Temporal Topology Provides an Interpretable Framework for Neuronal Morphogenesis.
The 2 matches
- [1] § Methods › Classification Process ↔ Code.zip/Code/Figure_3.ipynb, lines 186–196 · score 0.72 · DecisionTreeClassifier, LinearDiscriminantAnalysis, scikit-learn, QuadraticDiscriminant, classification, classes
- [2] § Methods › Classification Process ↔ Code.zip/Code/Figure_5.ipynb, lines 105–122 · score 0.71 · DecisionTreeClassifier, LinearDiscriminantAnalysis, scikit-learn, QuadraticDiscriminant, classification, classes
Paper
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The authors' code
Jupyter notebook · 340 lines · 14 KB · CC-BY-4.0 · 1 match
- # %% [markdown]
- # This notebook gathers the code used to produce the Figure 3 of "Quantifying neuronal differentiation using temporal topological persistence", from Ferreira Castro 2020 dataset for class I neurons and from Stuerner 2022 for class III neurons.
- # %%
- # One first imports all the necessary packages
- import os
- import tmd
- import numpy as np
- import matplotlib.pyplot as plt
- import pandas as pd
- import sys
- from tmd.view import plot
- from tmd.view import view
- from tmd.view import common
- from tmd.Population import Population
- from matplotlib import cm
- # Import methods defined in time_series_tmd.py using sys
- from time_series_tmd import vineyards, get_persistence_diagram_timelapse
- from advanced_plot import plot_persistent_homology_video, multiple_trees_plot
- from classification import *
- from NeuronAnalysis import *
- from classifier import classify_cell_in_groups
- # %% [markdown]
- # After ensuring one is working with the correct files, that have "R" entries fixed to 3 and not 1 (except for the first node), one loads class I neurons.
- # %%
- FOLDER = "Neuron_dataset/Class I/Curated"
- March = ["March1_14_1h", "March1_15_1h", "March2_15_1h", "March3_14_1h", "March3_15_1h", "March4_15_1h"]
- sa = ["sa1", "sa2", "sa3", "sa4"]
- sat = ["sat1", "sat2", "sat3", "sat4"]
- t_30 = ["t1_30", "t2_30", "t3_30", "t4_30", "t7_30"] # "t5_30" and "t6_30" are not considered as their dendrite morphologies have not differentiated yet
- tl_lothar_1b = ["tl_lothar_1b_2l", "tl_lothar_1b_3l", "tl_lothar_1b_4r", "tl_lothar_1b_5l", "tl_lothar_1b_6r"]
- tl_lothar_2B = ["tl_lothar_2B_3r", "tl_lothar_2B_4r", "tl_lothar_2B_5r"]
- tl_lothar_4A = ["tl_lothar_4A_2r", "tl_lothar_4A_3r", "tl_lothar_4A_5r", "tl_lothar_4A_6r", "tl_lothar_4A_7r"]
- tl_lothar_5A = ["tl_lothar_5A_4r", "tl_lothar_5A_5r", "tl_lothar_5A_6r"]
- tl_lothar_a = ["tl_lothar_a3", "tl_lothar_a4", "tl_lothar_a5", "tl_lothar_a6"]
- tl_nov_friday = ["tl_nov_friday1", "tl_nov_friday2", "tl_nov_friday3", "tl_nov_friday4", "tl_nov_friday5", "tl_nov_friday6"]
- tl_nov_thursday = ["tl_nov_thursday1", "tl_nov_thursday2", "tl_nov_thursday3", "tl_nov_thursday4", "tl_nov_thursday5"]
- tl_nov_tuesday = ["tl_nov_tuesday_late_1"]
- larval_series = March + sa + sat + t_30 + tl_nov_thursday + tl_nov_tuesday # tl_nov_friday is not considered as its dendrite morphologies have not differentiated yet
- embryonic_series = tl_lothar_1b + tl_lothar_2B + tl_lothar_4A + tl_lothar_5A + tl_lothar_a
- class_I_series = [larval_series, embryonic_series]
- # %% [markdown]
- # Class I neurons are formatted into a pandas data frame for each neuron type, that contains the path to data and the time of the measurement
- # %%
- larval_df = pd.DataFrame()
- embryonic_df = pd.DataFrame()
- for category in class_I_series:
- category_list = []
- for family in category:
- path_to_neuron = FOLDER +"/"+ family
- family_files = sorted(os.listdir(path_to_neuron))
- family_files = [file for file in family_files if file != ".DS_Store"] # to take out the DS store
- paths_to_neurons = []
- neurons_time = []
- neurons_indices = []
- for neuron in family_files:
- full_path = path_to_neuron + "/" + neuron
- endtime = full_path.rfind(".swc") # find the end of file name
- time = full_path.rfind("_") # find the last occurence of _ , that distinguishes the time
- index = full_path.rfind("_", 0, time) # find the one before last occurence of _ , that distinguishes the index
- paths_to_neurons.append(full_path)
- neurons_time.append(full_path[time+1:endtime])
- neurons_indices.append(full_path[index+1:time])
- category_list.append(pd.DataFrame(data={"Time": neurons_time, "Path": paths_to_neurons}, index=neurons_indices))
- if family in larval_series:
- larval_df = pd.concat(category_list, axis=1, keys=category, names=["Type", "Quantity"])
- else:
- embryonic_df = pd.concat(category_list, axis=1, keys=category, names=["Type", "Quantity"])
- class_I_df = pd.concat([larval_df, embryonic_df], axis=1, keys=["larval", "embryonic"])
- class_I_df.head()
- # %% [markdown]
- # One now loads class III neurons.
- # %%
- FOLDER = "Neuron_dataset/Class III/Curated"
- DAC161 = ["capu", "control", "singed", "spire"]
- DAC161_Paths = []
- DAMARCM_40A = ["arp", "control"]
- DAMARCM_40A_Paths = []
- DAMARCM_G13 = ["control", "ena", "twinstar"]
- DAMARCM_G13_Paths = []
- for neuron_class in DAC161:
- DAC161_Paths.append(FOLDER+"/DA_C161_"+neuron_class+"/timelapse_C161_"+neuron_class+"_data")
- for neuron_class in DAMARCM_40A:
- if neuron_class == "arp":
- DAMARCM_40A_Paths.append(FOLDER+"/DAMARCM_40A_"+neuron_class+"/timelapse_MARCM_"+neuron_class+"_data")
- else:
- DAMARCM_40A_Paths.append(FOLDER+"/DAMARCM_40A_"+neuron_class+"/timelapse_MARCM_"+neuron_class+"_40A_data")
- for neuron_class in DAMARCM_G13:
- if neuron_class == "control":
- DAMARCM_G13_Paths.append(FOLDER+"/DAMARCM_G13_"+neuron_class+"/timelapse_MARCM_"+neuron_class+"_G18_data")
- else:
- DAMARCM_G13_Paths.append(FOLDER+"/DAMARCM_G13_"+neuron_class+"/timelapse_MARCM_"+neuron_class+"_data")
- class_III_paths = DAC161_Paths + DAMARCM_40A_Paths + DAMARCM_G13_Paths
- class_III_paths_clean = [path+"_clean" for path in class_III_paths]
- class_III_folders = sorted(os.listdir(class_III_paths_clean[0])) # since all files are the same
- class_III_folders.pop(0) # to take out the DS store
- # %% [markdown]
- # A pandas dataframe is also created with class III neurons.
- # %%
- DAC161_df = pd.DataFrame()
- DAMARCM_40A_df = pd.DataFrame()
- DAMARCM_G13_df = pd.DataFrame()
- for path in class_III_paths_clean:
- category_list = []
- for folder in class_III_folders:
- path_to_neuron = path+"/"+folder
- family_files = sorted(os.listdir(path_to_neuron))
- family_files = [file for file in family_files if file != ".DS_Store"] # to take out the DS store
- paths_to_neurons = []
- neurons_indices = []
- neurons_time = []
- for neuron in family_files:
- full_path = path_to_neuron + "/" + neuron
- endtime = full_path.rfind(".swc") # find the end of file name
- time = full_path.rfind("/") # find the last occurence of / , that distinguishes the time
- paths_to_neurons.append(full_path)
- neurons_time.append(str(5*(float(full_path[time+1:endtime]) - 1))) # conversion according to the paper
- neurons_indices.append(full_path[time+1:endtime])
- category_list.append(pd.DataFrame(data={"Time": neurons_time, "Path": paths_to_neurons}, index=neurons_indices))
- class_name = path.split("/")[4].split("_")[2]
- class_keys = [class_name + "_" + f for f in class_III_folders]
- category_df = pd.concat(category_list, axis=1, keys=class_keys, names=["Type", "Quantity"])
- if "DA_C161" in path:
- DAC161_df = pd.concat([DAC161_df, category_df], axis=1)
- elif "DAMARCM_40A" in path:
- DAMARCM_40A_df = pd.concat([DAMARCM_40A_df, category_df], axis=1)
- else:
- DAMARCM_G13_df = pd.concat([DAMARCM_G13_df, category_df], axis=1)
- class_III_df = pd.concat([DAC161_df, DAMARCM_40A_df, DAMARCM_G13_df], axis=1, keys=["DA_C161", "DAMARCM_40A", "DAMARCM_G13"])
- class_III_df.head()
- # %% [markdown]
- # Both class I and class III dataframes are combined to a global dataframe.
- # %%
- total_df = pd.concat([class_I_df, class_III_df], axis=1, keys=["class_I", "class_III"])
- total_df.head()
- # %% [markdown]
- # The reconstructed dendritic trees, from example the one of a class I neuron, are represented as follows with the methods of the tmd package.
- # %%
- filename = total_df.class_I.larval.March1_14_1h["Path"][0]
- neu = tmd.io.load_neuron_from_morphio(filename)
- view.neuron(neu, title="");
- # %% [markdown]
- # The tmd package also computes the persistent image of the neuron.
- # %%
- tree = neu.neurites[0]
- ph = tmd.methods.get_persistence_diagram(tree)
- ph_apical = tmd.methods.get_ph_neuron(neu, neurite_type="apical_dendrite")
- plot.persistence_image(ph);
- # %% [markdown]
- # Classification of class I from class III neurons is performed with the methods implemented in Scikit-learn package. In what follows, one compares three classifiers: linear, quadratic and decision tree.
- # %%
- # The separation is the confusion matrix, so one plots it with the metrics package of sklearn
- from sklearn import metrics
- neurite_type = "apical_dendrite"
- # Possible modules and classifiers one can use:
- list_of_modules = ["discriminant_analysis", "discriminant_analysis", "tree"]
- list_of_classifiers = ["LinearDiscriminantAnalysis", "QuadraticDiscriminantAnalysis","DecisionTreeClassifier"]
- # %% [markdown]
- # In each classification task, labels are first assigned to neurons with the make_data_labels method, in order to define the desired classification. A model, called by leave_one_out_mixing method, is then trained on the dataset. The quality of classification is evaluated with the balanced accuracy and the confusion matrix.
- # %% [markdown]
- # ### Linear classification
- # %%
- chosen_module = list_of_modules[0]
- chosen_classifier = list_of_classifiers[0]
- n_trials = 5
- class_labels = ["class_I", "class_III"]
- printed_labels = ["class I", "class III"]
- FontSize = 16
- neuron_id = 0
- full_dataset = np.array([])
- full_labels = np.array([])
- for index,column in total_df.items():
- if index[3] == "Path": # one only keeps path and not time columns
- path_list = []
- for i, cat in enumerate(class_labels):
- if cat in index[0]: # one defines here the two categories
- neuron_id = i
- for path in column.values:
- if str(type(path)) != "<class 'float'>": # check if not nan and that all entries have less than two elements to have tables of the same size
- path_list.append(path)
- # Check that one adds well a non empty array
- if len(path_list) != 0:
- dataset, labels = make_data_labels(path_list, neurite_type, neuron_id)
- if len(full_dataset) == 0:
- full_dataset = dataset
- full_labels = labels
- else:
- full_dataset = np.concatenate((full_dataset, dataset), axis=0)
- full_labels = np.concatenate((full_labels, labels), axis=0)
- accuracy, cf_matrix = leave_one_out_mixing(chosen_module, chosen_classifier, full_dataset, full_labels)
- balanced_accuracy = np.mean(np.diag(cf_matrix)/np.sum(cf_matrix, axis = 1))
- print("The accuracy is ",accuracy)
- print("The balanced accuracy is ",balanced_accuracy)
- cm_display_lin = metrics.ConfusionMatrixDisplay(confusion_matrix = cf_matrix, display_labels=printed_labels)
- cm_display_lin.plot(cmap="Blues", values_format=".2f")
- cm_display_lin.ax_.set_title("Linear classifier")
- plt.savefig('Figures/FiguresIntermediaires/CI_C3_Lin.eps', format='eps')
- plt.show()
- # %% [markdown]
- # ### Quadratic classifier
- # %%
- chosen_module = list_of_modules[1]
- chosen_classifier = list_of_classifiers[1]
- neuron_id = 0
- full_dataset = np.array([])
- full_labels = np.array([])
- for index,column in total_df.items():
- if index[3] == "Path": # one only keeps path and not time columns
- path_list = []
- if index[0] == class_labels[0]: # one defines here the two categories
- neuron_id = 0
- elif index[0] == class_labels[1]:
- neuron_id = 1
- for path in column.values:
- if str(type(path)) != "<class 'float'>": # check if not nan and that all entries have less than two elements to have tables of the same size
- path_list.append(path)
- # Check that one adds well a non empty array
- if len(path_list) != 0:
- dataset, labels = make_data_labels(path_list, neurite_type, neuron_id)
- if len(full_dataset) == 0:
- full_dataset = dataset
- full_labels = labels
- else:
- full_dataset = np.concatenate((full_dataset, dataset), axis=0)
- full_labels = np.concatenate((full_labels, labels), axis=0)
- accuracy, cf_matrix = leave_one_out_mixing(chosen_module, chosen_classifier, full_dataset, full_labels)
- balanced_accuracy = np.mean(np.diag(cf_matrix)/np.sum(cf_matrix, axis = 1))
- print("The accuracy is ",accuracy)
- print("The balanced accuracy is ",balanced_accuracy)
- cm_display_quad = metrics.ConfusionMatrixDisplay(confusion_matrix = cf_matrix, display_labels=printed_labels)
- cm_display_quad.plot(cmap="Blues", values_format=".2f")
- cm_display_quad.ax_.set_title("Quadratic classifier")
- plt.savefig('Figures/FiguresIntermediaires/C1_C3_Quad.eps', format='eps')
- plt.show()
- # %% [markdown]
- # ### Tree classifier
- # %%
- chosen_module = list_of_modules[2]
- chosen_classifier = list_of_classifiers[2]
- neuron_id = 0
- full_dataset = np.array([])
- full_labels = np.array([])
- for index,column in total_df.items():
- if index[3] == "Path": # one only keeps path and not time columns
- path_list = []
- if index[0] == class_labels[0]: # one defines here the two categories
- neuron_id = 0
- elif index[0] == class_labels[1]:
- neuron_id = 1
- for path in column.values:
- if str(type(path)) != "<class 'float'>": # check if not nan and that all entries have less than two elements to have tables of the same size
- path_list.append(path)
- # Check that one adds well a non empty array
- if len(path_list) != 0:
- dataset, labels = make_data_labels(path_list, neurite_type, neuron_id)
- if len(full_dataset) == 0:
- full_dataset = dataset
- full_labels = labels
- else:
- full_dataset = np.concatenate((full_dataset, dataset), axis=0)
- full_labels = np.concatenate((full_labels, labels), axis=0)
- accuracy, cf_matrix = leave_one_out_mixing(chosen_module, chosen_classifier, full_dataset, full_labels)
- balanced_accuracy = np.mean(np.diag(cf_matrix)/np.sum(cf_matrix, axis = 1))
- print("The accuracy is ",accuracy)
- print("The balanced accuracy is ",balanced_accuracy)
- cm_display_tree = metrics.ConfusionMatrixDisplay(confusion_matrix = cf_matrix, display_labels=printed_labels)
- cm_display_tree.plot(cmap="Blues", values_format=".2f")
- cm_display_tree.ax_.set_title("Tree classifier")
- plt.savefig('Figures/FiguresIntermediaires/C1_C3_Tree.eps', format='eps')
- plt.show()
Figure_3.ipynb, under CC-BY-4.0 · at the source
Overview
- The Quantum Plumbing Lab, École Polytechnique Fédérale de Lausanne (EPFL),1015 Lausanne, Switzerland
- School of Life Sciences, Technical University of Munich,Freising, Germany
- Mathematical Institute, University of Oxford,Oxford, UK
Abstract
Neuronal morphogenesis arises through coordinated neurite dynamics that generate cell-type specific dendritic branching during development. Recent advances in high-throughput time-lapse imaging techniques have transformed our ability to track such growth dynamics, yielding comprehensive anatomical datasets of neuronal morphologies. However, quantifying these structural trajectories during neuronal development remains a major challenge. We introduce the Temporal Topological Morphology Descriptor (TTMD), a framework that combines persistent topology with time-resolved neuronal imaging to quantify developmental trajectories of neuronal architecture. Applying TTMD to datasets of Drosophila sensory neurons, we show that developmental stages, branching processes, and mutant-specific growth dynamics can be decoded directly from topology without manual feature selection. Topological Morphology Descriptor (TMD) accurately resolves major developmental transitions in Class I Drosophila neurons, whereas temporal topology (TTMD) is required to uncover subtle alterations in branch dynamics caused by mutations in actin regulatory pathways in Class III Drosophila neurons. TTMD further enables automated topological tracking of branch emergence and retraction across development, overcoming the limitations of labor-intensive manual annotation. These results demonstrate that temporal topology provides a unified and interpretable language for neuronal morphogenesis, enabling the automated analysis of developmental neuroanatomy, and identifying pathological alterations in neuronal structure.
Supplementary Information: The online version contains supplementary material available at 10.1007/
Reproduced under the paper's license (CC BY), from the paper cited above.
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Zenodo 20813267
Availability: 1 check, the latest on 27 September 2026: the link answers (HTTP 200)
- 27 September 2026: the link answers (HTTP 200)
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Data Availability
All data that were analysed and the respective codes are available in Zenodo 10.5281/
Reproduced under the paper's license (CC BY), from the paper cited above.
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Recorded: type, language, journal, volume, issue, pages, dates, 3 authors, 5 keywords, 8 MeSH terms, 2 funders, 48 references.
Cite
This paper
Rigaux, K., Castro, A. F., & Kanari, L. (2026). Temporal Topology Provides an Interpretable Framework for Neuronal Morphogenesis. Neuroinformatics, 24(3), 48. https://
BibTeX
@article{rigaux2026tempo
author = {Rigaux, Killian and Castro, André Ferreira and Kanari, Lida},
title = {{Temporal Topology Provides an Interpretable Framework for Neuronal Morphogenesis}},
journal = {Neuroinformatics},
year = {2026},
month = jul,
volume = {24},
number = {3},
pages = {48},
publisher = {Springer Science+Business Media},
issn = {1539-2791},
doi = {10.1007/
url = {https://
pmid = {42496825},
pmcid = {PMC13400593}
}
RIS
TY - JOUR
AU - Rigaux, Killian
AU - Castro, André Ferreira
AU - Kanari, Lida
TI - Temporal Topology Provides an Interpretable Framework for Neuronal Morphogenesis
T2 - Neuroinformatics
J2 - Neuroinformatics
PY - 2026
DA - 2026/
VL - 24
IS - 3
SP - 48
SN - 1539-2791
PB - Springer Science+Business Media
DO - 10.1007/
UR - https://
LA - en
ER -
CSL-JSON
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"id": "10.1007/
"type": "article-journal",
"title": "Temporal Topology Provides an Interpretable Framework for Neuronal Morphogenesis",
"container-title": "Neuroinformatics",
"author": [
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"family": "Rigaux",
"given": "Killian"
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"family": "Castro",
"given": "André Ferreira"
},
{
"family": "Kanari",
"given": "Lida"
}
],
"container-title-short":
"volume": "24",
"issue": "3",
"page": "48",
"DOI": "10.1007/
"PMID": "42496825",
"PMCID": "PMC13400593",
"ISSN": "1539-2791",
"publisher": "Springer Science+Business Media",
"URL": "https://
"language": "en",
"issued": {
"date-parts": [
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2026,
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]
}
}
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