Accurate computation of ionic concentrations in the synaptic cleft requires the full Poisson-Nernst-Planck (PNP) equations.

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Paper

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The authors' code

MATLAB · 47 lines · 1.4 KB · GPL-3.0

function ds = AMPA_receptor_kinetics(states, c)
%ds = AMPA_receptor_kinetics(states, c)
% AMPA receptor model from Jonas, P., Major, G., & Sakmann, B. (1993).
% Quantal components of unitary EPSCs at the mossy fibre synapse on CA3
% pyramidal cells of rat hippocampus. The Journal of physiology, 472(1),
% 615-663.
% Extract glutamate concentration
glu = c(:, 5);
% Define parameters
k1p = 4.59; % 1/(mM*ms)
k1m = 4.26; % 1/ms
k2p = 28.4; % 1/(mM*ms)
k2m = 3.26; % 1/ms
k3p = 1.27; % 1/(mM*ms)
k3m = 0.0457; % 1/ms
a = 4.24; % 1/ms
b = 0.9; % 1/ms
a1 = 2.89; % 1/ms
b1 = 0.0392; % 1/ms
a2 = 0.172; % 1/ms
b2 = 7.27e-4; % 1/ms
a3 = 0.0177; % 1/ms
b3 = 4.0e-3; % 1/ms
a4 = 0.0168; % 1/ms
b4 = 0.1904; % 1/ms
% Load states
C0 = states(:,1);
C1 = states(:,2);
C2 = states(:,3);
C3 = states(:,4);
C4 = states(:,5);
C5 = states(:,6);
O = 1 - (C0 + C1 + C2 +C3 + C4 + C5);
% Set up temporal derivatives
ds = zeros(size(states));
ds(:,1) = -k1p*glu.*C0 + k1m*C1; % [C0]
ds(:,2) = k1p*glu.*C0 - (k1m + k2p*glu + a1).*C1 + k2m*C2 + b1*C3; % [C1]
ds(:,3) = k2p*glu.*C1 - (k2m + a + a2)*C2 + b*O + b2*C4; % [C2]
ds(:,4) = a1*C1 - (b1 + k3p*glu).*C3 + k3m*C4; % [C3]
ds(:,5) = k3p*glu.*C3 + a2*C2 - (k3m + b2 + a4)*C4 + b4*C5; % [C4]
ds(:,6) = a3*O + a4*C4 - (b3 + b4)*C5; % [C5]
end

AMPA_receptor_kinetics.m at commit 3e4a4b2, under GPL-3.0 · at the source

Overview

Authors: Karoline Horgmo Jæger¹, Aslak Tveito¹

ORCID iDs: Karoline Horgmo Jæger

Department of Computational Physiology, Simula Research Laboratory, Oslo, Norway

Institutions: Simula Research Laboratory (Norway)

Journal: PLoS computational biology, volume 22, issue 5, article e1014341

Dates: received 12 March 2026; accepted 18 May 2026; published online 28 May 2026

Type: Research article · Language: English

License: CC BY

Identifiers: DOI 10.1371/journal.pcbi.1014341 · PMID 42207852 · PMCID PMC13235942 · OpenAlex W7162691769

Open access: gold, a free copy (OpenAlex)

Status: code verified

Categories: computational modeling (no new data) (modality), none (in silico) (organism), cellular / molecular (subfield)

MeSH: Ions*, Models, Neurological*, Synapses*, Animals, Computational Biology, Computer Simulation, Diffusion, Glutamic Acid, Neurotransmitter Agents, Poisson Distribution, Synaptic Transmission (* major topic)

Journal subjects: Biology and Life Sciences, Biochemistry, Neurochemistry, Neurotransmitters, Glutamate, Neuroscience, Anatomy, Nervous System, Synapses, Synaptic Vesicles, Medicine and Health Sciences, Physiology, Electrophysiology, Neurophysiology, Cell Biology, Cellular Structures and Organelles, Vesicles, Proteins, Intracellular Receptors, Signal Transduction, Physical Sciences, Chemistry, Chemical Physics, Mass Diffusivity, Physics, Cell Signaling, Membrane Receptor Signaling, Membrane Potential, Cell Membranes, Intracellular Membranes

Topic: Neuroscience and Neuropharmacology Research (Cellular and Molecular Neuroscience, Neuroscience), according to OpenAlex

Funding: Research Council of Norway (355113, 322312, 360005); Utdannings- og forskningsdepartementet (SUURPh)

Citations: not cited yet (Europe PMC); 33 references in the paper

Abstract

The synaptic cleft between neighboring neurons is the site of neurotransmitter-mediated communication that underlies normal brain function, including learning and memory. When an action potential reaches the presynaptic terminal, released neurotransmitters cross the cleft under the combined influence of diffusion and electrical forces to activate postsynaptic receptors. Despite this, synaptic-cleft transport is commonly modeled using a pure diffusion model, neglecting electrical drift. Here, we quantify the relative contributions of diffusion and electrical terms in the Poisson–Nernst–Planck (PNP) framework and assess whether the pure diffusion approximation is adequate. We solve the full PNP system in a three-dimensional computational model of the synaptic cleft at nanometer-scale resolution, tracking five ionic species (Na+, K+, Ca2+, Cl−, Glu−) with full spatial and temporal detail. Solutions are compared directly with those of the pure diffusion (D) model. The D and PNP models produce markedly different ionic concentration fields. Analysis of ionic fluxes confirms that diffusive and electrical contributions are of comparable magnitude across all species. These discrepancies are robust across parameter variations, including the number of AMPA receptors, the amount of released glutamate, the cleft height, and the cleft diffusion coefficient, and are amplified as the number of AMPA receptors or released glutamate ions increases, when the cleft becomes narrower or when diffusion becomes more restricted. However, because of competing effects, the resulting difference in the associated AMPA current is modest. The quantitative and qualitative differences between the pure D model and the full PNP model demonstrate that neglecting electrical forces in the synaptic cleft has consequences. These discrepancies are large enough to alter the predicted dynamics and biological interpretation of synaptic transmission, establishing that accurate computation of ionic concentrations in the synaptic cleft requires the full PNP equations.

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

Repository

Its files are read in the Code ↔ Paper reader above.

karolihj/PNP-synapse-FDM-2026

License: GPL-3.0

State: the link answers, verified on 28 September 2026

Evidence: files inventoried

Commit: 3e4a4b2280905916310d6560541847f110e13b5c, 12 May 2026

Languages: MATLAB (23)

Size: 25 files, 23 scripts

Software Heritage: not archived

Found in: “Data Availability”

Holds: README, license file

Not found: CITATION.cff, environment file, tests, continuous integration, documentation

Availability: 1 check, the latest on 28 September 2026: the link answers

28 September 2026: the link answers

25 files

AMPA_receptor_kinetics.m, MATLAB, 47 lines
diffusion_coefficient.m, MATLAB, 13 lines
in_cell.m, MATLAB, 19 lines
in_cleft.m, MATLAB, 7 lines
in_membrane.m, MATLAB, 26 lines
in_vesicle.m, MATLAB, 9 lines
in_vesicle_opening.m, MATLAB, 8 lines
initial_conditions.m, MATLAB, 10 lines
ion_channel_flux.m, MATLAB, 32 lines
model_parameters.m, MATLAB, 75 lines
permittivity.m, MATLAB, 8 lines
run_simulation_D.m, MATLAB, 36 lines
run_simulation_PNP.m, MATLAB, 36 lines
set_up_channels.m, MATLAB, 251 lines
set_up_dx.m, MATLAB, 90 lines
set_up_dy.m, MATLAB, 161 lines
set_up_dz.m, MATLAB, 87 lines
set_up_matrix_D.m, MATLAB, 133 lines
set_up_matrix_PNP.m, MATLAB, 250 lines
set_up_mesh.m, MATLAB, 124 lines
solve_system_D.m, MATLAB, 124 lines
solve_system_PNP.m, MATLAB, 134 lines
x_y_z_from_idx.m, MATLAB, 18 lines
LICENSE, License, 674 lines
README.txt, Text, 5 lines

At the source: github.com/karolihj/PNP-synapse-FDM-2026

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

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

What the map holds:

1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
23 scripts, each with its path and the digest of its content;
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Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

No dataset and no data link were found in the paper.

Data Availability

There are no primary data in the paper. The code used in our simulations are publicly available at Github (https://github.com/karolihj/PNP-synapse-FDM-2026).

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

Versions

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Version 1, 28 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 2 authors, 11 MeSH terms, 2 funders, 29 references.

Cite

This paper

Jæger, K. H., & Tveito, A. (2026). Accurate computation of ionic concentrations in the synaptic cleft requires the full Poisson-Nernst-Planck (PNP) equations. PLoS computational biology, 22(5), e1014341. https://doi.org/10.1371/journal.pcbi.1014341

BibTeX

@article{jger2026accurate, author = {Jæger, Karoline Horgmo and Tveito, Aslak}, title = {{Accurate computation of ionic concentrations in the synaptic cleft requires the full Poisson-Nernst-Planck (PNP) equations}}, journal = {PLoS computational biology}, year = {2026}, month = may, volume = {22}, number = {5}, pages = {e1014341}, publisher = {PLOS}, issn = {1553-734X}, doi = {10.1371/journal.pcbi.1014341}, url = {https://doi.org/10.1371/journal.pcbi.1014341}, pmid = {42207852}, pmcid = {PMC13235942} }

RIS

TY - JOUR AU - Jæger, Karoline Horgmo AU - Tveito, Aslak TI - Accurate computation of ionic concentrations in the synaptic cleft requires the full Poisson-Nernst-Planck (PNP) equations T2 - PLoS computational biology J2 - PLoS Comput Biol PY - 2026 DA - 2026/05/28 VL - 22 IS - 5 SP - e1014341 SN - 1553-734X PB - PLOS DO - 10.1371/journal.pcbi.1014341 UR - https://doi.org/10.1371/journal.pcbi.1014341 LA - en ER -

CSL-JSON

{ "id": "10.1371/journal.pcbi.1014341", "type": "article-journal", "title": "Accurate computation of ionic concentrations in the synaptic cleft requires the full Poisson-Nernst-Planck (PNP) equations", "container-title": "PLoS computational biology", "author": [ { "family": "Jæger", "given": "Karoline Horgmo" }, { "family": "Tveito", "given": "Aslak" } ], "container-title-short": "PLoS Comput Biol", "volume": "22", "issue": "5", "page": "e1014341", "DOI": "10.1371/journal.pcbi.1014341", "PMID": "42207852", "PMCID": "PMC13235942", "ISSN": "1553-734X", "publisher": "PLOS", "URL": "https://doi.org/10.1371/journal.pcbi.1014341", "language": "en", "issued": { "date-parts": [ [ 2026, 5, 28 ] ] } }

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