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High reelin expression may explain why a subgroup of entorhinal cortex neurons functions as an initial nucleation site of Alzheimer's disease.

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The authors' code

Jupyter notebook · 227 lines · 8.9 KB · CC-BY-4.0

  1. # %% [markdown]
  2. # This notebook generates Figure 5 from the manuscript `Asgeir Kobro-Flatmoen, Jagir R. Hussan, Peter J. Hunter, Stig W. Omholt, "High reelin expression can explain why the entorhinal cortex is a cradle for Alzheimer’s disease", [doi: https://doi.org/10.1101/2025.06.04.655278]`. Readers should consult the paper for details regarding the model equations and parameter values.
  4. # %% [markdown]
  5. # #### Sobol sensitivity analysis requires significant computational resources. This may require a large cluster of processors to complete within reasonable time.
  6. # #### The sensitivityanalysis folder provides the code base necessary to perform these simulations in parallel and save the results to disk. This notebook loads the data and generates the require visualisations.
  8. # %%
  9. from SALib.analyze import sobol
  10. import numpy as np
  11. import matplotlib
  12. import matplotlib.pyplot as plt
  14. # %% [markdown]
  15. # # Figure 5
  16. # ### Median endpoint A $\beta reelin_L$ log soma concentration for multiparameter variations centered around the nominal parameter sets for the Re $^+$ alECII and LR neurons.
  18. # %% [markdown]
  19. # ### Transformation parameters
  21. # %%
  22. ## Volume of abeta+reelin complex
  23. rad_abetaR = 0.005 # micrometer assuming that abeta is tiny in comparison
  24. volume_abetaR = (4 / 3) * 3.14 * rad_abetaR**3 # cubic micrometers
  26. soma_diameter_LR = 21 # micrometer
  27. volume_soma_LR = (4 / 3) * 3.14 * (soma_diameter_LR / 2) ** 3
  28. volume_soma_litre_LR = volume_soma_LR * 10**-15
  29. nM_trans_LR = 10**9 *(1 / (6.022 * 10**23)) / volume_soma_litre_LR
  31. soma_diameter_Re = 21 # 27 40 #micrometer
  32. volume_soma_Re = (4 / 3) * 3.14 * (soma_diameter_Re / 2) ** 3
  33. nM_trans_Re = 10**9 *(1 / (6.022 * 10**23)) / (volume_soma_Re * 10**-15)
  34. phi = 0.2145 # 1/3 of lepler packing 0.65
  36. # %%
  37. lrnominalsolvefile = 'LR_solutions_nominal.npz'
  38. renominalsolvefile = 'Re_solutions_nominal.npz'
  40. with open(lrnominalsolvefile,'rb') as npz:
  41. ndata = np.load(npz,allow_pickle=True)
  42. des = ndata['design']
  43. sol = ndata['solutions']
  44. iex = sol.reshape((3,-1))
  45. #fmax,fmin,fmed,fstd,ostd,omed,omax,omin
  46. lrnominalnommedi = iex[1,0]*nM_trans_LR
  47. lrnominalnomminx = iex[0,0]*nM_trans_LR
  48. lrnominalnommaxx = iex[2,0]*nM_trans_LR
  50. lrnominalnommediocc = iex[1,0]*volume_abetaR/(volume_soma_LR * phi)
  51. lrnominalnomminxocc = iex[0,0]*volume_abetaR/(volume_soma_LR * phi)
  52. lrnominalnommaxxocc = iex[2,0]*volume_abetaR/(volume_soma_LR * phi)
  54. with open(renominalsolvefile,'rb') as npz:
  55. ndata = np.load(npz,allow_pickle=True)
  56. des = ndata['design']
  57. sol = ndata['solutions']
  58. iex = sol.reshape((3,-1))
  59. #fmax,fmin,fmed,fstd,ostd,omed,omax,omin
  60. renominalnommedi = iex[1,0]*nM_trans_Re
  61. renominalnomminx = iex[0,0]*nM_trans_Re
  62. renominalnommaxx = iex[2,0]*nM_trans_Re
  64. renominalnommediocc = iex[1,0]*volume_abetaR/(volume_soma_Re * phi)
  65. renominalnomminxocc = iex[0,0]*volume_abetaR/(volume_soma_Re * phi)
  66. renominalnommaxxocc = iex[2,0]*volume_abetaR/(volume_soma_Re * phi)
  68. # %%
  69. print(lrnominalnommedi,lrnominalnomminx,lrnominalnommaxx)
  70. print(renominalnommedi,renominalnomminx,renominalnommaxx)
  72. # %%
  73. display("Volume occupancy")
  74. display(f"LR Neurons {lrnominalnomminxocc*100:0.3f}, {lrnominalnommediocc*100:0.3f}, {lrnominalnommaxxocc*100:0.3f}")
  75. display(f"Re Neurons {renominalnomminxocc*100:0.3f}, {renominalnommediocc*100:0.3f}, {renominalnommaxxocc*100:0.3f}")
  77. # %% [markdown]
  78. # ### Load the solutions
  80. # %%
  81. parameternames = ["$\\alpha_{infection}$","$\\beta$","$\gamma$","$\\tau$","$\\rho$","$\delta$","$\\theta_1$","$n_1$","$T_1$"]
  84. # %% [markdown]
  85. # ### LR parameter bounds
  86. #
  87. # | Parameter | Value | Bounds/Steps |
  88. # |---------------|-------------|---------------------------|
  89. # | alpha_base | 1560.0000 | Fixed |
  90. # | alpha_infection | 44000.0000 | $\pm$ 30%, 11 steps |
  91. # | beta | 0.1000 | $\pm$ 30%, 11 steps |
  92. # | gamma | 0.0050 | 0.0005–0.05, 11 steps |
  93. # | tau | 14500.0000 | $\pm$ 30%, 11 steps |
  94. # | rho | 0.0500 | $\pm$ 30%, 11 steps |
  95. # | delta | 0.0200 | $\pm$ 30%, 11 steps |
  96. # | theta1 | 250000.0000 | $\pm$ 30%, 11 steps |
  97. # | n1 | 6.0000 | 3, 4, 5, 6 |
  98. # | T1 | 790000.0000 | $\pm$ 30%, 11 steps |
  99. # | epsilon1 | 1.0000 | Fixed |
  101. # %% [markdown]
  102. # ### RE parameter bounds
  103. #
  104. # | Parameter | Value | Bounds/Steps |
  105. # |-----------------|--------------|---------------------------|
  106. # | alpha_base | 4680.0000 | Fixed |
  107. # | alpha_infection | 109000.0000 | $\pm$ 30%, 11 steps |
  108. # | beta | 0.1000 | $\pm$ 30%, 11 steps |
  109. # | gamma | 0.0050 | 0.0005–0.05, 11 steps |
  110. # | tau | 79000.0000 | $\pm$ 30%, 11 steps |
  111. # | rho | 0.0500 | $\pm$ 30%, 11 steps |
  112. # | delta | 0.0200 | $\pm$ 30%, 11 steps |
  113. # | theta1 | 250000.0000 | $\pm$ 30%, 11 steps |
  114. # | n1 | 6.0000 | 3, 4, 5, 6 |
  115. # | T1 | 790000.0000 | $\pm$ 30%, 11 steps |
  116. # | epsilon1 | 1.0000 | Fixed |
  118. # %% [markdown]
  119. # Load LR results
  121. # %%
  122. lrproblem = {
  123. 'num_vars': 9,
  124. 'names': parameternames,
  125. 'bounds': [
  126. [44000*0.7,44000*1.3],
  127. [0.1*0.7,0.1*1.3],
  128. [0.0005,0.05],
  129. [14500*0.7,14500*1.3],
  130. [0.0500*0.7,0.0500*1.3],
  131. [0.0200*0.7,0.0200*1.3],
  132. [250000*0.7,250000*1.3],
  133. [3,6],
  134. [790000*0.7,790000*1.3]
  135. ]
  136. }
  137. lrsobolfile = 'sobolLRresults.npz'
  138. with open(lrsobolfile,'rb') as ser:
  139. lrdata = np.load(ser,allow_pickle=True)
  140. lrdesigns = lrdata["results"]
  142. lrparams = lrdesigns[:,:9] #First 9 are design parameters values
  143. lrnormalisedparams = (lrparams - np.min(lrparams,axis=0))/(np.max(lrparams,axis=0)-np.min(lrparams,axis=0))
  144. lrY = lrdesigns[:,10] # mins,meds,maxs
  145. lrsY = np.argsort(lrY)
  146. lrnexpts = lrY.shape[0]
  147. LRSi = sobol.analyze(lrproblem, lrY, print_to_console=False)
  149. # %% [markdown]
  150. # Load Re $^+$ aECII neuron results
  152. # %%
  153. reproblem = {
  154. 'num_vars': 9,
  155. 'names': parameternames,
  156. 'bounds': [
  157. [109000*0.7,109000*1.3],
  158. [0.1*0.7,0.1*1.3],
  159. [0.0005,0.05],
  160. [79000*0.7,79000*1.3],
  161. [0.0500*0.7,0.0500*1.3],
  162. [0.0200*0.7,0.0200*1.3],
  163. [250000*0.7,250000*1.3],
  164. [3,6],
  165. [790000*0.7,790000*1.3]
  166. ]
  167. }
  168. resobolfile = 'sobolReresults.npz'
  169. with open(resobolfile,'rb') as ser:
  170. redata = np.load(ser,allow_pickle=True)
  171. redesigns = redata["results"]
  173. reparams = redesigns[:,:9] #First 9 are design parameters values
  174. renormalisedparams = (reparams - np.min(reparams,axis=0))/(np.max(reparams,axis=0)-np.min(reparams,axis=0))
  175. reY = redesigns[:,10] # mins,meds,maxs
  176. resY = np.argsort(reY)
  177. renexpts = reY.shape[0]
  178. RESi = sobol.analyze(reproblem, reY, print_to_console=False)
  180. # %%
  181. # Build a rectangle in axes coords
  182. left, width = .35, 0.9
  183. bottom, height = .01, 0.9
  184. right = left + width
  185. top = bottom + height
  186. import matplotlib.ticker as ticker
  187. formatter = ticker.ScalarFormatter(useMathText=True)
  188. formatter.set_powerlimits((4, 4)) # Forces 10^4 scaling
  189. fig = plt.figure(1, figsize=(7,24))
  190. cmap = plt.get_cmap('jet', renexpts)
  191. recolors = [matplotlib.colors.to_hex(cmap(i)) for i in range(renexpts)]
  192. axre = fig.add_subplot(713)
  193. axre.scatter(list(range(lrnexpts)), reY[resY]*nM_trans_Re, marker='*', s=10, color=recolors,alpha=0.4)
  194. axre.axhline(y=renominalnommedi,lw=2,color='g')
  195. axre.axhline(y=renominalnommaxx,lw=2,linestyle='--',color='r')
  196. axre.axhline(y=renominalnomminx,lw=2,linestyle='--',color='y')
  197. axre.set_xticks([])
  198. axre.tick_params(axis='y', labelsize=14)
  199. axre.yaxis.set_major_formatter(formatter)
  200. axre.set_ylabel(r"$A\beta_{Reelin,L}$ (nM)", fontsize=14)
  201. #axre.set_xlabel("Parameter sets")
  202. #axre.legend(['Re$^{+}$alECLII neuron'],loc="lower right")
  203. axre.text(left, top, 'Re$^{+}$alECLII neuron',
  204. horizontalalignment='right',
  205. verticalalignment='top', fontsize=14,
  206. transform=axre.transAxes)
  208. cmap = plt.get_cmap('jet', lrnexpts)
  209. colors = [matplotlib.colors.to_hex(cmap(i)) for i in range(lrnexpts)]
  210. axlr = fig.add_subplot(714)
  211. axlr.scatter(list(range(lrnexpts)), lrY[lrsY]*nM_trans_LR, marker='*', s=10, color=colors,alpha=0.4)
  212. axlr.axhline(y=lrnominalnommedi,lw=2,color='g')
  213. axlr.axhline(y=lrnominalnommaxx,lw=2,linestyle='--',color='r')
  214. axlr.axhline(y=lrnominalnomminx,lw=2,linestyle='--',color='y')
  215. axlr.set_xticks([])
  216. axlr.tick_params(axis='y', labelsize=14)
  217. axlr.yaxis.set_major_formatter(formatter)
  218. axlr.set_ylabel(r"$A\beta_{Reelin,L}$ (nM)", fontsize=14)
  219. axlr.set_xlabel("Parameter sets", fontsize=14)
  220. axlr.text(left-0.15, top, 'LR neuron',
  221. horizontalalignment='right',
  222. verticalalignment='top', fontsize=14,
  223. transform=axlr.transAxes)
  225. save_dir = "images/"
  226. fig.savefig(save_dir + "Figure_5.pdf", dpi=600, bbox_inches="tight")

AD_Model_Figure5.ipynb, under CC-BY-4.0 · at the source

Overview

Authors: Asgeir Kobro-Flatmoen1,2, Jagir R. Hussan3, Peter J. Hunter3, Stig W. Omholt1,2
ORCID iDs: Asgeir Kobro-Flatmoen
  1. Kavli Institute for Systems Neuroscience, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
  2. Norwegian Health Association Centre for Dementia Research, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
  3. Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand
Institutions: Norwegian University of Science and Technology (Norway); University of Auckland (New Zealand)
Journal: PLoS computational biology, volume 22, issue 8, article e1014532
Dates: received 25 February 2026; accepted 3 July 2026; published online 25 August 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1371/journal.pcbi.1014532 · PMID 42640981 · PMCID PMC13506104 · OpenAlex W7204187799
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: human (organism), Alzheimer's / dementia (population)
MeSH: Alzheimer Disease*, Cell Adhesion Molecules, Neuronal*, Entorhinal Cortex*, Extracellular Matrix Proteins*, Nerve Tissue Proteins*, Neurons*, Serine Endopeptidases*, Amyloid beta-Peptides, Animals, Humans, Peptide Fragments, Reelin Protein, tau Proteins (* major topic)
Journal subjects: Biology and Life Sciences, Cell Biology, Cellular Types, Animal Cells, Neurons, Neuroscience, Cellular Neuroscience, Immunology, Immune Response, Inflammation, Medicine and Health Sciences, Clinical Medicine, Signs and Symptoms, Cellular Structures and Organelles, Lysosomes, Mental Health and Psychiatry, Dementia, Alzheimer's Disease, Neurology, Medical Conditions, Neurodegenerative Diseases, Physical Sciences, Chemistry, Stoichiometry, Biochemistry, Proteins, Post-Translational Modification, Phosphorylation, Cell Processes, Cell Death, Neuronal Death, Anatomy, Brain, Cerebral Cortex, Entorhinal Cortex
Topic: Alzheimer's disease research and treatments (Physiology, Medicine), according to OpenAlex
Funding: Stiftelsen Kristian Gerhard Jebsen (SKGJ-MED-022); Department of Neurology and Clinical Neurophysiology, University Hospital of Trondheim; Helse Midt-Norge (P-103253-02-01-04); Kavli Foundation; Nasjonalforeningen for Folkehelsen; Norges Forskningsråd (332640)
Citations: not cited yet (Europe PMC); 84 references in the paper
Research resources: RRID:AB_2179313

Abstract

The entorhinal cortex (EC) plays a crucial role in memory functions. Long before the clinical symptoms of Alzheimer’s disease (AD) emerge, it has already undergone significant degeneration, making it a primary site for the onset of the disease. The reasons for this remain elusive. Layer II (LII) neurons of the anterolateral EC are especially prone to display a very early increase in intracellular amounts of amyloid-β peptide (Aβ) and hyperphosphorylated tau protein (p-tau). The expression of the large glycoprotein reelin is extraordinarily high in ECLII neurons compared to most other cortical neurons and proximity ligation assay data and other immunohistochemical data strongly support the notion that reelin binds to Aβ in these neurons. Here, based on the premise that reelin may function as a sink for intracellular Aβ, we show by computational modeling that, in a senescent physiology predisposing to frequent inflammation-driven Aβ42 production bursts over a decades-long period, the intracellular amount of Aβ42-reelin complexes can accumulate to extraordinarily high levels in anterolaterally positioned LII neurons compared to the vast majority of cortical neurons. This is consistent with experimental data showing that intracellular accumulations of Aβ42 positive material ranged from 20 to 80% of total soma volume in EC neurons from patients with idiopathic AD. Based on known tau protein biology, we also show that this extreme intracellular aggregation that overloads the lysosomal degradation machinery, manifesting chronic homeostatic dysregulation, can lead to the production of p-tau fragments prone to aggregation. Together, our findings may contribute to the resolution of why the EC is so strongly associated with the very early etiology of AD.

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

Repository

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Zenodo 15680979

License: CC-BY-4.0
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Languages: Jupyter (7)
Size: 14 files, 7 scripts
Software Heritage: not checked
Found in: “Data Availability”
Holds: README, environment (requirements.txt), 7 notebooks
Not found: license file, CITATION.cff, tests, continuous integration, documentation
Tools: NumPy (18 files), SciPy (11 files), Matplotlib (8 files), Numba (5 files), pandas (3 files)
Availability: 1 check, the latest on 27 September 2026: the link answers (HTTP 200)
  • 27 September 2026: the link answers (HTTP 200)
19 files
At the source: zenodo.org/records/15680979

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

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Data Availability

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

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Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 4 authors, 13 MeSH terms, 6 funders, 82 references, 1 RRID.

Cite

This paper

Kobro-Flatmoen, A., Hussan, J. R., Hunter, P. J., & Omholt, S. W. (2026). High reelin expression may explain why a subgroup of entorhinal cortex neurons functions as an initial nucleation site of Alzheimer's disease. PLoS computational biology, 22(8), e1014532. https://doi.org/10.1371/journal.pcbi.1014532

BibTeX

@article{kobroflatmoen2026high,
author = {Kobro-Flatmoen, Asgeir and Hussan, Jagir R. and Hunter, Peter J. and Omholt, Stig W.},
title = {{High reelin expression may explain why a subgroup of entorhinal cortex neurons functions as an initial nucleation site of Alzheimer's disease}},
journal = {PLoS computational biology},
year = {2026},
month = aug,
volume = {22},
number = {8},
pages = {e1014532},
publisher = {PLOS},
issn = {1553-734X},
doi = {10.1371/journal.pcbi.1014532},
url = {https://doi.org/10.1371/journal.pcbi.1014532},
pmid = {42640981},
pmcid = {PMC13506104}
}

RIS

TY - JOUR
AU - Kobro-Flatmoen, Asgeir
AU - Hussan, Jagir R.
AU - Hunter, Peter J.
AU - Omholt, Stig W.
TI - High reelin expression may explain why a subgroup of entorhinal cortex neurons functions as an initial nucleation site of Alzheimer's disease
T2 - PLoS computational biology
J2 - PLoS Comput Biol
PY - 2026
DA - 2026/08/25
VL - 22
IS - 8
SP - e1014532
SN - 1553-734X
PB - PLOS
DO - 10.1371/journal.pcbi.1014532
UR - https://doi.org/10.1371/journal.pcbi.1014532
LA - en
ER -

CSL-JSON

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"author": [
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{
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"container-title-short": "PLoS Comput Biol",
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"DOI": "10.1371/journal.pcbi.1014532",
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"PMCID": "PMC13506104",
"ISSN": "1553-734X",
"publisher": "PLOS",
"URL": "https://doi.org/10.1371/journal.pcbi.1014532",
"language": "en",
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2026,
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}

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