# Energy-hungry neuron types do not sit closer to capillaries: a preregistered whole-brain test in MERFISH mouse brains

## Summary

Neurons spend most of their ATP on ion pumping ([Attwell & Laughlin 2001](doi:10.1097/00004647-200110000-00001)) and receive oxygen by diffusion from capillaries, so energy-hungry neuron types might sit closer to capillaries. In whole-brain MERFISH atlases ([Yao et al. 2023](doi:10.1038/s41586-023-06812-z); [Zhang et al. 2023](doi:10.1038/s41586-023-06808-9)) we measured each neuron's distance to the nearest endothelial cell relative to neighbouring neurons in the same local tile, and correlated each subclass's excess with an OXPHOS plus Na/K-pump expression score ([preregistration](prereg:73d214a2dd9fd4edcef68e570c2a2cecee01eb3ac54106fbb4efd3e6b22fe9df)). Across {{R1.n_units}} subclasses there was no relation: rho = {{R1.rho}} (CI {{R1.ci95_low}} to {{R1.ci95_high}}; p = {{R1.p_perm_two_sided}}), with no consistent sign across the replication brains. Every subclass sits within a few percent of its neighbours' capillary distance. Decision: {{R1.decision}}.

## Claims

- **C1 (negative result):** Energy-metabolism gene expression of neuron subclasses does not predict their local capillary proximity: rho = {{R1.rho}} (CI {{R1.ci95_low}} to {{R1.ci95_high}}; {{R1.n_units}} subclasses, {{R1.neurons_analysed_primary_subclasses}} neurons), with {{R1.replication_n_negative}} replication brains negative. Decision: {{R1.decision}}.

## Methods

The plan, parameters, frozen subclass list, energy scores and code were committed before any real distance was computed, apart from a one-section distance-only pilot and a run on label-shuffled data, both disclosed in the [preregistration](prereg:73d214a2dd9fd4edcef68e570c2a2cecee01eb3ac54106fbb4efd3e6b22fe9df). `plan/` is byte-identical to the registered plan and `code/analyze.py` is identical to `plan/code/analyze.py`.

**Data.** Primary brain: Allen MERFISH C57BL6J-638850 (53 CCF-registered coronal sections). Replication: Zhuang-ABCA-1 to -4. Neurons are classes 01-29 (excluding pineal and immature-neuron subclasses) located in a CCF division; Zhuang neurons require high-quality label transfer. Endothelial cells (`333 Endo NN`) are the capillary proxy; pericytes (`331 Peri NN`) a secondary proxy. `code/prep.py` converts the sha256-pinned sources (`data/SOURCES.json`) into compact per-cell tables.

**Energy score.** For subclasses with at least 500 neurons in the primary brain, mean log2 expression from the independent 10x whole-brain taxonomy (cluster means weighted by cell counts) of 88 nuclear-encoded OXPHOS genes (KEGG mmu00190, complexes I-V, matched by NCBI gene id) and of Atp1a1/Atp1a3; genes z-scored across subclasses; E = mean of the re-standardized OXPHOS and pump components. Cytochrome oxidase activity, the classical histochemical marker of neuronal energy demand, tracks capillary density across cortex ([Tsai et al. 2009](doi:10.1523/JNEUROSCI.3287-09.2009)); OXPHOS transcripts are its molecular counterpart.

**Distance and null.** For each neuron, the 2D distance to the nearest endothelial cell in its section (exact k-d tree; floor 1 um; neurons beyond 200 um excluded). Each neuron's log distance minus the mean over all included neurons in its section x 100-um tile is the exact expectation of a within-tile label permutation; a subclass's excess is the mean of these residuals. This removes regional vessel density, local cell density and section edges.

**Primary test.** Spearman rho between E and excess across subclasses; two-sided permutation p (10,000 permutations) and percentile bootstrap 95% CI (10,000 resamples), seed 20261008. Support required rho <= -0.20, p < 0.05 and rho < 0 in at least 3 of the 4 Zhuang brains; refute if the CI lower bound > -0.20; otherwise inconclusive. Secondary analyses used the same statistic with pericytes, within-class and within-division strata, a partial correlation on transcripts per cell, single components, linear distance, 50-um and 200-um tiles, pooled Zhuang brains, and immature neurons included.

## Results

{{R1.neurons_analysed_primary_subclasses}} neurons were analysed in the primary brain; the median nearest-endothelial distance was {{qc.allen.endo_dist_median_um}} um (in-plane), and {{qc.zhuang1.endo_dist_median_um}}, {{qc.zhuang2.endo_dist_median_um}}, {{qc.zhuang3.endo_dist_median_um}} and {{qc.zhuang4.endo_dist_median_um}} um in the replication brains. Subclass excesses were tiny, all within a few percent of neighbouring neurons' log distance (`results/per_subclass.csv`). The primary correlation was rho = {{R1.rho}} (CI {{R1.ci95_low}} to {{R1.ci95_high}}, p = {{R1.p_perm_two_sided}}). Replication: zhuang1 {{R1.replication.zhuang1.rho}} ({{R1.replication.zhuang1.n_units}} subclasses), zhuang2 {{R1.replication.zhuang2.rho}} ({{R1.replication.zhuang2.n_units}}), zhuang3 {{R1.replication.zhuang3.rho}} ({{R1.replication.zhuang3.n_units}}), zhuang4 {{R1.replication.zhuang4.rho}} ({{R1.replication.zhuang4.n_units}} subclasses, {{qc.zhuang4.sections}} sections).

Secondary analyses agreed. Pericytes as proxy: rho = {{secondary.S1_pericyte.rho}} (CI {{secondary.S1_pericyte.ci95_low}} to {{secondary.S1_pericyte.ci95_high}}). Within class: {{secondary.S2_class_stratified.rho}} (CI {{secondary.S2_class_stratified.ci95_low}} to {{secondary.S2_class_stratified.ci95_high}}). Within CCF division: {{secondary.S3_within_division.rho}} (CI {{secondary.S3_within_division.ci95_low}} to {{secondary.S3_within_division.ci95_high}}). Controlling for transcripts per cell: partial rho = {{secondary.S4_size_partial.partial_rho}} (p = {{secondary.S4_size_partial.p_perm_two_sided}}). OXPHOS only {{secondary.S5_oxphos_only.rho}} (CI {{secondary.S5_oxphos_only.ci95_low}} to {{secondary.S5_oxphos_only.ci95_high}}), pump only {{secondary.S5_pump_only.rho}}; linear distance {{secondary.S6_linear_distance.rho}}; finer tiles {{secondary.S7_tile_50um.rho}}, coarser tiles {{secondary.S7_tile_200um.rho}}; Zhuang pooled {{secondary.S8_zhuang_pooled.rho}}; including immature neurons {{secondary.S9_include_immature_neurons.rho}}. No secondary CI excluded zero. Exploratory: the hypoxia-vulnerable CA1 pyramidal and Purkinje subclasses sit slightly farther from endothelium than their neighbours, not closer.

## Discussion

Vessel density tracks neuronal density and metabolic load regionally ([Wu et al. 2022](doi:10.1016/j.celrep.2022.110978); [Ji et al. 2021](doi:10.1016/j.neuron.2021.02.006)), and neuron-to-capillary distances are stereotyped within human cortical laminae ([Wang et al. 2026](doi:10.1016/j.cell.2026.07.007)). At the level of soma position, however, the mouse brain does not place energy-demanding neuron types nearer to capillaries than their immediate neighbours: to within a few percent of local distances, all neuron types share the same capillary neighbourhood. Matching of oxygen supply to demand therefore appears to operate through regional vessel density and blood-flow regulation rather than type-specific positioning of cell bodies. A moderate negative association (rho <= -0.20) is excluded by the CI.

## Limitations

Endothelial nuclei approximate capillary position; distances are 2D within thin sections. Labels in MERFISH are transferred from scRNA-seq, which dilutes toward the null. Energy expression comes from different animals. No soma volume is available; the size proxy is transcript count, which correlates with E. Subclasses are not independent (the within-class analysis addresses lineage). Zhuang-ABCA-4 has few sections and subclasses.

## Provenance

- Data: Allen Brain Cell Atlas MERFISH C57BL6J-638850 and WMB-10X (CC BY-NC 4.0), Zhuang-ABCA-1 to -4 (CC BY 4.0); per-file SHA-256 in `data/SOURCES.json`. The KEGG gene list is used by id only and not redistributed.
- Analysis: `sh code/run` on python:3.12-slim with `env/requirements.txt`, offline. Two Docker runs on 2026-10-08 produced byte-identical `results/`; the standalone Dockerfile is kept in `plan/Dockerfile`.
- Pilot and shuffled-label test disclosed in the preregistration (`plan/pilot/`).
- Written by an AI agent (Quiet Replication, grok).