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Cellular and subcellular heterogeneity of astrocytic Na⁺ homeostasis tuning astrocytes into functionally distinct subgroups in the mouse brain.

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The authors' code

Python · 271 lines · 13 KB · MIT

  1. import numpy as np
  2. import time
  3. from utils import *
  4. from numba import njit
  5. from numba.typed import Dict
  6. from numba.core import types
  7. from pathlib import Path
  8. class Astrocyte:
  9. def __init__(self, dt, N, Ra, Cm1, astrocyte_data, stim_start_nt, stim_end_nt, glut_stim, pot_stim, stim_comp_glut, stim_comp_pot, stim_dur=0.0, n_stim=0, n_stimulated=0):
  10. self.dt = dt
  11. self.N = N
  12. self.Ra = Ra # intracellular resistivity
  13. self.Cm1 = Cm1
  14. self.stim_start_nt = stim_start_nt
  15. self.stim_end_nt = stim_end_nt
  16. self.stim_dur = stim_dur
  17. self.stim_comp_glut = stim_comp_glut
  18. self.stim_comp_pot = stim_comp_pot
  19. self.glut_stim = glut_stim
  20. self.pot_stim = pot_stim
  21. self.n_stim = n_stim
  22. self.n_stimulated = n_stimulated
  23. # Load astrocyte data
  24. self.astrocyte = np.loadtxt(astrocyte_data)
  25. self.parents = self.astrocyte[:, 6].astype(int)
  26. self.parents[0] = 0 # Root of tree
  27. self.xaxis, self.yaxis, self.zaxis, self.radius, self.identifier = self.astrocyte[:, 2], self.astrocyte[:, 3], self.astrocyte[:, 4], self.astrocyte[:, 5], self.astrocyte[:, 1]
  28. self.ids = self.astrocyte[:, 0].astype(int)
  29. # Initialize variables
  30. self.init_variables()
  31. def init_variables(self):
  32. #self.tau1, self.tau2, self.tau3, self.tau4, self.tau5 = 30.0, 35.0, 40.0, 45.0, 50.0
  33. # Initialize geometry-related variables
  34. self.distance_from_soma = np.zeros(self.N)
  35. self.length = np.zeros(self.N)
  36. self.area = np.zeros(self.N)
  37. self.area_cross = np.zeros(self.N)
  38. self.volume = np.zeros(self.N)
  39. self.rho = np.zeros(self.N)
  40. self.Rm = np.zeros(self.N)
  41. self.Cm = np.zeros(self.N)
  42. self.g_l = np.zeros(self.N)
  43. self.DiffK = np.zeros(self.N)
  44. self.DiffNa = np.zeros(self.N)
  45. self.DiffCa = np.zeros(self.N)
  46. self.gamma = np.zeros(self.N)
  47. self.rho2 = np.zeros(self.N)
  48. # Calculate geometric properties and initialize electrical parameters
  49. for i in range(self.N):
  50. self.calculate_geo_res(i)
  51. self.distance_from_soma[:] = 0.0
  52. for i in range(self.N):
  53. j = self.parents[i] # parent ID
  54. if j > 0: # parent row index
  55. self.distance_from_soma[i] = self.distance_from_soma[j-1] + self.length[i]
  56. else:
  57. # roots / soma samples start at 0
  58. self.distance_from_soma[i] = 0.0
  59. for i in range(self.N):
  60. self.calculate_gamma(i)
  61. self.branch_to_comps , self.branch_max_dict = self.compute_branch_groups()
  62. self.nb_branch_to_comps, self.nb_branch_max = self.convert_to_numba_dict()
  63. def compute_branch_groups(self):
  64. # """
  65. # Returns:
  66. # - branch_to_indices: {"branch_1": [row_idx0, row_idx1, ...], ...}
  67. # - branch_to_ids : {"branch_1": [id0, id1, ...], ...} (SWC IDs)
  68. # - branch_heads_id : {"branch_1": head_id, ...} (SWC ID of head)
  69. # - branch_max_dict : {"branch_1": max_distance, ...}
  70. # - branch_label : np.ndarray (N,) with the head row-index label for each node (-1 for soma/root)
  71. # Notes:
  72. # * A "primary branch" is the subtree whose root is any node whose parent <= 0.
  73. # * Uses parent-row = parent_id - 1 (j-1).
  74. # """
  75. # 1) Label each node by its primary branch head (child of soma)
  76. labels = np.full(self.N, -1, dtype=int)
  77. for i in range(self.N):
  78. if self.parents[i] <= 0:
  79. continue # soma/root nodes are not inside any branch
  80. k = i
  81. while self.parents[k] > 0 and self.parents[self.parents[k] - 1] > 0:
  82. k = self.parents[k] - 1
  83. labels[i] = k # k is the row index of the branch head
  84. # 2) Keep heads in order of first appearance (stable branch_1, branch_2, ...)
  85. heads, seen = [], set()
  86. for k in labels:
  87. if k >= 0 and k not in seen:
  88. heads.append(k); seen.add(k)
  89. # 3) Build groups and compute max per branch (include the head itself)
  90. branch_to_indices = {}
  91. branch_to_comps = {}
  92. branch_heads_id = {}
  93. branch_max_dict = {}
  94. for idx, h in enumerate(heads, start=1):
  95. name = f"branch_{idx}"
  96. mask = (labels == h) | (np.arange(self.N) == h) # include head
  97. idxs = np.nonzero(mask)[0] # all row indices in this branch
  98. branch_to_indices[name] = idxs.tolist()
  99. branch_to_comps [name] = [int(self.ids[j])-1 for j in idxs]
  100. branch_heads_id[name] = int(self.ids[h])
  101. branch_max_dict[name] = float(np.max(self.distance_from_soma[idxs]))
  102. return branch_to_comps, branch_max_dict
  103. # Convert to Numba typed dictionary
  104. def convert_to_numba_dict(self):
  105. # Create typed dicts
  106. nb_branch_to_comps = Dict.empty(
  107. key_type=types.int64,
  108. value_type=types.int64[:]
  109. )
  110. nb_branch_max = Dict.empty(
  111. key_type=types.int64,
  112. value_type=types.float64
  113. )
  114. # Map branch names to integers and fill dicts
  115. for idx, (bname, comps) in enumerate(self.branch_to_comps.items()):
  116. nb_branch_to_comps[idx] = np.array(comps, dtype=np.int64)
  117. nb_branch_max[idx] = self.branch_max_dict[bname]
  118. return nb_branch_to_comps, nb_branch_max
  119. def calculate_geo_res(self, i):
  120. # self.distance_from_soma[i] = np.sqrt((self.xaxis[i] - self.xaxis[0])**2 + (self.yaxis[i] - self.yaxis[0])**2 + (self.zaxis[i] - self.zaxis[0])**2)
  121. # self.distance_from_soma, _, _ = self.cumulative_distance_from_soma(self.ids, self.parents, self.x, self.y, self.z)
  122. j = self.parents[i]
  123. if i == 0:
  124. self.length[i] = self.radius[i]
  125. self.area[i] = 4.0 * np.pi * self.radius[i]**2
  126. self.volume[i] = 4.0/3.0 * np.pi * self.radius[i]**3
  127. else:
  128. self.length[i] = np.sqrt((self.xaxis[i] - self.xaxis[j-1])**2 + (self.yaxis[i] - self.yaxis[j-1])**2 + (self.zaxis[i] - self.zaxis[j-1])**2)
  129. self.area[i] = 2.0 * np.pi * self.radius[i] * self.length[i]
  130. self.volume[i] = np.pi * self.radius[i]**2 * self.length[i]
  131. self.area_cross[i] = np.pi * self.radius[i]**2
  132. self.rho[i] = self.Ra * 1.0e4 * self.length[i] / (2.0 * np.pi * self.radius[i]**2) #ohms
  133. if self.identifier[i] not in [1, 2]:
  134. self.Rm[i] = 50000.0
  135. self.Cm[i] = self.Cm1 * 2.0
  136. else:
  137. self.Rm[i] = 50000.0
  138. self.Cm[i] = self.Cm1
  139. self.g_l[i] = 1000.0 / self.Rm[i]
  140. def calculate_gamma(self, i):
  141. for i in range(self.N):
  142. j = self.parents[i]
  143. if i == 0:
  144. if self.N == 1:
  145. self.rho2[i] = 0
  146. self.gamma[i] = 0
  147. else:
  148. self.rho2[i] = 1.0 / (self.rho[i] + self.rho[i+1]) # 1/ohms i+1 last
  149. self.gamma[i] = 1.0e11 * self.rho2[i] / (2.0 * np.pi * self.radius[i+1] * self.length[i+1])* 1.0e-5 #mS/cm^2 i+1 both
  150. else:
  151. self.rho2[i] = 1.0 / (self.rho[i] + self.rho[j-1])
  152. self.gamma[i] = 1.0e11 * self.rho2[i] / (2.0 * np.pi * self.radius[i] * self.length[i]) * 1.0e-5 #mS/cm^2
  153. self.DiffK[i] = 250.0 * self.area_cross[i]/ (self.length[i] * self.volume[i]) # /s. 250 is the diffusion coefficent in um^2/s
  154. self.DiffNa[i] = 600.0 * self.area_cross[i]/ (self.length[i] * self.volume[i]) # /s #600
  155. # self.DiffCa[i] = 5.0 * self.area_cross[i]/ (self.length[i] * self.volume[i])
  156. def astrocyte_dynamics_diffusion(self, iskip, last):
  157. v, Kos, Naks, Clks, Kks, Nass, time_array, JNaKks, phis, phos, Icoups, IdiffKs, IdiffNas, IdiffCas, Caks, JNaks, JTRPVks, Iks, JNBCks, JNHEs, JNKCC1ks, JNCXs, JNaKks_alpha2beta1, JNaKks_alpha2beta2, JGluTs = update_astrocyte_dynamics(self.dt, self.identifier, self.gamma, self.parents, self.DiffNa, self.DiffK, self.DiffCa, self.g_l, self.distance_from_soma, self.radius, self.area, self.area_cross, self.volume, self.Cm, self.stim_start_nt, self.stim_end_nt, self.stim_dur, self.glut_stim, self.pot_stim, self.stim_comp_glut, self.stim_comp_pot, self.n_stim, self.n_stimulated, self.N, last, iskip, self.nb_branch_max, self.nb_branch_to_comps)
  158. return v, Kos, Naks, Clks, Kks, Nass, time_array, JNaKks, phis, phos, Icoups, IdiffKs, IdiffNas, IdiffCas, Caks, JNaks, JTRPVks, Iks, JNBCks, JNHEs, JNKCC1ks, JNCXs, JNaKks_alpha2beta1, JNaKks_alpha2beta2, JGluTs
  159. if __name__ == "__main__":
  160. start_time = time.time()
  161. select_cell = "Astrocyte"
  162. if select_cell == "Astrocyte":
  163. astrocyte_data_file = Path("NMO_282188.txt") # edit path. SHould be good as long as the file is in the same dir as this script
  164. if not astrocyte_data_file.is_file():
  165. raise FileNotFoundError(
  166. f"[ERROR] File not found: {astrocyte_data_file.resolve()}\n"
  167. "Please make sure a valid astrocytic morphology .txt file path is provided."
  168. )
  169. else:
  170. df = np.loadtxt(astrocyte_data_file)
  171. xaxis, yaxis, zaxis, parents, identifier = df[:, 2], df[:, 3], df[:, 4] , df[:,6].astype(int), df[:, 1]
  172. parents[0] = 0
  173. ids = df[:, 0].astype(int)
  174. # Uncomment for parent-child visualization purpose
  175. # # Build segments (parent -> child, then None to break)
  176. # id2idx = {nid: i for i, nid in enumerate(ids)}
  177. # Xs, Ys, Zs = [], [], []
  178. # for i, pid in enumerate(parents):
  179. # if pid > 0 and pid in id2idx:
  180. # p = id2idx[pid]
  181. # Xs += [xaxis[p], xaxis[i], None]
  182. # Ys += [yaxis[p], yaxis[i], None]
  183. # Zs += [zaxis[p], zaxis[i], None]
  184. data_size = df.shape[0]
  185. N = 3 # number of compartment to simulate. 1 if modeling a single cell with whole cell attributes else "data_size" for all compartments
  186. N_1 = 0
  187. N_2 = 3
  188. # save mutiple csv's for distance and branches
  189. astrocyte_init = Astrocyte(dt=0.00000010, N=N, Ra=400.0, Cm1=1.0, astrocyte_data=astrocyte_data_file, stim_start_nt=None, stim_end_nt=None, glut_stim=None, pot_stim=None, stim_comp_glut=None, stim_comp_pot=None)
  190. df_dist_soma = pd.DataFrame({
  191. 'Compartment_Index': range(len(astrocyte_init.distance_from_soma)),
  192. 'Distance_from_Soma_um': astrocyte_init.distance_from_soma
  193. })
  194. df_dist_soma.to_csv("distance_from_soma.csv", index=False)
  195. df_branch_to_comps = pd.DataFrame(list(astrocyte_init.branch_to_comps.items()), columns=['branch', 'compartments'])
  196. df_branch_to_comps.to_csv("branch_to_comps.csv", index=False)
  197. df_branch_max_dict = pd.DataFrame.from_dict(astrocyte_init.branch_max_dict, orient='index', columns=['max_value'])
  198. df_branch_max_dict.to_csv("branch_to_max_distance.csv")
  199. ################################################ Adjust for stimulation timing modifications ##################################################################
  200. stim_start_nt = 220000000 #220000000 #22nd second 1000000000
  201. stim_end_nt = 230000000 #230000000 #23rd second
  202. stim_type = "Potassium"
  203. if stim_type == "Potassium":
  204. pot_stim_freq = "Single"
  205. if pot_stim_freq == "Single":
  206. pot_stim_comps = {}
  207. pot_stims = {}
  208. pot_stim_comps["stim_comp_0"] = 0
  209. pot_stims["pot_stim_0"] = 7000
  210. pot_stim_comps_array = np.array(list(pot_stim_comps.values()), dtype=np.int64)
  211. pot_stims_array = np.array(list(pot_stims.values()), dtype=np.float64)
  212. astrocyte = Astrocyte(dt=0.00000010, N=N, Ra=400.0, Cm1=1.0, astrocyte_data=astrocyte_data_file, stim_start_nt=stim_start_nt, stim_end_nt=stim_end_nt, glut_stim=None, pot_stim=pot_stims_array, stim_comp_glut=None, stim_comp_pot=pot_stim_comps_array)
  213. iskip = 1000 #for testing/identifying only the base and the peak if needed, use 1000; else 16000
  214. last = 300000000 # for testing/identifying only the base and the peak if needed, use 300000000; else 10000000000 for 1000s
  215. vs, Kos, Naks, Clks, Kks, Nass, time_array, JNaKks, phis, phos, Icoups, IdiffKs, IdiffNas, IdiffCas, Caks, JNaks, JTRPVks, Iks, JNBCks, JNHEs, JNKCC1ks, JNCXs, JNaKks_alpha2beta1, JNaKks_alpha2beta2, JGluTs = astrocyte.astrocyte_dynamics_diffusion(iskip, last)
  216. comb_df = concat_ast_param(vs, Naks, Kos, Kks, Caks, phos, phis, IdiffNas, JNaks, JNaKks, Iks, time_array, JNBCks, JNHEs, JNKCC1ks, JNCXs, JNaKks_alpha2beta1, JNaKks_alpha2beta2, JGluTs, N_1, N_2)
  217. output_path = Path(__file__).with_name("comb_astro_data.csv")
  218. comb_df.to_csv(output_path, index=False)
  219. end_time = time.time()
  220. elapsed_time = end_time - start_time
  221. print(f"Simulation Completed! Total time elapsed: {elapsed_time} seconds")

ast_modeling.py at commit f315644, under MIT · at the source

Overview

  1. Institute of Neurobiology, Faculty of Mathematics and Natural Sciences, Heinrich Heine University Düsseldorf,Düsseldorf, Germany
  2. Department of Physics, University of South Florida,Tampa, FL USA
  3. Institute of Cellular Neurosciences I, Medical Faculty, University of Bonn,Bonn, Germany
  4. Department of Neurosurgery, University Hospital Erlangen, Friedrich-Alexander-Universität,Erlangen, Germany
  5. German Center for Neurodegenerative Diseases,Bonn, Germany
Journal: Nature communications, volume 17, issue 1, article 4515
Dates: received 8 August 2025; accepted 4 May 2026; published online 20 May 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1038/s41467-026-73435-z · PMID 42161940 · PMCID PMC13190688 · OpenAlex W7161781727
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: mouse (organism), cellular / molecular (subfield)
Methods: Spectral & time-frequency, Statistics, fMRI & imaging, Physiology & signal measures
Keywords: Astrocyte, Neurophysiology
MeSH: Astrocytes*, Brain*, Homeostasis*, Sodium*, Animals, Male, Mice, Mice, Inbred C57BL, Potassium, Sodium-Potassium-Exchanging ATPase (* major topic)
Topic: Neuroscience and Neuropharmacology Research (Cellular and Molecular Neuroscience, Neuroscience), according to OpenAlex
Funding: Deutsche Forschungsgemeinschaft (DFG) (Project #461542557, RO 2327/13-2,14-2); Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) (Project SynGluCross); National Institutes of Health (R01R01NS130916, R21AG087910); China Scholarship Council (202306370039)
Citations: cited by 1 paper (Europe PMC); 73 references in the paper
Research resources: We modeled a reconstructed astrocyte35 RRID:SCR_002145

Abstract

Astrocytes maintain extracellular ion and transmitter homeostasis, with the Na⁺ inward gradient playing a crucial role. Earlier studies suggested a rather low, uniform Na⁺ distribution in astrocytes, consistent with the view that these basic homeostatic properties are well-protected. Here, we employed multi-photon fluorescence lifetime imaging to quantitatively determine astrocytic [Na+] in mouse brain tissue slices and in vivo. Our data reveals a significant subcellular and cellular heterogeneity in astrocytic [Na+], accompanied by differences in the capacity for Na+/K+-ATPase (NKA)-mediated uptake of extracellular K+. RNAscope and immunohistochemistry indicate differential spatial expression patterns of NKA ß1 and ß2 subunits in astrocytes. Biophysical modeling of differential NKA expression together with varying strength of Na+ influx replicate the experimentally observed heterogeneity in astrocytic [Na+]. Altogether, our results suggest the existence of functionally distinct astrocytes and astrocyte subdomains in which Na+ homeostasis is locally adapted to the specific requirements of surrounding neural networks.

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

Repositories

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

Zenodo 19487413

License: MIT
State: the link answers, verified on 28 September 2026
Evidence: files inventoried
Size: 1 file
Software Heritage: not checked
Found in: “Code availability”
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Availability: 1 check, the latest on 28 September 2026: the link answers (HTTP 200)
  • 28 September 2026: the link answers (HTTP 200)
At the source:

banalok/modeling

License: MIT
State: the link answers, verified on 28 September 2026
Evidence: files inventoried
Commit: f315644b6ccc320d7d655f8b21e1136a84ab6f54, 17 February 2026
Languages: Python (3)
Size: 9 files, 3 scripts
Software Heritage: not archived
Found in: the Zenodo archive record
Holds: README, license file, environment (requirements.txt)
Not found: CITATION.cff, tests, continuous integration, documentation
Tools: NumPy (3 files), Numba (2 files), pandas (2 files), Matplotlib (1 file), Plotly (1 file), SciPy (1 file), seaborn (1 file)
Availability: 1 check, the latest on 28 September 2026: the link answers
  • 28 September 2026: the link answers
5 files

Code availability

The code used to compute the results and statistics, as well as generate visualizations of biophysical simulations, is deposited in a GitHub public repository at 10.5281/zenodo.19487413.

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

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  • neither the text of the paper nor the code itself.

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

The source data generated in this study are provided in the Source Data file. Further data are available from the lead contact upon request. Source data are provided in this paper.

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, 13 authors, 2 keywords, 10 MeSH terms, 4 funders, 72 references, 1 RRID.

Cite

This paper

Meyer, J., Bornemann, V., Bhattarai, A., Eitelmann, S., Unichenko, P., Durry, S., Kafitz, K. W., Chalmers, N., Fan, J., Beckervordersandforth, R., Henneberger, C., Ullah, G., & Rose, C. R. (2026). Cellular and subcellular heterogeneity of astrocytic Na⁺ homeostasis tuning astrocytes into functionally distinct subgroups in the mouse brain. Nature communications, 17(1), 4515. https://doi.org/10.1038/s41467-026-73435-z

BibTeX

@article{meyer2026cellular,
author = {Meyer, Jan and Bornemann, Viola and Bhattarai, Alok and Eitelmann, Sara and Unichenko, Petr and Durry, Simone and Kafitz, Karl W. and Chalmers, Nicholas and Fan, Jianfeng and Beckervordersandforth, Ruth and Henneberger, Christian and Ullah, Ghanim and Rose, Christine R.},
title = {{Cellular and subcellular heterogeneity of astrocytic Na⁺ homeostasis tuning astrocytes into functionally distinct subgroups in the mouse brain}},
journal = {Nature communications},
year = {2026},
month = may,
volume = {17},
number = {1},
pages = {4515},
publisher = {Nature Publishing Group},
issn = {2041-1723},
doi = {10.1038/s41467-026-73435-z},
url = {https://doi.org/10.1038/s41467-026-73435-z},
pmid = {42161940},
pmcid = {PMC13190688}
}

RIS

TY - JOUR
AU - Meyer, Jan
AU - Bornemann, Viola
AU - Bhattarai, Alok
AU - Eitelmann, Sara
AU - Unichenko, Petr
AU - Durry, Simone
AU - Kafitz, Karl W.
AU - Chalmers, Nicholas
AU - Fan, Jianfeng
AU - Beckervordersandforth, Ruth
AU - Henneberger, Christian
AU - Ullah, Ghanim
AU - Rose, Christine R.
TI - Cellular and subcellular heterogeneity of astrocytic Na⁺ homeostasis tuning astrocytes into functionally distinct subgroups in the mouse brain
T2 - Nature communications
J2 - Nat Commun
PY - 2026
DA - 2026/05/20
VL - 17
IS - 1
SP - 4515
SN - 2041-1723
PB - Nature Publishing Group
DO - 10.1038/s41467-026-73435-z
UR - https://doi.org/10.1038/s41467-026-73435-z
LA - en
ER -

CSL-JSON

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"PMCID": "PMC13190688",
"ISSN": "2041-1723",
"publisher": "Nature Publishing Group",
"URL": "https://doi.org/10.1038/s41467-026-73435-z",
"language": "en",
"issued": {
"date-parts": [
[
2026,
5,
20
]
]
}
}

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