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Dynamic Landscape Analysis of cell fate decisions provides predictive models of neural development from single-cell data.

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  1. [1] § Results › Mapping the complete neural progenitor landscape ↔ FittingGlobalModel/Fitting_RNAseq_SAG500.ipynb, lines 30–51 · score 0.57 · DPTrans, pMNTrans, MNDiff, progenitors, cluster, attractor

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Jupyter notebook · 327 lines · 13 KB · no license · 1 match

  1. # %% [markdown]
  2. # # Fitting the landscape model to scRNA-seq
  3. # *Condition: 500 nM SAG*
  4. #
  5. # <br>
  6. #
  7. # In this notebook, we simulate and fit the global landscape model in [1] to the scRNA-seq data from days D4 to D7 obtained from mouse embryonic stem cells generated in response to **500nM** SAG treatment.
  8. # This covers __Section B7__ (Fitting the model to the scRNA-seq data) in Appendix B (Modelling & estimation) [2] of [1].
  9. #
  10. # The fitting machinery is in `fitting_core.py`, the landscape model in `landscape_global.py`, and the plotting helpers in `fitting_plots.py`.
  11. #
  12. # [1] M. Fontaine, J.M. Delas, M. Saez, R.J. Maizels, E. Finnie, J. Briscoe, D.A. Rand, (2025). *Dynamic Landscape Analysis of Cell Fate Decisions: Predictive Models of Neural Development From Single-Cell Data*. bioR$\chi$iv doi: https://doi.org/10.1101/2025.05.28.656648.
  13. #
  14. # [2] M. Fontaine, J.M. Delas, M. Saez, R.J. Maizels, E. Finnie, J. Briscoe, D.A. Rand, (2025). *Appendix B: Modelling & estimation*. figshare doi: https://doi.org/10.6084/m9.figshare.31342816.
  15. #
  16. # ---
  17. # <sub>Author: Marine Fontaine (Warwick)</sub>
  19. # %% [markdown]
  20. # ### **1.** Load packages
  22. # %%
  23. import os
  24. import sys
  25. import tempfile
  26. import pandas as pd
  27. import numpy as np
  28. import matplotlib.pyplot as plt
  30. # %% [markdown]
  31. # ### **2.** Import experimental proportions
  33. # %%
  34. wd = 'Experimental_and_Simulated_Proportions_Mouse/' # relative to this notebook
  36. adata = pd.read_csv(wd + 'Proportions_RNAseq_Progenitors_SAG500.csv')
  38. #keep only attractor clusters
  39. pattern = r'\b(?:PreNTrans|NMPTrans|MN$|^MN$|V3$|V3Trans|pMNTrans|DPTrans)\b'
  40. adata1 = adata.loc[:, ~adata.columns.str.contains(pattern, regex=True)].copy()
  42. # Add new columns using .loc
  43. adata1.loc[:, 'p2'] = adata['p2'] + adata['pMNTrans']
  44. adata1.loc[:, 'MNDiff'] = adata['MNDiff'] + adata['MN']
  45. adata1.loc[:, 'p3'] = adata['p3'] + adata['V3Trans'] + adata['V3']
  47. # Convert DataFrame to numpy array, divide by 100, and round to two decimal places
  48. processed_data = np.round(adata1.to_numpy() /100, 2)
  49. # Create dictionary with the processed data for Pyabc
  50. data = {'X_2': processed_data.flatten()}
  51. data
  53. # %%
  54. adata1
  56. # %% [markdown]
  57. # ### **3.** Setting up the model
  59. # %% [markdown]
  60. # **Setting up the model.** The fitting machinery lives in `fitting_core`; the *model* is the landscape function you pass to it. The cell below brings the pieces together:
  61. #
  62. # - **`compute_landscape`** (from a `landscape_*` module) — the model itself: the drift + noise of the landscape at each point. Pass a different one (or your own `@njit` function) to fit a different model.
  63. # - **`cellstates`** — the approximated attractor positions (one `[x, y]` per state; approximate because an attractor can move when the parameters change). Cells within `radius` of a cellstate are counted as that state when computing proportions.
  64. # - **`parSDE`** — the SDE settings (time step, total time, number of cells, measurement times); taken from the landscape's `default_parSDE`.
  65. # - **`start_centers` / `samples`** — the initial condition: where cells start and how many in each cluster. Edit these to start from a different mixture.
  66. # - **`make_model(...)`** — builds the PyABC model that simulates the SDE and returns the per-timepoint cluster proportions.
  67. # - **`get_idx_remove(states_byDay, [...])` + `make_distance(...)`** — build the PyABC distance, dropping the listed timepoints (here D3) before comparing simulation to data.
  69. # %%
  70. # --- Choosing the model ---
  71. from fitting_core import make_model, make_distance, get_idx_remove
  72. from landscape_global import compute_landscape, default_parSDE
  74. parSDE = default_parSDE
  76. # Attractor positions for this scRNA-seq SAG500 fit.
  77. cellstates = {
  78. 'PreNeural': [-0.0497558, 4.85763],
  79. 'p0/p1': [-1.37061, 2.8106],
  80. 'p2': [-1.9, 1.1],
  81. 'pMN': [-2.2, 0.15],
  82. 'MNDiff': [-3.34239, -0.520129],
  83. 'DP': [-0.8, 0.1],
  84. 'EarlyVentral':[1.37061, 2.8106],
  85. 'Earlyp3': [1.71, 0.4],
  86. 'p3': [0.0416318, -0.380528],
  87. 'FP': [1.85, -1.38294],
  88. }
  90. # Initial condition: single NMP cluster (100%); edit to a mixture if needed.
  91. start_centers = [(1.40765, 6.86026)] # NMP
  92. samples = [int(100*parSDE['ncells']/100)] # 100% NMP
  94. # scRNA-seq drops only D3 (flow cytometry drops D3/D7/FP).
  95. model = make_model(compute_landscape, cellstates, parSDE,
  96. samples=samples, start_centers=start_centers, radius=0.4)
  97. # Timepoints simulated, and which to drop before comparing to data.
  98. days = ['D3','D4','D5','D6','D7'] # all timepoints the SDE records
  99. drop = ['D3'] # timepoints/states excluded from the fit (and from the comparison below)
  100. states_byDay = [f'{s}-{d}' for d in days for s in cellstates]
  101. distance = make_distance(get_idx_remove(states_byDay, list(cellstates), days, drop))
  103. # %% [markdown]
  104. # ### **4.** ABC Fitting
  105. #
  106. # To fit the model we use the PyABC package developed for Python in [3,4].
  107. # The procedure begins by defining priors distributions for the parameters $\mathbf{p}$ comprising the sub-landscapes parameters $\boldsymbol{\theta}_i=(u_i, v_i)$ for $i=1,\dots, 6$, the scaling parameters $vel_A, vel_B, vel_C$ and the noise parameters $\sigma_A, \sigma_B, \sigma_C, \sigma_D$ (see [2] Appendix B Section B3). In our case the priors are taken as uniform distributions supported in the parameter domain $D$ of the stochastic differential equation. Here we use a sampling population of $N=1500$ and a maximal number of 8 generations. See Appendix B Sections B4 (Fitting the model to simulated proportions) and B7 in [2] for details.
  108. #
  109. # [3] Y. Schälte, E. Klinger, E. Alamoudi, and J. Hasenauer, (2022). *pyABC: Efficient and robust easy-to-use approximate Bayesian computation*. Journal of Open Source Software, 7(74), 4304, https://doi.org/10.21105/joss.04304.
  110. #
  111. # [4] E. Klinger, D. Rickert, and J. Hasenauer, (2018). *pyABC: distributed, likelihood-free inference*. Bioinformatics, 34(20). https://doi.org/10.1093/bioinformatics/bty361.
  113. # %%
  114. import pyabc
  115. from pyabc import ABCSMC, RV, Distribution, LocalTransition, MedianEpsilon
  116. from pyabc.visualization import plot_kde_matrix
  118. # Create path to store Pyabc history
  119. path = '.../DynamicalLandscapeAnalysis_v2/FittingGlobalModel'
  120. db_path = "sqlite:///" + os.path.join(tempfile.gettempdir(), "FittingRNAseqSAG500.db")
  122. # Population size (number of accepted particles per ABC generation).
  123. # Defined once here and reused by ABCSMC and process_simulations.
  124. population_size = 1500
  126. # Define priors limits
  127. limits = dict(u1=(-2.5, 0),
  128. v1=(-2, -0.5),
  129. u2=(-3,0.5),
  130. v2=(-2.2, -0.5),
  131. noiseA=(0.2, 0.8),
  132. velA=(0.05,1.2),
  133. u3=(6,23),
  134. v3=(-4, 10),
  135. velB=(0.05,1.2),
  136. noiseB=(0.2, 1.1),
  137. u4=(-12,0.3),
  138. v4=(-9, -1),
  139. u5=(5,8),
  140. v5=(-2,0.2),
  141. noiseC=(0.2, 0.8),
  142. velC=(0.05,1.2),
  143. u6=(2,8),
  144. v6=(6,14),
  145. noiseD=(0.2, 0.8))
  147. # Choose uniform distributions
  148. prior = Distribution(**{key: RV("uniform", a, b - a)
  149. for key, (a,b) in limits.items()})
  151. # %%
  152. abc = ABCSMC(
  153. models=model,
  154. parameter_priors=prior,
  155. distance_function=distance,
  156. population_size=population_size,
  157. transitions=LocalTransition(k_fraction=0.3),
  158. eps=pyabc.QuantileEpsilon(alpha=0.2),
  159. )
  161. abc.new(db_path, data);
  164. h = abc.run(minimum_epsilon=0.1, max_nr_populations=8)
  165. run_id = h.id
  166. print("Run ID:", run_id)
  168. # %% [markdown]
  169. # #### **4.1** Visualise the posterior parameter distributions
  171. # %%
  172. df, w = h.get_distribution(m=0)
  173. plot_kde_matrix(df, w, limits=limits);
  175. # %% [markdown]
  176. # #### **4.2** Decrease of the $\varepsilon$-threshold over the 8 generations
  178. # %%
  179. # Given epsilon values and x-axis points
  180. epsilons = h.get_all_populations()["epsilon"].tolist()
  181. epsilons=epsilons[1:]
  182. x_axis = list(range(8)) # 8 is the number of generations
  184. # Create the line plot
  185. plt.figure(figsize=(8, 5),dpi=50)
  186. plt.plot(x_axis, epsilons, marker='o', linestyle='-', color='navy', linewidth=2,
  187. label=f"Minimum Epsilon: {min(epsilons):.2f}")
  189. plt.xlabel("Generation", fontsize=20)
  190. plt.ylabel("Epsilon", fontsize=20)
  191. plt.title("SAG 500nM", fontsize=20)
  192. plt.legend(loc="upper right", fontsize=20)
  193. plt.grid(False)
  194. plt.xticks(fontsize=20)
  195. plt.yticks(fontsize=20)
  196. plt.show()
  199. # %% [markdown]
  200. # ### **5.** Compare simulated and experimental proportions
  202. # %%
  203. # Import the function to process the simulations (merged module)
  204. from fitting_core import process_simulations, simulation_todf, get_idx_remove
  205. # Import the function to plot the distributions of simulated data
  206. from fitting_plots import plot_data, plot_histogram_grid
  208. # Process simulations (use the same dropped timepoints as the fit: D3 only)
  209. simulation_accepted, dist, simulation_mean = process_simulations(population_size, h, data, parSDE, list(cellstates), idx_remove=get_idx_remove(states_byDay, list(cellstates), days, drop))
  211. # %% [markdown]
  212. # #### **5.1** Barplots
  214. # %%
  215. # define colors for plot
  216. colorpalette={'NMP':'#D2C1E1',
  217. 'Meso':'#BFBC47',
  218. 'p3':'#0D6453',
  219. 'MNDiff':'#9F1812',
  220. 'pMN':'#DA2222',
  221. 'DP':'#511A13',
  222. 'p2':'#F9D575',
  223. 'p0/p1':'#122859',
  224. 'PreNeural':'#5D4082',
  225. 'FP':'#000000',
  226. 'EarlyVentral':'#288c9c',
  227. 'Earlyp3':'#CFECE7'}
  229. # %% [markdown]
  230. # The simulation records proportions at **all five** timepoints (`days = ['D3','D4','D5','D6','D7']`), but the fit only used a subset of them — the rest are listed in `drop`. To compare like with like, we keep only the rows of the simulated array whose day is **not** in `drop` (`kept`), rather than slicing by position. This uses the *same* `drop` set defined in the model cell, so the comparison automatically follows whatever timepoints the fit excluded.
  232. # %%
  233. # Usage
  234. states = ['PreNeural','p0/p1','p2','pMN','MNDiff','DP','EarlyVentral','Earlyp3','p3','FP'] # attractor clusters (columns)
  235. # x_labels = the days we actually compare: the simulated `days` minus the dropped ones.
  236. x_labels = [d for d in days if d not in drop] # timepoints shown
  238. # Reshape simulated means to (day, state) and keep only the compared days.
  239. # `kept` are the row indices of the days NOT in `drop` -- the same drop set used in the fit,
  240. # so we never hard-code which rows to slice.
  241. column_reshaped = simulation_mean.reshape(len(days), len(states))
  242. kept = [i for i, d in enumerate(days) if d not in drop]
  243. simulated_data = pd.DataFrame(column_reshaped[kept], columns=states)
  245. # Experimental proportions for the same days.
  246. data500 = pd.DataFrame(adata1.values, columns=states, index=x_labels) # experimental proportions
  248. # Create figure and axes
  249. fig, axes = plt.subplots(1, 2, figsize=(18, 10))
  250. fig.tight_layout(pad=5)
  252. # barplot of the experimental proportions (average)
  253. plot_data(
  254. ax=axes[0],
  255. data=data500,
  256. title=r'$\bf{SAG500 RNAseq}$',
  257. x_labels=x_labels,
  258. palette=colorpalette,
  259. background="data")
  261. # barplot of the simulated proportions (average)
  262. plot_data(
  263. ax=axes[1],
  264. data=simulated_data,
  265. title=r'$\bf{SAG500 RNAseq}$',
  266. x_labels=x_labels,
  267. palette=colorpalette,
  268. background="simulation")
  270. plt.show()
  272. # %% [markdown]
  273. # #### **5.2** Save results
  275. # %%
  276. # save simulations
  277. Xsim_df=simulation_todf(states, ['D3','D4','D5','D6','D7'], simulation_accepted)
  278. Xsim_df.to_csv(wd+'RNAseq_SAG500_simulation.csv', index=False)
  280. # Add distance to experimental data and save parameters
  281. df['distance']=dist
  282. df.to_csv(wd+'RNAseq_SAG500_parameters.csv', index=False)
  284. # Save probability weights for posterior
  285. #dw=pd.DataFrame(w,columns=['w'])
  286. #dw.to_csv(wd+'RNAseq_SAG500_weights.csv', index=False)
  288. # %%
  289. Xsim_df.head(3)
  291. # %%
  292. df.head(3)
  294. # %%
  297. # %% [markdown]
  298. # #### **5.3** Distributions of the simulated proportions
  300. # %%
  301. plot_histogram_grid(
  302. states=states, # attractor clusters
  303. times=['D4','D5','D6','D7'], # timepoints
  304. simulation_accepted=Xsim_df, # simulated proportions
  305. data=data500, # experimental proportions
  306. colorpalette=colorpalette, # colors
  307. bins=15) # number of bins
  309. # %%
  310. # Tendency plot: experimental vs simulation mean per state, with a 5-95 percentile band.
  311. # Uses the same kept timepoints (x_labels) and experimental proportions as the barplot above;
  312. # plot_tendencies selects the matching '<state>-<day>' columns from Xsim_df.
  313. from fitting_plots import plot_tendencies
  315. plot_tendencies(
  316. states, # attractor clusters (one panel each)
  317. x_labels, # timepoints shown (kept days)
  318. Xsim_df[[f'{s}-{d}' for d in x_labels for s in states]], # simulated proportions for those days/states
  319. data500, # experimental proportions (0-100 scale)
  320. colorpalette) # state -> colour
  323. # %%
  326. # %%

Fitting_RNAseq_SAG500.ipynb at commit 6ea1fc4, no license · at the source

Overview

Authors: Marine Fontaine1,2, M. Joaquina Delás3, Meritxell Sáez4, Rory J. Maizels3, Elizabeth Finnie3, James Briscoe3, David A. Rand1,2
ORCID iDs: Marine Fontaine, M. Joaquina Delás, Meritxell Sáez, Rory J. Maizels, Elizabeth Finnie, James Briscoe, David A. Rand
  1. Mathematics Institute, University of Warwick, Coventry, United Kingdom
  2. Zeeman Institute for Systems Biology and Infectious Epidemiology Research, University of Warwick, Coventry, United Kingdom
  3. The Francis Crick Institute, London, United Kingdom
  4. IQS, Universitat Ramon Llull, Barcelona, Spain
Institutions: University of Warwick (United Kingdom); The Francis Crick Institute (United Kingdom); Institut Químic de Sarrià (Spain); Universitat Ramon Llull (Spain)
Journal: PLoS biology, volume 24, issue 8, article e3003953
Dates: received 5 December 2025; accepted 31 July 2026; published online 26 August 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1371/journal.pbio.3003953 · PMID 42647569 · PMCID PMC13588503 · OpenAlex W7204260922
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: human (organism)
MeSH: Neurogenesis*, Single-Cell Analysis*, Animals, Cell Differentiation, Cell Lineage, Hedgehog Proteins, Humans, Models, Biological, Neural Tube, Signal Transduction, Single-Cell Gene Expression Analysis (* major topic)
Journal subjects: Research and Analysis Methods, Spectrum Analysis Techniques, Spectrophotometry, Cytophotometry, Flow Cytometry, Computer and Information Sciences, Systems Science, Dynamical Systems, Physical Sciences, Mathematics, Biology and Life Sciences, Genetics, Gene Expression, Developmental Biology, Embryology, Mesoderm, Cell Differentiation, Neuroscience, Cognitive Science, Cognitive Psychology, Decision Making, Psychology, Social Sciences, Cognition, Topology, Manifolds, Molecular Development, Morphogens
Topic: Single-cell and spatial transcriptomics (Molecular Biology, Biochemistry, Genetics and Molecular Biology), according to OpenAlex
Funding: Cancer Research UK (CRUK) (CC001051); Medical Research Council (CC001051); Wellcome Trust (CC001051, 220379/D/20/Z, 227326/Z/23/Z); Engineering and Physical Sciences Research Council (EP/P019811/1, EP/T031573/1, EP/Z535953/1); National Science Foundation (PHY-2309135)
Citations: not cited yet (Europe PMC); 90 references in the paper

Abstract

Building a mechanistic understanding of cell fate decisions remains a fundamental goal of developmental biology, with implications for stem cell therapies, regenerative medicine and understanding disease mechanisms. Single-cell transcriptomics provides a detailed picture of the cellular states observed during these decisions, but building dynamic and predictive models from these data remains a challenge. Here, we present dynamic landscape analysis (DLA), an integrative framework that applies dynamical systems theory to identify stable cell states, map transition pathways, and generate a predictive cell fate decision landscape from single-cell data. Applying this framework to vertebrate neural tube development revealed that progenitor specification by Sonic Hedgehog (Shh) can be captured in a landscape with an unexpected topology in which initially divergent lineages converge to the same fate through multiple distinct routes. The model accurately predicted cellular responses and cell fate allocation for unseen dynamic signalling regimes. Cross-species validation using human embryonic organoid data demonstrated conservation of this decision-making architecture. By modelling the dynamic responses that drive cell fate decisions, the DLA framework provides a quantitative and generative framework for extracting mechanistic insights from high-dimensional single-cell data.

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

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Zenodo 15584010

License: CC-BY-4.0
State: the link answers, verified on 27 September 2026
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Found in: the text, “Identification and validation of attractor clust”
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Availability: 1 check, the latest on 27 September 2026: the link answers (HTTP 200)
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At the source: doi.org/10.5281/zenodo.15584010

MarineAFontaine/Dynamic-Landscape-Analysis-DLA-

License: none: the authors keep all their rights
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Commit: 6ea1fc4905ebf4f9244ac39adc1823c0b6a550ce, 16 August 2026
Languages: Jupyter (18), Python (12)
Size: 81 files, 30 scripts
Software Heritage: not archived
Found in: “Data Availability”
Holds: README, environment (FittingGlobalModel/requirements.txt, FittingTutorial/requirements.txt, FlowDataAnalysis/requirements.txt, TransitionAnalysis/requirements.txt, RNAseqDataAnalysis/Clustering/requirements.txt), 18 notebooks
Not found: license file, CITATION.cff, tests, continuous integration, documentation
Tools: Matplotlib (7 files), NumPy (7 files), pandas (7 files)
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7 files
At the source: github.com/MarineAFontaine/Dynamic-Landscape-Analysis-DLA-

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Data

Datasets cited

Data Availability

The pre-processed flow cytometry data generated in this study have been deposited at https://crick.figshare.com/projects/Neural_Tube_Decision_Landscape/250460 and are publicly available as of the date of preprint publication, prior to peer review. The published sequencing data for mouse embryonic stem cells (Ref [40]) and 3D human notoroids (Ref [38]) analysed in this study can be found respectively in the GEO repositories GSE236520 and GSE255338. Original code has been deposited at Zenodo under the DOI https://doi.org/10.5281/zenodo.15584010 and Github https://github.com/MarineAFontaine/Dynamic-Landscape-Analysis-DLA-.

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Recorded: type, language, journal, volume, issue, pages, dates, 7 authors, 11 MeSH terms, 5 funders, 81 references.

Cite

This paper

Fontaine, M., Delás, M. J., Sáez, M., Maizels, R. J., Finnie, E., Briscoe, J., & Rand, D. A. (2026). Dynamic Landscape Analysis of cell fate decisions provides predictive models of neural development from single-cell data. PLoS biology, 24(8), e3003953. https://doi.org/10.1371/journal.pbio.3003953

BibTeX

@article{fontaine2026dynamic,
author = {Fontaine, Marine and Delás, M. Joaquina and Sáez, Meritxell and Maizels, Rory J. and Finnie, Elizabeth and Briscoe, James and Rand, David A.},
title = {{Dynamic Landscape Analysis of cell fate decisions provides predictive models of neural development from single-cell data}},
journal = {PLoS biology},
year = {2026},
month = aug,
volume = {24},
number = {8},
pages = {e3003953},
publisher = {PLOS},
issn = {1544-9173},
doi = {10.1371/journal.pbio.3003953},
url = {https://doi.org/10.1371/journal.pbio.3003953},
pmid = {42647569},
pmcid = {PMC13588503}
}

RIS

TY - JOUR
AU - Fontaine, Marine
AU - Delás, M. Joaquina
AU - Sáez, Meritxell
AU - Maizels, Rory J.
AU - Finnie, Elizabeth
AU - Briscoe, James
AU - Rand, David A.
TI - Dynamic Landscape Analysis of cell fate decisions provides predictive models of neural development from single-cell data
T2 - PLoS biology
J2 - PLoS Biol
PY - 2026
DA - 2026/08/26
VL - 24
IS - 8
SP - e3003953
SN - 1544-9173
PB - PLOS
DO - 10.1371/journal.pbio.3003953
UR - https://doi.org/10.1371/journal.pbio.3003953
LA - en
ER -

CSL-JSON

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"issue": "8",
"page": "e3003953",
"DOI": "10.1371/journal.pbio.3003953",
"PMID": "42647569",
"PMCID": "PMC13588503",
"ISSN": "1544-9173",
"publisher": "PLOS",
"URL": "https://doi.org/10.1371/journal.pbio.3003953",
"language": "en",
"issued": {
"date-parts": [
[
2026,
8,
26
]
]
}
}

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