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Extracellular space diffusion modelling identifies distinct functional advantages of glutamatergic and GABAergic synapse geometries.

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  1. [1] § Results › Tensor mapping identifies diffusion directionality based on ECS geometry ↔ src/findextremes.m, the whole file · a weak match · score 0.66 · linear regression, cumulative distribution, goes, cloud, perimeter, curve · Report a mismatch
  2. [2] § Results › Tensor mapping identifies diffusion directionality based on ECS geometry ↔ src/tensormap.m, lines 101 to 153 · score 0.54 · green box, tensor map, 210 deg · Report a mismatch

Paper

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The authors' code

MATLAB · 88 lines · 3.2 KB · BSD-3-Clause · 1 match

  1. % Find the furthest points of the diffusion cloud from the souce
  2. function [Xmaxd,Ymaxd,Area_perm,Area,maxD]=findextremes(AUX,S0,i)
  3. Ys=S0(1,1);
  4. Xs=S0(1,2);
  6. [r,c]=find(AUX);
  8. if range(r)==0 && range(c)==0
  9. k=0
  10. Xmaxd=S0(1,2);
  11. Ymaxd=S0(1,1);
  12. Area_perm=0;
  13. Area=0;
  14. maxD=0;
  16. else
  17. if range(r)==0 || range(c)==0
  18. k=1:length(r);
  19. k
  20. else
  21. k=convhull(c,r);
  22. end
  23. % Calculate distances
  24. distance = sqrt((r - S0(1,1)).^2 + (c - S0(1,2)).^2);
  25. dis_perimeter=sqrt((r(k) - S0(1,1)).^2 + (c(k) - S0(1,2)).^2);
  26. % Find maximum distance index
  27. [maxD, I] = max(distance);
  28. Xmaxd = c(I);
  29. Ymaxd = r(I);
  30. dis_norm=distance./max(distance);
  31. % dis_norm_perm=dis_perimeter./max(dis_perimeter);
  32. [f,x_dis]=ecdf(dis_norm);
  33. [f_perm,x_disperm]=ecdf(dis_perimeter);
  34. %make sure the cumulative distribution of the distance goes from 0 to 1
  35. %and the for the area under the curve is estimated from 0-1
  36. limit=max(x_disperm)+0.01;
  37. x_disperm=[0; x_disperm;limit;18];
  38. f_perm=[0; f_perm;0;0];
  40. Area_perm=trapz(x_disperm,f_perm);
  41. Area=trapz(x_dis,f);
  44. % if i<10 % i==589|| i==230|| i==218 || i==110|| i==102 %i==100 || i==438 || i==419 ||i==326 || i==275 || i==302
  45. %
  46. % % figure
  47. % % plot(x_dis,f,'r-')
  48. % % title(['CDF Indx ',num2str(i)])
  49. %
  50. % figure
  51. % plot(x_disperm,f_perm,'k-')
  52. % title(['CDF perimeter Indx ',num2str(i)])
  53. % end
  55. % Calculate linear regression
  56. if abs(Ys - Ymaxd) > abs(Xs - Xmaxd)
  57. P = polyfit([Ymaxd; Ys], [Xmaxd; Xs], 1);
  58. yfit = (min(r):max(r))';
  59. xfit = polyval(P, yfit);
  60. %rsq = 1 - (sum((polyval(P, r) - c).^2) / sum((c - mean(c)).^2));
  61. %SMS=sum((polyval(P, r) - c).^2);
  62. %Chi2=sum(((polyval(P, r) - c).^2)./c); %Pearsons Chi square test goodnesss of the fit
  63. else
  64. P = polyfit([Xmaxd; Xs], [Ymaxd; Ys], 1);
  65. xfit = (min(c):max(c))';
  66. yfit = polyval(P, xfit);
  67. %rsq = (1 - sum((polyval(P, c) - r).^2) / sum((r - mean(r)).^2));
  68. %SMS=sum((polyval(P, c) - r).^2);
  69. %Chi2=sum(((polyval(P, c) - r).^2)./r); %Pearsons Chi square test goodnesss of the fit
  70. end
  72. %Display cloud and fitted line
  73. % if i<10 % i==589|| i==230|| i==218 || i==110|| i==102 %i==100 || i==438 || i==419 ||i==326 || i==275 || i==302
  74. % figure
  75. % plot(c,r,'.')
  76. % hold on
  77. % plot(Xs,Ys,'r*','MarkerSize',5)
  78. % xlim([min(c),min(c)+50]);
  79. % ylim([min(r),min(r)+50]);
  80. % set(gca, 'YDir','reverse');
  81. % hold on;
  82. % plot(xfit,yfit,'k--');
  83. % plot(Xmaxd,Ymaxd,'r.','MarkerSize',10);
  84. % title(['Indx ',num2str(i)]);
  85. % end
  86. end
  88. end

findextremes.m at commit 7a6eb97, under BSD-3-Clause · at the source

Overview

Authors: Paula Gimenez1,2,3,4, Rohisha T Shakya5, Fidel Santamaria5, Jan Tønnesen1,2,3,4
ORCID iDs: Jan Tønnesen
  1. Neuronal Excitability Lab, Instituto Biofisika (CSIC-UPV), Leioa, 48940 Spain
  2. Aligning Science Across Parkinson’s (ASAP) Collaborative Research Network, Chevy Chase, MD 20815 USA
  3. Neuronal Excitability Lab, Achucarro Basque Center for Neuroscience, Leioa, 48940 Spain
  4. Department of Neuroscience, Faculty of Medicine and Nursing, University of the Basque Country (UPV/EHU), Leioa, 48940 Spain
  5. Department of Neuroscience, Developmental and Regenerative Biology, The University of Texas at San Antonio, San Antonio, TX 78349 USA
Institutions: University of the Basque Country (Spain); Achucarro Basque Center for Neuroscience (Spain); Instituto Biofisika (Spain); Aligning Science Across Parkinson's (United States); The University of Texas at San Antonio (United States)
Journal: Fluids and barriers of the CNS, volume 23, issue 1, article 52
Dates: received 4 December 2025; accepted 16 March 2026; published online 25 March 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1186/s12987-026-00797-3 · PMID 41882711 · PMCID PMC13045132 · OpenAlex W7140323574
Open access: gold, a free copy (OpenAlex)
Status: code verified (how the code is found and verified)
Categories: mouse (organism), cellular / molecular (subfield)
Keywords: Brain, Extracellular space, Molecular diffusion, Signaling, GABA, Glutamate
MeSH: CA1 Region, Hippocampal*, Extracellular Space*, GABAergic Neurons*, gamma-Aminobutyric Acid*, Glutamic Acid*, Models, Neurological*, Synapses*, Animals, Diffusion, Mice, Mice, Inbred C57BL (* major topic)
Topic: Neuroscience and Neuropharmacology Research (Cellular and Molecular Neuroscience, Neuroscience), according to OpenAlex
Funding: Aligning Science Across Parkinson&apos;s (ASAP-020205); Agencia Estatal de Investigación (PCI2022-135040-2); Ministerio de Economía y Competitividad (PID2020-113894RB-I00); Euskal Herriko Unibertsitatea (GIU21/048); National Institute of Neurological Disorders and Stroke (R01NS130759); Aligning Science Across Parkinson's (ASAP-020205); NextGenerationEU; NINDS NIH HHS (R01NS130759); National Science Foundation (EFRI BEGIN OI 2515404); Sigma Xia
Citations: cited by 1 paper (Europe PMC); 46 references in the paper
Research resources: RRID:SCR_027941, DifFlux diffusion model RRID:SCR_027942

Abstract

Background: The brain extracellular space (ECS) is a convoluted compartment of nano- to microscale interconnected ducts filled with interstitial fluid and lined by neural cell membranes. A key step in signaling between neural cells is diffusion through the ECS of transmitter molecules released from point sources distributed throughout the parenchyma. Yet, signaling is generally considered solely from the stance of cellular properties, while disregarding ECS sojourn time and putative signal modulation at this phase. Where ECS diffusion is considered, it is commonly done based on volume-averaging techniques blind to individual signaling events or actual ECS structural geometry. This has precluded knowledge on how specific ECS geometries may impact diffusion and modulate signaling arising from individual transmitter release events. We hypothesized that ECS geometry can shape local diffusion gradients resulting from individual point source release events and thereby tune signaling, and we further propose that this modulation can impart non-random functionality.

Methods: To access the scale of individual transmitter release events and true ECS geometries, we used super-resolution STED microscopy to image the ECS in the hippocampal CA1 stratum radiatum of live mouse brain slices. We then developed a computational diffusion model, DifFlux, based on super-resolved images of hippocampal ECS and applied this along single molecule Monte Carlo diffusion simulations. Our approach allows us to simulate diffusion of molecules of our choosing in actual live ECS geometries.

Results: We observed local anomalous and anisotropic diffusion imposed by ECS geometry, whereby diffusion along larger structures was more directional than in denser neuropil of finer cellular structures. Further, we identified that the perisynaptic ECS geometries around respective glutamatergic and GABAergic synapses imposed distinct functional advantages, shedding light on the longstanding conundrum of why glutamatergic and GABAergic synapses are so conspicuously morphologically different.

Conclusions: Our modelling broadly identifies ECS structure as a direct modulator of extrasynaptic signaling that can operate in parallel to conventional regulation mechanisms. This ultimately provides a metabolic and computational advantage to the brain.

Supplementary Information: The online version contains supplementary material available at 10.1186/s12987-026-00797-3.

Reproduced under the paper's license (CC BY), from the paper cited above.

Repositories

Its files are read in the Code ↔ Paper reader above, with 2 matches between paragraphs and lines of code.

Zenodo 18750224

License: BSD-3-Clause
State: the link answers, verified on 30 September 2026
Evidence: files inventoried
Size: 1 file
Software Heritage: not checked
Found in: “Data availability”
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Curve Fitting Toolbox (1 file)
Availability: 1 check, the latest on 30 September 2026: the link answers (HTTP 200)
  • 30 September 2026: the link answers (HTTP 200)
27 files
At the source:

tonnesenlab/diffusion-model

License: BSD-3-Clause
State: the link answers, verified on 30 September 2026
Evidence: files inventoried
Commit: 7a6eb97be1e12f45bccd0ce39851033f7a70fecc, 3 November 2025
Languages: MATLAB (25)
Size: 90 files, 25 scripts
Software Heritage: not archived
Found in: the Zenodo archive record
Holds: README, license file
Not found: CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Curve Fitting Toolbox (1 file)
Availability: 1 check, the latest on 30 September 2026: the link answers
  • 30 September 2026: the link answers
27 files
At the source: github.com/TonnesenLab/Diffusion-Model/tree/diffusion

The paper's code and data availability statement is in the Data section.

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  • 2 repositories of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 50 scripts, each with its path and the digest of its content;
  • 2 matches between paragraphs of the paper and lines of the code (method lexical-v1);
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Data

Datasets cited

Data availability

All simulations were programmed in MATLAB (Natick, MA). The code and analyses are freely available from Github: DifFlux diffusion model (RRID: SCR_027942; 10.5281/zenodo.18750224) and Monte Carlo diffusion with obstacles model (RRID: SCR_027941; https://doi.org/10.5281/zenodo.18834019). All images, results and key resource identifiers are available through the Zenodo repository (https://doi.org/10.5281/zenodo.18750437).

Reproduced under the paper's license (CC BY), from the paper cited above.

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Version 1, 30 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 4 authors, 6 keywords, 11 MeSH terms, 10 funders, 45 references, 2 RRIDs.

Cite

This paper

Gimenez, P., Shakya, R. T., Santamaria, F., & Tønnesen, J. (2026). Extracellular space diffusion modelling identifies distinct functional advantages of glutamatergic and GABAergic synapse geometries. Fluids and barriers of the CNS, 23(1), 52. https://doi.org/10.1186/s12987-026-00797-3

BibTeX

@article{gimenez2026extracellular,
author = {Gimenez, Paula and Shakya, Rohisha T and Santamaria, Fidel and Tønnesen, Jan},
title = {{Extracellular space diffusion modelling identifies distinct functional advantages of glutamatergic and GABAergic synapse geometries}},
journal = {Fluids and barriers of the CNS},
year = {2026},
month = mar,
volume = {23},
number = {1},
pages = {52},
publisher = {BMC},
issn = {2045-8118},
doi = {10.1186/s12987-026-00797-3},
url = {https://doi.org/10.1186/s12987-026-00797-3},
pmid = {41882711},
pmcid = {PMC13045132}
}

RIS

TY - JOUR
AU - Gimenez, Paula
AU - Shakya, Rohisha T
AU - Santamaria, Fidel
AU - Tønnesen, Jan
TI - Extracellular space diffusion modelling identifies distinct functional advantages of glutamatergic and GABAergic synapse geometries
T2 - Fluids and barriers of the CNS
J2 - Fluids Barriers CNS
PY - 2026
DA - 2026/03/25
VL - 23
IS - 1
SP - 52
SN - 2045-8118
PB - BMC
DO - 10.1186/s12987-026-00797-3
UR - https://doi.org/10.1186/s12987-026-00797-3
LA - en
ER -

CSL-JSON

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"id": "10.1186/s12987-026-00797-3",
"type": "article-journal",
"title": "Extracellular space diffusion modelling identifies distinct functional advantages of glutamatergic and GABAergic synapse geometries",
"container-title": "Fluids and barriers of the CNS",
"author": [
{
"family": "Gimenez",
"given": "Paula"
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{
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"family": "Santamaria",
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"family": "Tønnesen",
"given": "Jan"
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"container-title-short": "Fluids Barriers CNS",
"volume": "23",
"issue": "1",
"page": "52",
"DOI": "10.1186/s12987-026-00797-3",
"PMID": "41882711",
"PMCID": "PMC13045132",
"ISSN": "2045-8118",
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"language": "en",
"issued": {
"date-parts": [
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