraction limit: 200-300 nm laterally, 500-700 nm axially.
4. Winnubst et al., Cell 179(1):268-281.e13, 2019, doi:10.1016/j.cell.2019.07.042.Whole-brain single-neuron reconstruction; more than 85 m of axon across more than 1,000 projection neurons.
5. Emmenegger, Qi, Wang & Feldmeyer, Cerebral Cortex 28(4):1439-1457, 2018, doi:10.1093/cercor/bhx352, attributing Marx et al., Nature Protocols 7(2):394-407, 2012, doi:10.1038/nprot.2011.449.The x1.1 and x2.1 correction factors, and the laboratory whose cells make up most of the fully-qualified set.
6. Megias, Emri, Freund & Gulyas, Neuroscience 102(3):527-540, 2001, doi:10.1016/S0306-4522(00)00496-6.Where dendritic spines are on a CA1 pyramidal cell; it carries no membrane-area factor, though it is often cited for one.
7. Eyal et al., eLife 5:e16553, 2016, doi:10.7554/eLife.16553.The spine membrane-area factor, F = 1.78-2.39, applied only beyond 60 um from the soma.
8. Katz & Miledi, Proceedings of the Royal Society B 161(985):483-495, 1965, doi:10.1098/rspb.1965.0016.The measured synaptic delay: a minimum of 0.4-0.5 ms and a modal value near 0.75 ms, at 20 C in low-calcium Ringer.
9. Sabatini & Regehr, Nature 384(6605):170-172, 1996, doi:10.1038/384170a0.Transmitter release 150 us after the onset of the presynaptic action potential, at physiological temperature.
10. Blackman, Grabuschnig, Legenstein & Sjostrom, Frontiers in Neuroanatomy 8:65, 2014, doi:10.3389/fnana.2014.00065.The same eight cells reconstructed two ways: 1.80 +/- 0.15 um against 0.91 +/- 0.09 um.
11. Gillette, Brown & Ascoli, Neuroinformatics 9(2-3):233-245, 2011, doi:10.1007/s12021-011-9117-y.Diameter left out of the DIADEM competition as too subjective at the resolutions used for whole-arbor reconstruction.
12. Fernholz, Guggiana Nilo, Bonhoeffer & Kist, PLoS Computational Biology 20(2):e1011774, 2024, doi:10.1371/journal.pcbi.1011774.Inter-operator agreement on a traced arbor, and one person's agreement with themselves.
13. van Pelt, van Ooyen & Uylings, Frontiers in Neuroanatomy 8:54, 2014, doi:10.3389/fnana.2014.00054.How much intracortical axon a 300 um slice removes: 48-49%, against 15-17% of dendrite.
14. Gardella et al., Journal of Neuroscience Methods 124(1):45-59, 2003, doi:10.1016/S0165-0270(02)00363-1.Measured shrinkage by embedding method; 80 um vibratome sections finished at 31.78 um.
15. Mohan et al., Cerebral Cortex 25(12):4839-4853, 2015, doi:10.1093/cercor/bhv188.63 +/- 10% z shrinkage measured in 350 um slices, and the finding that total dendritic length rises only 11 +/- 2% when corrected.
16. Gouwens et al., Nature Neuroscience 22(7):1182-1195, 2019, doi:10.1038/s41593-019-0417-0.The Allen Cell Types morphologies, and the decision to exclude z-derived features rather than correct the coordinates.
17. Lee et al., eLife 10:e65482, 2021, doi:10.7554/eLife.65482.Where a per-cell shrinkage correction is applied: downstream, in the Patch-seq pipeline, not in the distributed files.