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Learning stochastic dynamics and cell-fate landscapes from single-cell snapshots via optimal transport.

Code ↔ Paper

9 matches between paragraphs of the paper and lines of its authors' code, computed by the harvester (lexical-v1). Click a colored paragraph or line to see its counterpart.

The 9 matches
  1. [1] § MATERIALS AND METHODS › Data preprocessing ↔ Notebooks/Mouse hematopoietic.ipynb, lines 1–27 · score 0.94 · highly variable genes, mouse hematopoietic, dendritic cells, log transformed, undifferentiated cells, eliminated cell
  2. [2] § MATERIALS AND METHODS › Data preprocessing ↔ Kukreja_CellCycle_2024/scRNA-seq_data_analysis/10.diff_delay_by_classification.ipynb, lines 276–286 · score 0.63 · spinal cord, Neural crest, arch, muscle, seq, cells
  3. [3] § MATERIALS AND METHODS › Data preprocessing ↔ Kukreja_CellCycle_2024/scRNA-seq_data_analysis/14.proliferation_score_tree.ipynb, lines 218–228 · score 0.63 · spinal cord, Neural crest, arch, muscle, seq, cells
  4. [4] § MATERIALS AND METHODS › Total loss of DiffusionOT and training details › Stage 2: Unified training ↔ Notebooks/MISA.ipynb, lines 1–55 · score 0.63 · MISA model, gene regulatory, epochs, configurations, DiffusionOT, Adam
  5. [5] § MATERIALS AND METHODS › MISA simulation model ↔ Notebooks/MISA.ipynb, lines 1–55 · score 0.59 · MISA model, Hill function, mutually inhibit, DiffusionOT, activated, regulatory
  6. [6] § RESULTS › Reconstructing cellular dynamics from spatial Stereo-seq data ↔ Kukreja_CellCycle_2024/scRNA-seq_data_analysis/10.diff_delay_by_classification.ipynb, lines 276–286 · score 0.53 · spinal cord, neural crest, muscle, seq, cell
  7. [7] § RESULTS › Reconstructing cellular dynamics from spatial Stereo-seq data ↔ Kukreja_CellCycle_2024/scRNA-seq_data_analysis/14.proliferation_score_tree.ipynb, lines 218–228 · score 0.53 · spinal cord, neural crest, muscle, seq, cell
  8. [8] § RESULTS › Identifying multiple cell fate bifurcations ↔ Notebooks/Mouse hematopoietic.ipynb, lines 1–27 · score 0.53 · mouse hematopoietic, undifferentiated cells, DiffusionOT, megakaryocytes, erythrocyte, Mk
  9. [9] § MATERIALS AND METHODS › Total loss of DiffusionOT and training details › Stage 2: Unified training ↔ Notebooks/EMT.ipynb, lines 1–68 · score 0.52 · gene regulatory, epochs, configurations, DiffusionOT, Adam, weighted

Paper

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The authors' code

Jupyter notebook · 308 lines · 11 KB · MIT · 2 matches

  1. # %% [markdown]
  2. # # **Introduction**
  3. #
  4. # In this tutorial, we demonstrate how to use autoencoer (AE) on Mouse hematopoietic dataset. The mouse hematopoietic dataset is time-series scRNA-seq datasewas downloaded from the NCBI Gene Expression Omnibus (GEO) under accession number GSE140802, or alternatively from thets [1].
  5. #
  6. # For the mouse hematopoietic data, which includes three time points (2d, 4d, 6d), we first removed genes with expression levels below `1%` in all cells and further eliminated cell types with a small number of samples. The remaining cell types included erythrocytes (Er), megakaryocytes (Mk), basophils (Ba), mast cells (Ma), eosinophils (Eos), neutrophils (Neu), monocytes (Mo), dendritic cells (plasmocytoid pDC; Ccr7+migratory cDC) and undifferentiated cells (Ud). We then log-transformed the gene expression data and retained the top $3000$ highly variable genes for subsequent analysis, resulting in a dataset size of $43,968$ cells × $3000$ genes.
  7. #
  8. # References:
  9. # 1. Weinreb C, Rodriguez-Fraticelli A, Camargo FD, Klein AM. Lineage tracing on transcriptional landscapes links state to fate during differentiation. Science 367, eaaw3381 (2020).42
  11. # %% [markdown]
  12. # ## Using AE to dimension reduction
  14. # %%
  15. import numpy as np
  16. import torch
  17. import torch.nn as nn
  18. import pandas as pd
  19. import scanpy as sc
  20. from matplotlib.pyplot import rc_context
  21. import os
  22. from pathlib import Path
  23. import matplotlib.pyplot as plt
  24. import gc
  25. import sys
  26. sys.path.append(r'C:\Users\JTliu\Desktop\DiffusionOT-main')
  27. from AE import AutoEncoder, Trainer
  29. def load_data(dataset:str,path_to_data):
  31. if dataset=='EMT':
  32. adata = sc.read_h5ad(path_to_data+'emt.h5ad')
  33. X=adata.X
  35. elif dataset=='Mouse':
  36. adata = sc.read_h5ad(path_to_data+'mouse_pre.h5ad')
  37. adata.obs.rename(columns={'Time point': 'time','Cell type annotation':'cell type'}, inplace=True)
  38. adata.obs['time'] = adata.obs['time'].astype(str)
  39. X=adata.X
  41. else:
  42. raise NotImplementedError
  43. return adata,X
  45. def folder_dir(dataset:str='EMT',
  46. seed:int=42,
  47. n_latent:int=6,
  48. n_hidden:int=300,
  49. n_layers: int=1,
  50. activation: str = 'relu',
  51. dropout:float=0.2,
  52. weight_decay:float=1e-4,
  53. lr:float=1e-3,
  54. batch_size: int=32,):
  55. folder=Path('results/'+dataset+'_'+str(seed)+\
  56. '_'+str(n_latent)+'_'+str(n_layers)+'_'+str(n_hidden)+\
  57. '_'+str(dropout)+'_'+str(weight_decay)+'_'+str(lr)+'_'+str(batch_size)+'/')
  58. return folder
  60. def generate_plots(folder,model, adata,seed,n_neighbors=10,min_dist=0.5,plots='umap',name='time'):
  61. model.eval()
  62. with torch.no_grad():
  63. X_latent_AE=model.get_latent_representation(torch.tensor(adata.X).type(torch.float32).to('cpu'))
  64. adata.obsm['X_AE']=X_latent_AE.detach().cpu().numpy()
  65. sc.pp.neighbors(adata, n_neighbors=n_neighbors,use_rep='X_AE')
  67. color_wanted = ['#d62728', '#2ca02c', '#8c564b',
  68. '#e377c2', '#17becf', '#bcbd22',
  69. '#1f77b4', '#9467bd', '#ff7f0e',
  70. '#7f7f7f','#2f7f2e']
  72. if dataset in ['EMT','Mouse']:
  73. color=[name]
  74. #color=['cell type']
  75. else:
  76. raise NotImplementedError
  77. if plots=='umap':
  78. sc.tl.umap(adata,random_state=seed,min_dist=min_dist)
  79. with rc_context({'figure.figsize': (8, 8*len(color))}):
  80. fig = sc.pl.umap(adata, color=color,
  81. #palette=color_wanted,
  82. legend_loc='on data',
  83. legend_fontsize=12,
  84. legend_fontoutline=2,
  85. return_fig = True)
  86. fig.savefig(str(folder) + '/umap_{}.png'.format(name),bbox_inches='tight',dpi=300)
  87. #plt.close()
  88. plt.show()
  89. elif plots=='embedding':
  90. #fig, axs = plt.subplots() # 创建子图
  91. with rc_context({'figure.figsize': (8*len(color), 8)}):
  92. fig = sc.pl.embedding(adata, 'X_AE',color=color,
  93. palette=color_wanted,
  94. legend_loc='on data',
  95. legend_fontsize=12,
  96. legend_fontoutline=2,
  97. return_fig = True)
  98. #plt.legend(frameon=False)
  99. #plt.xticks([plt.xlim()[0], 0., plt.xlim()[1]])
  100. #plt.yticks([plt.ylim()[0], 0., plt.ylim()[1]])
  101. fig.savefig(str(folder) + '/embedding_{}.png'.format(name),bbox_inches='tight',dpi=300)
  102. plt.show()
  104. def loss_plots(folder,model):
  105. fig,axs=plt.subplots(1, 1, figsize=(4, 4))
  106. axs.set_title('AE loss')
  107. axs.plot(model.history['epoch'], model.history['train_loss'])
  108. axs.plot(model.history['epoch'], model.history['val_loss'])
  109. plt.yscale('log')
  110. axs.legend(['train loss','val loss'])
  111. plt.savefig(str(folder)+'/loss.pdf')
  112. plt.show()
  114. def main(dataset:str='EMT',
  115. seed:int=42,
  116. n_latent:int=6,
  117. n_hidden:int=300,
  118. n_layers: int=1,
  119. activation: str='relu',
  120. dropout:float=0.2,
  121. weight_decay:float=1e-4,
  122. lr:float=1e-3,
  123. max_epoch:int=500,
  124. batch_size: int=32,
  125. mode='training',
  126. path_to_data='Path to data'
  127. ):
  128. adata,X = load_data(dataset,path_to_data)
  130. model=AutoEncoder(in_dim=X.shape[1],
  131. n_latent=n_latent,
  132. n_hidden=n_hidden,
  133. n_layers=n_layers,
  134. activate_type=activation,
  135. dropout=dropout,
  136. norm=True,
  137. seed=seed,)
  139. trainer=Trainer(model,X=X,
  140. test_size=0.1,
  141. lr=lr,
  142. batch_size=batch_size,
  143. weight_decay=weight_decay,
  144. seed=seed)
  146. folder=folder_dir(dataset=dataset,
  147. seed=seed,
  148. n_latent=n_latent,
  149. n_hidden=n_hidden,
  150. n_layers=n_layers,
  151. dropout=dropout,
  152. activation=activation,
  153. weight_decay=weight_decay,
  154. lr=lr,
  155. batch_size=batch_size,)
  157. folder=Path(os.path.join(path_to_data,folder))
  158. if mode=='training':
  159. print('training the model')
  160. trainer.train(max_epoch=max_epoch,patient=30,tol=0.001)##no improvement times tol=0.01
  162. # model.eval()
  163. if not os.path.exists(folder):
  164. folder.mkdir(parents=True)
  165. torch.save({
  166. 'func_state_dict': model.state_dict(),
  167. 'optimizer_state_dict': trainer.optimizer.state_dict(),
  168. 'loss_history':trainer.model.history,
  169. }, os.path.join(folder,'model.pt'))
  170. elif mode=='loading':
  171. print('loading the model')
  172. check_pt = torch.load(os.path.join(folder, 'model.pt'))
  174. model.load_state_dict(check_pt['func_state_dict'])
  175. trainer.optimizer.load_state_dict(check_pt['optimizer_state_dict'])
  176. model.history=check_pt['loss_history']
  177. return model,trainer,adata,folder
  179. # %% [markdown]
  180. # Here we consider the dimension of latent space is 2.
  182. # %%
  183. #######
  184. seed=42
  185. n_layers = 1
  186. batch_size=128
  187. dataset='Mouse'
  189. lr=1e-3
  190. n_hidden=300
  191. n_latent = 2
  193. path_to_data = "C:/Users/JTliu/Desktop/DiffusionOT-main/Rawdata/"
  195. model,trainer, adata,folder=main(dataset=dataset,seed=seed,
  196. n_layers=n_layers,n_latent=n_latent,n_hidden=n_hidden,
  197. activation='relu',
  198. lr=lr,batch_size=batch_size,
  199. max_epoch=500,
  200. mode='training',#mode='training','loading'
  201. path_to_data = path_to_data)
  203. model=model.to('cpu')
  204. adata.obs['time'] = adata.obs['time'].astype(str)
  205. generate_plots(folder,model,adata,seed,n_neighbors=20,min_dist=0.5,plots='embedding',name='time')
  207. # %%
  208. generate_plots(folder,model,adata,seed,n_neighbors=20,min_dist=0.5,plots='embedding',name='cell type')
  210. # %%
  211. loss_plots(folder,model)
  213. # %% [markdown]
  214. # Normalize and Convert latent spaces data to the desired format
  216. # %%
  217. model.eval()
  218. with torch.no_grad():
  219. X_latent_AE=model.get_latent_representation(torch.tensor(adata.X).type(torch.float32).to('cpu'))
  220. adata.obsm['X_AE']=X_latent_AE.detach().cpu().numpy()
  221. np.max(X_latent_AE.detach().cpu().numpy(),axis=0)
  222. np.min(X_latent_AE.detach().cpu().numpy(),axis=0)
  223. time_label = adata.obs['time'].to_numpy(dtype=object)
  224. type_label = adata.obs['cell type'].to_numpy(dtype=object)
  225. X_latent_AE_np = X_latent_AE.detach().cpu().numpy()
  226. # Convert points_all to the desired format
  227. np.savez("C:/Users/JTliu/Desktop/DiffusionOT-main/Input/Mouse_latent_ae_scaled.npz",
  228. latent_ae_scaled=X_latent_AE_np,
  229. time_label=time_label,
  230. type_label=type_label)
  232. # %% [markdown]
  233. # ## Visualization
  235. # %%
  236. import os
  237. import numpy as np
  238. import torch
  239. import torch.nn as nn
  240. import torch.optim as optim
  241. import sys
  242. sys.path.append('C:\\Users\\JTliu\\Desktop\\DiffusionOT-main\\')
  243. from utility import *
  244. args = create_args()
  246. # %% [markdown]
  247. # ## Load data and model
  249. # %%
  250. save_dir=args.save_dir
  251. random.seed(args.seed)
  252. torch.manual_seed(args.seed)
  253. device = torch.device('cpu')
  254. # load dataset
  255. data = np.load(args.input_dir+'/Mouse_latent_ae_scaled.npz', allow_pickle=True)
  256. latent_ae_scaled = data['latent_ae_scaled']
  257. time_label = data['time_label']
  258. type_label = data['type_label']
  259. time_all = ['2','4','6']
  260. data_train = []
  261. data_type = []
  262. for k in range(len(time_all)):
  263. indices = [i for i, l in enumerate(time_label) if l == time_all[k]]
  264. samples = latent_ae_scaled[indices,]
  265. cell_type = type_label[indices,]
  266. samples = torch.from_numpy(samples).type(torch.float32).to(device)
  267. data_train.append(samples)
  268. data_type.append(cell_type)
  270. #data_train = loaddata(args,device)
  271. integral_time = args.timepoints
  272. time_pts = range(len(data_train))
  273. leave_1_out = []
  274. train_time = [x for i,x in enumerate(time_pts) if i!=leave_1_out]
  276. # model
  277. func = RUOT(in_out_dim=data_train[0].shape[1], hidden_dim=args.hidden_dim,n_hiddens=args.n_hiddens,activation=args.activation,d =args.d).to(device)
  278. # load trained networks
  279. if args.save_dir is not None:
  280. if not os.path.exists(args.save_dir):
  281. os.makedirs(args.save_dir)
  282. ckpt_path = os.path.join(args.save_dir, 'ckpt_Mouse.pth')#'ckpt6_MISA3_D_{:.3f}.pth'.format(D0) 'ckpt6_MISA4.pth''ckpt_EMT.pth'ckpt_Simulation_itr2000_D_0.040
  283. if os.path.exists(ckpt_path):
  284. checkpoint = torch.load(ckpt_path,map_location=torch.device('cpu'))
  285. func.load_state_dict(checkpoint['func_state_dict'])
  286. print('Loaded ckpt from {}'.format(ckpt_path))
  288. D_t=diffusion_fit(func,args,data_train,train_time,integral_time,device,time_tt=0.1)
  289. D=torch.mean(D_t)
  290. func.d=torch.nn.Parameter(D)
  292. # %% [markdown]
  293. # ## Cell velocity
  295. # %%
  296. plot_2d_v(func,data_train,train_time,integral_time,args,device)
  298. # %% [markdown]
  299. # ## Cell fate landscape
  301. # %%
  302. plot_3d_landscape(func,data_train,train_time,integral_time,args,device)
  304. # %% [markdown]
  305. # ## Plot trajectory and growth
  307. # %%
  308. plot_2d(func,data_train,train_time,integral_time,args,device)

Mouse hematopoietic.ipynb at commit bb3c5bd, under MIT · at the source

Overview

Authors: Juntan Liu1,2, Peijie Zhou3,4,5,6, Qing Nie7, Chunhe Li1,2,8
ORCID iDs: Juntan Liu, Peijie Zhou, Qing Nie, Chunhe Li
  1. Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai 200433, China
  2. Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200433, China
  3. Center for Machine Learning Research, Peking University, Beijing 100871, China
  4. Center for Quantitative Biology, Peking University, Beijing 100871, China
  5. National Engineering Laboratory for Big Data Analysis and Applications, Beijing 100871, China
  6. AI for Science Institute, Beijing 100084, China
  7. Department of Mathematics and Department of Developmental & Cell Biology, University of California, Irvine, Irvine, CA 92612, USA
  8. School of Mathematical Sciences, Center for Applied Mathematics, Shanghai Key Laboratory for Contemporary Applied Mathematics, and MOE Frontiers Center for Brain Science, Fudan University, Shanghai 200433, China
Institutions: Fudan University (China); Peking University (China); University of California, Irvine (United States); Frontiers Center for Brain Science of the Ministry of Education (China)
Journal: Science advances, volume 12, issue 37, article eaeb4205
Dates: received 13 August 2025; accepted 6 August 2026; published online 9 September 2026; in print September 2026
Type: Research article · Language: English
License: CC BY-NC
Identifiers: DOI 10.1126/sciadv.aeb4205 · PMID 42715336 · PMCID PMC13557085 · OpenAlex W7211988907
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: human (organism), cellular / molecular (subfield)
Methods: Connectivity, Smoothing, state filtering, decompositions, Machine learning
MeSH: Cell Differentiation*, Cell Lineage*, Machine Learning*, Single-Cell Analysis*, Algorithms, Animals, Gene Regulatory Networks, Humans, Single-Cell Gene Expression Analysis, Stochastic Processes (* major topic)
Journal subjects: Biomedicine and Life Sciences, Systems Biology, Computational Biology
Topic: Single-cell and spatial transcriptomics (Molecular Biology, Biochemistry, Genetics and Molecular Biology), according to OpenAlex
Funding: National Natural Science Foundation of China (12171102); National Key R&D Program of China (2019YFA0709502)
Citations: not cited yet (Europe PMC); 90 references in the paper

Abstract

The temporal dynamics and stochasticity of gene expression are critical to cell fate decisions, yet integrating snapshot omics data across multiple time points remains a major challenge. Here, we introduce DiffusionOT, a dynamic machine learning framework that infers cellular trajectories from multi–time point single-cell transcriptomics by incorporating stochastic effects. DiffusionOT transforms stochastic differential equations into ordinary differential equations, using optimal transport and neural networks to solve a high-dimensional landscape model. Through an unsupervised learning of the stochastic force in the data, DiffusionOT allows robust inference of the underlying stochastic dynamics of cell-state transitions. The framework includes a stochastic trajectory analysis module for lineage tracing and a gene perturbation module for in silico knockout and overexpression experiments. Benchmarks on simulated and four real-world datasets, including a spatial Stereo-seq dataset, demonstrate DiffusionOT’s accuracy and efficiency in inferring state-transition velocities, cellular trajectories, population growth, gene regulatory networks, and cell-fate landscape.

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

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allonkleinlab/paper-data

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At the source: github.com/AllonKleinLab/paper-data/tree/master/Lineage_tracing_on_transcriptional_landscapes_links_state_to_fate_during_differentiation#experiment-3-in-vitro-cytokine-perturbations

liujuntan/DiffusionOT

License: MIT
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Commit: bb3c5bd0c18066e90929961e92b79ffd9abb5e86, 7 August 2025
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Size: 46 files, 9 scripts
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At the source: github.com/liujuntan/DiffusionOT

Zenodo 18251638

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Data

Datasets cited

Data, code, and materials availability

All data and code needed to evaluate and reproduce the results in the paper are present in the paper and/or the Supplementary Materials. This study did not generate new materials. Data for the single-cell lung cancer TGFβ − induced EMT were downloaded from a source data file available at www.nature.com/articles/s41467-019-13441-6#Sec3042 (51). Data for the single-cell mouse hematopoietic dataset were downloaded from the NCBI Gene Expression Omnibus (GEO) under accession number GSE140802 or alternatively from https://github.com/AllonKleinLab/paper-data/tree/master/Lineage_tracing_on_transcriptional_landscapes_links_state_to_fate_during_differentiation#experiment-3-in-vitro-cytokine-perturbations (58). Data for zebrafish sensory HC regeneration were obtained from NCBI GEO under accession number GSE196211 and can also be accessed via www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE196211 (64). Data for spatial Stereo-seq mouse embryo data were downloaded from https://db.cngb.org/stomics/mosta/download/ (66). All source codes and models are publicly available at https://github.com/liujuntan/DiffusionOT and archived on Zenodo at https://zenodo.org/records/18251638.

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Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 4 authors, 10 MeSH terms, 2 funders, 60 references.

Cite

This paper

Liu, J., Zhou, P., Nie, Q., & Li, C. (2026). Learning stochastic dynamics and cell-fate landscapes from single-cell snapshots via optimal transport. Science advances, 12(37), eaeb4205. https://doi.org/10.1126/sciadv.aeb4205

BibTeX

@article{liu2026learning,
author = {Liu, Juntan and Zhou, Peijie and Nie, Qing and Li, Chunhe},
title = {{Learning stochastic dynamics and cell-fate landscapes from single-cell snapshots via optimal transport}},
journal = {Science advances},
year = {2026},
month = sep,
volume = {12},
number = {37},
pages = {eaeb4205},
publisher = {American Association for the Advancement of Science},
issn = {2375-2548},
doi = {10.1126/sciadv.aeb4205},
url = {https://doi.org/10.1126/sciadv.aeb4205},
pmid = {42715336},
pmcid = {PMC13557085}
}

RIS

TY - JOUR
AU - Liu, Juntan
AU - Zhou, Peijie
AU - Nie, Qing
AU - Li, Chunhe
TI - Learning stochastic dynamics and cell-fate landscapes from single-cell snapshots via optimal transport
T2 - Science advances
J2 - Sci Adv
PY - 2026
DA - 2026/09/09
VL - 12
IS - 37
SP - eaeb4205
SN - 2375-2548
PB - American Association for the Advancement of Science
DO - 10.1126/sciadv.aeb4205
UR - https://doi.org/10.1126/sciadv.aeb4205
LA - en
ER -

CSL-JSON

{
"id": "10.1126/sciadv.aeb4205",
"type": "article-journal",
"title": "Learning stochastic dynamics and cell-fate landscapes from single-cell snapshots via optimal transport",
"container-title": "Science advances",
"author": [
{
"family": "Liu",
"given": "Juntan"
},
{
"family": "Zhou",
"given": "Peijie"
},
{
"family": "Nie",
"given": "Qing"
},
{
"family": "Li",
"given": "Chunhe"
}
],
"container-title-short": "Sci Adv",
"volume": "12",
"issue": "37",
"page": "eaeb4205",
"DOI": "10.1126/sciadv.aeb4205",
"PMID": "42715336",
"PMCID": "PMC13557085",
"ISSN": "2375-2548",
"publisher": "American Association for the Advancement of Science",
"URL": "https://doi.org/10.1126/sciadv.aeb4205",
"language": "en",
"issued": {
"date-parts": [
[
2026,
9,
9
]
]
}
}

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