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Harnessing biological variability for mechanistic inference: A stochastic framework applied to neural stem cell dynamics.

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  1. [1] § STAR★Methods › Quantification and statistical analysis › Data preprocessing and parameter estimation ↔ data/filterLognormalGaussian.m, the whole file · a weak match · score 0.78 · truncation bounds, probability density, cutting, threshold, curve, Filtered

Paper

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The authors' code

MATLAB · 97 lines · 3.6 KB · CC-BY-4.0 · 1 match

  1. function [filtered_data, mu_gauss, std_gauss, summary] = filterLognormalGaussian(data, sigma_cut, makePlot, alpha)
  2. % Fits Gaussians and filters NSC or fraction data
  4. if nargin < 2 || isempty(sigma_cut), sigma_cut = 2; end
  5. if nargin < 3, makePlot = true; end
  6. if nargin < 4, alpha = 0.01; end
  8. % --- Convert input to numeric column vector ---
  9. if iscell(data)
  10. data = cell2mat(data);
  11. end
  12. data = data(:);
  14. if isempty(data)
  15. filtered_data = [];
  16. mu_gauss = NaN;
  17. std_gauss = NaN;
  18. summary = struct();
  19. return
  20. end
  22. if any(data <= 0)
  23. error('All data must be positive for lognormal fitting.');
  24. end
  26. %% Step 1: Fit lognormal
  27. metrics = lognfit(data);
  28. mu_ln = metrics(1);
  29. sigma_ln = metrics(2);
  30. mode_ln = exp(mu_ln - sigma_ln^2);
  32. %% Step 2: Define truncation bounds from PDF height threshold
  33. x = linspace(1e-6, max(data)*2, 5000);
  34. pdf_ln = lognpdf(x, mu_ln, sigma_ln);
  35. max_pdf = max(pdf_ln);
  37. left_bound = x(find(pdf_ln >= alpha*max_pdf, 1, 'first'));
  38. l = mode_ln - left_bound;
  39. right_bound = mode_ln + l;
  41. %% Step 3: Truncate the fitted lognormal curve
  42. mask = (x >= left_bound & x <= right_bound);
  43. x_trunc = x(mask);
  44. pdf_trunc = pdf_ln(mask);
  45. pdf_trunc = pdf_trunc / trapz(x_trunc, pdf_trunc);
  47. %% Step 4: Fit Gaussian to truncated lognormal
  48. mu_gauss = trapz(x_trunc, x_trunc .* pdf_trunc);
  49. var_gauss = trapz(x_trunc, (x_trunc - mu_gauss).^2 .* pdf_trunc);
  50. std_gauss = sqrt(var_gauss);
  52. %% Step 5: Filter actual data by ±sigma_cut * std_gauss
  53. lower_cut = mu_gauss - sigma_cut * std_gauss;
  54. upper_cut = mu_gauss + sigma_cut * std_gauss;
  55. filtered_data = data(data >= lower_cut & data <= upper_cut);
  57. %% Step 6: Prepare summary
  58. summary = struct( ...
  59. 'mu_lognorm', mu_ln, ...
  60. 'sigma_lognorm', sigma_ln, ...
  61. 'mode_lognorm', mode_ln, ...
  62. 'alpha', alpha, ...
  63. 'left_bound', left_bound, ...
  64. 'right_bound', right_bound, ...
  65. 'left_tail_width', l, ...
  66. 'mu_gauss', mu_gauss, ...
  67. 'std_gauss', std_gauss, ...
  68. 'sigma_cut', sigma_cut, ...
  69. 'n_total', numel(data), ...
  70. 'n_kept', numel(filtered_data));
  72. %% Step 7: Plot
  73. if makePlot && ~isempty(filtered_data)
  74. pdf_gauss = normpdf(x, mu_gauss, std_gauss);
  75. figure; hold on
  76. histogram(data, 'Normalization', 'pdf', 'FaceAlpha', 0.3, 'DisplayName', 'Data');
  77. plot(x, pdf_ln, 'r-', 'LineWidth', 1.5, 'DisplayName', 'Lognormal fit');
  78. plot(x_trunc, pdf_trunc * max(pdf_ln) / max(pdf_trunc), 'b-', 'LineWidth', 1.5, 'DisplayName', 'Truncated lognormal');
  79. plot(x, pdf_gauss, 'g--', 'LineWidth', 1.5, 'DisplayName', 'Gaussian fit');
  80. xline(mode_ln, '--r', 'DisplayName', 'Mode');
  81. xline(left_bound, ':k', 'DisplayName', sprintf('Left bound (%.0f%%)', alpha*100));
  82. xline(right_bound, ':k', 'DisplayName', sprintf('Right bound (%.0f%%)', alpha*100));
  83. scatter(filtered_data, zeros(size(filtered_data)), 'k', 'filled', 'DisplayName', 'Kept points');
  84. plot(data,zeros(1,length(data)),'.r','MarkerSize',10,'DisplayName','Original points');
  85. legend show
  86. title(sprintf('Lognormal → Truncated (α=%.3f) → Gaussian Fit → ±%dσ Filter', alpha, sigma_cut))
  87. xlabel('Data values'); ylabel('Probability density');
  88. hold off
  89. end
  91. %% Step 8: Print summary
  92. fprintf('\nLognormal fit: mu = %.3f, sigma = %.3f\n', mu_ln, sigma_ln);
  93. fprintf('Mode = %.3f\n', mode_ln);
  94. fprintf('Truncation bounds: [%.3f, %.3f] (pdf ≈ %.1f%% of max)\n', left_bound, right_bound, alpha*100);
  95. fprintf('Gaussian fit: mean = %.3f, std = %.3f\n', mu_gauss, std_gauss);
  96. fprintf('Kept %d of %d data points inside ±%dσ\n', numel(filtered_data), numel(data), sigma_cut);
  97. end

filterLognormalGaussian.m, under CC-BY-4.0 · at the source

Overview

Authors: Ren-Yi Wang1, Diana-Patricia Danciu2, Filip Z Klawe2, Anna Marciniak-Czochra2,3
ORCID iDs: Anna Marciniak-Czochra
  1. Herbert and Florence Irving Institute for Cancer Dynamics, Columbia University, 1190 Amsterdam Ave, New York, NY 10027, USA
  2. Heidelberg University, Institute for Mathematics, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
  3. Interdisciplinary Center for Scientific Computing (IWR), Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
Institutions: Columbia University (United States); Heidelberg University (Germany)
Journal: iScience, volume 29, issue 9, article 117269
Dates: received 26 February 2026; accepted 23 July 2026; published online 22 August 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1016/j.isci.2026.117269 · PMID 42668621 · PMCID PMC13524777 · OpenAlex W7203979335
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: mouse (organism)
Methods: Connectivity, Physiology & signal measures
Keywords: stem cell dynamics, functional limit theorem, stochastic process, non-linear regulation, fluctuation analysis
Topic: Neurogenesis and neuroplasticity mechanisms (Developmental Neuroscience, Neuroscience), according to OpenAlex
Funding: European Research Council (101071786); German Research Foundation (SFB1324); Columbia University
Citations: not cited yet (Europe PMC); 48 references in the paper

Abstract

Inter-individual heterogeneity is often treated as noise, yet its temporal evolution can reveal regulatory mechanisms hidden from mean-field behavior. We present a stochastic framework that exploits variability for mechanistic inference in cell population dynamics. Using adult neurogenesis as a case study, we develop a state-dependent stochastic model of transitions between quiescent and active states and derive a diffusion approximation for the dynamics of both mean and variance. Applied to repeated cross-sectional data from wild-type and interferon-receptor knockout mice, we show that distinct regulatory mechanisms can produce similar mean dynamics but different fluctuation patterns. Jointly fitting mean and variance identifies proliferation-rate regulation as the dominant contributor to variability, while activation and self-renewal primarily govern average and long-term dynamics. Wild-type mice exhibit regulation of all three processes, whereas knockout mice lose activation control. These results show that population-level variability provides mechanistic information beyond average dynamics and helps distinguish between competing mechanistic models.

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

Repository

Its files are read in the Code ↔ Paper reader above, with 1 match between paragraphs and lines of code.

Zenodo 18399730

License: CC-BY-4.0
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Size: 2 files
Software Heritage: not checked
Found in: “Data and code availability”
Holds: README
Not found: license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Optimization Toolbox (1 file), Statistics and Machine Learning Toolbox (1 file)
Availability: 1 check, the latest on 27 September 2026: the link answers (HTTP 200)
  • 27 September 2026: the link answers (HTTP 200)
26 files
At the source: doi.org/10.5281/zenodo.18399730

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

Tracing map

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What the map holds:

  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 26 scripts, each with its path and the digest of its content;
  • 1 match between paragraphs of the paper and lines of the code (method lexical-v1);
  • 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 and code availability

This paper analyzes existing, publicly available data, accessible at https://doi.org/10.1016/j.cell.2019.01.040 and https://doi.org/10.15252/emmm.202216434.

All original code has been deposited at Zenodo (https://doi.org/10.5281/zenodo.18399730) and will be publicly available as of the date of publication.

Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

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

Versions

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Version 2, 28 September 2026

  • Authors: added Anna Marciniak-Czochra (0000-0002-5831-6505); removed Anna Marciniak-Czochra

Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 4 authors, 5 keywords, 3 funders, 31 references.

Cite

This paper

Wang, R.-Y., Danciu, D.-P., Klawe, F. Z., & Marciniak-Czochra, A. (2026). Harnessing biological variability for mechanistic inference: A stochastic framework applied to neural stem cell dynamics. iScience, 29(9), 117269. https://doi.org/10.1016/j.isci.2026.117269

BibTeX

@article{wang2026harnessing,
author = {Wang, Ren-Yi and Danciu, Diana-Patricia and Klawe, Filip Z and Marciniak-Czochra, Anna},
title = {{Harnessing biological variability for mechanistic inference: A stochastic framework applied to neural stem cell dynamics}},
journal = {iScience},
year = {2026},
month = aug,
volume = {29},
number = {9},
pages = {117269},
publisher = {Elsevier},
issn = {2589-0042},
doi = {10.1016/j.isci.2026.117269},
url = {https://doi.org/10.1016/j.isci.2026.117269},
pmid = {42668621},
pmcid = {PMC13524777}
}

RIS

TY - JOUR
AU - Wang, Ren-Yi
AU - Danciu, Diana-Patricia
AU - Klawe, Filip Z
AU - Marciniak-Czochra, Anna
TI - Harnessing biological variability for mechanistic inference: A stochastic framework applied to neural stem cell dynamics
T2 - iScience
J2 - iScience
PY - 2026
DA - 2026/08/22
VL - 29
IS - 9
SP - 117269
SN - 2589-0042
PB - Elsevier
DO - 10.1016/j.isci.2026.117269
UR - https://doi.org/10.1016/j.isci.2026.117269
LA - en
ER -

CSL-JSON

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