Universality in the mechanical behavior of vertex models for biological tissues
Data files
Jul 08, 2025 version files 1.32 MB
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data_fig1a.csv
7.47 KB
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data_fig1b.csv
7.64 KB
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data_fig2d_inset.csv
1.92 KB
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data_fig2d.csv
5.04 KB
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data_fig3c.csv
7.60 KB
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data_fig3d.csv
7.70 KB
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data_fig4a_inset.csv
609 B
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data_fig4a.csv
2.06 KB
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data_fig4b.csv
2.08 KB
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data_fig5e_inset.csv
493 B
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data_fig5e.csv
1.08 KB
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plot_data.ipynb
1.27 MB
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README.md
9 KB
Abstract
This dataset contains numerical simulation results. The dataset includes tabulated mechanical observables, such as the static shear modulus, storage modulus G', and loss modulus G'', computed for distinct vertex models under varying geometric and mechanical parameters. These include the standard vertex model, active foam model, spring-edge model, and dynamical vertex models with internal degrees of freedom. The data is organized to directly reproduce figures from the main text. The Jupyter notebook demonstrates how to load, process, and visualize this data. This repository is intended to support both the direct reproduction of published figures and enable further comparative studies of mechanical responses in vertex-based models of biological tissues. Detailed simulation protocols and modeling assumptions are provided in the associated manuscript.
Authors: O. K. Damavandi*, S. Arzash*, E. Lawson-Keister, M. L. Manning
*These authors contributed equally to this work.
Corresponding publication: PRX Life (2025)
DOI: https://doi.org/10.1103/9ktk-6rqc
This dataset supports the figures and analysis in the paper Universality in the Mechanical Behavior of Vertex Models for Biological Tissues. It contains simulation outputs for various vertex models used to probe the zero-strain-rate shear modulus, frequency-dependent viscoelastic moduli, and model universality. Each CSV file corresponds to one or more figure panels in the main text. A Jupyter notebook (plot_data.ipynb) is included for reproducing the figures.
Description of Dataset and Files
1. data_fig1a.csv
Purpose: Contains viscoelastic moduli for the standard vertex model in the solid regime (target shape factors (p_0 = 3.4) and (p_0 = 3.6)).
Columns:
Omega_list: Frequency of applied oscillatory strain ((\omega)).G_prime_p034_mean: Mean storage modulus (G') for (p_0 = 3.4).G_prime_p034_std: Standard deviation of (G') for (p_0 = 3.4).G_double_prime_p034_mean: Mean loss modulus (G'') for (p_0 = 3.4).G_double_prime_p034_std: Standard deviation of (G'') for (p_0 = 3.4).G_prime_p036_mean: Mean storage modulus (G') for (p_0 = 3.6).G_prime_p036_std: Standard deviation of (G') for (p_0 = 3.6).G_double_prime_p036_mean: Mean loss modulus (G'') for (p_0 = 3.6).G_double_prime_p036_std: Standard deviation of (G'') for (p_0 = 3.6).
2. data_fig1b.csv
Purpose: Contains viscoelastic moduli for the standard vertex model in the fluid regime ((p_0 = 4.0) and (p_0 = 4.2)).
Columns:
Omega_list: Frequency of applied oscillatory strain ((\omega)).G_prime_p04_mean: Mean storage modulus (G') for (p_0 = 4.0).G_prime_p04_std: Standard deviation of (G') for (p_0 = 4.0).G_double_prime_p04_mean: Mean loss modulus (G'') for (p_0 = 4.0).G_double_prime_p04_std: Standard deviation of (G'') for (p_0 = 4.0).G_prime_p042_mean: Mean storage modulus (G') for (p_0 = 4.2).G_prime_p042_std: Standard deviation of (G') for (p_0 = 4.2).G_double_prime_p042_mean: Mean loss modulus (G'') for (p_0 = 4.2).G_double_prime_p042_std: Standard deviation of (G'') for (p_0 = 4.2).
3. data_fig2d.csv
Purpose: Contains frequency-dependent viscoelastic moduli for the confluent active foam model, for two different values of interfacial tension (\Lambda).
Columns:
Omega_list: Frequency of applied oscillatory strain ((\omega)).G_prime_tension_01_mean: Mean (G') for (\Lambda = 0.1).G_prime_tension_01_std: Standard deviation of (G') for (\Lambda = 0.1).G_double_prime_tension_01_mean: Mean (G'') for (\Lambda = 0.1).G_double_prime_tension_01_std: Standard deviation of (G'') for (\Lambda = 0.1).G_prime_tension_001_mean: Mean (G') for (\Lambda = 0.01).G_prime_tension_001_std: Standard deviation of (G') for (\Lambda = 0.01).G_double_prime_tension_001_mean: Mean (G'') for (\Lambda = 0.01).G_double_prime_tension_001_std: Standard deviation of (G'') for (\Lambda = 0.01).
4. data_fig2d_inset.csv
Purpose: Provides zero-frequency shear modulus (G) as a function of interfacial tension (\Lambda) for the active foam model.
Columns:
Tension_list: Values of line tension (\Lambda).G_mean: Mean zero-frequency shear modulus (G).G_std: Standard deviation of (G) across samples.
5. data_fig3c.csv
Purpose: Viscoelastic moduli for the spring-edge vertex model in the solid-like regime ( rest lengths (l_0 = 0.4) and (l_0 = 0.6)).
Columns:
Omega_list: Frequency of applied oscillatory strain ((\omega)).G_prime_l0_04_mean: Mean storage modulus (G') for (l_0 = 0.4).G_prime_l0_04_std: Standard deviation of (G') for (l_0 = 0.4).G_double_prime_l0_04_mean: Mean loss modulus (G'') for (l_0 = 0.4).G_double_prime_l0_04_std: Standard deviation of (G'') for (l_0 = 0.4).G_prime_l0_06_mean: Mean storage modulus (G') for (l_0 = 0.6).G_prime_l0_06_std: Standard deviation of (G') for (l_0 = 0.6).G_double_prime_l0_06_mean: Mean loss modulus (G'') for (l_0 = 0.6).G_double_prime_l0_06_std: Standard deviation of (G'') for (l_0 = 0.6).
6. data_fig3d.csv
Purpose: Viscoelastic moduli for the spring-edge vertex model in the fluid-like regime ( rest lengths (l_0 = 0.75) and (l_0 = 0.8)).
Columns:
Omega_list: Frequency of applied oscillatory strain ((\omega)).G_prime_l0_075_mean: Mean storage modulus (G') for (l_0 = 0.75).G_prime_l0_075_std: Standard deviation of (G') for (l_0 = 0.75).G_double_prime_l0_075_mean: Mean loss modulus (G'') for (l_0 = 0.75).G_double_prime_l0_075_std: Standard deviation of (G'') for (l_0 = 0.75).G_prime_l0_08_mean: Mean storage modulus (G') for (l_0 = 0.8).G_prime_l0_08_std: Standard deviation of (G') for (l_0 = 0.8).G_double_prime_l0_08_mean: Mean loss modulus (G'') for (l_0 = 0.8).G_double_prime_l0_08_std: Standard deviation of (G'') for (l_0 = 0.8).
7. data_fig4a.csv
Purpose: Frequency-dependent viscoelastic moduli for the active spring model, for two different waiting times tw in the solid-like regime.
Columns:
Omega_list: Frequency of applied oscillatory strain ((\omega)).G_prime_tw_num_0_mean,G_prime_tw_num_0_std: Mean and standard deviation of storage modulus (G') at short (t_w) highlighted in the inset.G_double_prime_tw_num_0_mean,G_double_prime_tw_num_0_std: Mean and standard deviation of loss modulus (G'') at short (t_w) highlighted in the inset.G_prime_tw_num_1_mean,G_prime_tw_num_1_std: Mean and standard deviation of storage modulus (G') at a slightly larger (t_w) highlighted in the inset.G_double_prime_tw_num_1_mean,G_double_prime_tw_num_1_std: Mean and standard deviation of loss modulus (G'') at a slightly larger (t_w) highlighted in the inset.
8. data_fig4a_inset.csv
Purpose: Time evolution of moduli at fixed small frequency to show fluidization trend in active spring model.
Columns:
Tw_list: Waiting times.G_prime_omega_num_0_mean: Mean storage modulus at low frequency.G_double_prime_omega_num_0_mean: Mean loss modulus.
9. data_fig4b.csv
Purpose: Frequency-dependent viscoelastic moduli for the active spring model, for two different waiting times tw in the fluid-like regime.
Columns:
Omega_list: Frequency of applied oscillatory strain ((\omega)).G_prime_tw_num_9_mean,G_prime_tw_num_9_std: Mean and standard deviation of storage modulus (G') at long (t_w) highlighted in the inset.G_double_prime_tw_num_9_mean,G_double_prime_tw_num_9_std: Mean and standard deviation of loss modulus (G'') at long (t_w) highlighted in the inset.G_prime_tw_num_10_mean,G_prime_tw_num_10_std: Mean and standard deviation of storage modulus (G') at a slightly larger (t_w) highlighted in the inset.G_double_prime_tw_num_10_mean,G_double_prime_tw_num_10_std: Mean and standard deviation of loss modulus (G'') at a slightly larger (t_w) highlighted in the inset.
10. data_fig5e.csv
Purpose: Frequency-dependent viscoelastic moduli for the active tension network at long waiting time tw.
Columns:
Omega_list: Frequency of applied oscillatory strain ((\omega)).G_prime_mean,G_prime_std: Mean and standard deviation of storage modulus (G') at long (t_w) highlighted in the inset.G_double_prime_mean,G_double_prime_std: Mean and standard deviation of loss modulus (G'') at long (t_w) highlighted in the inset.
11. data_fig5e_inset.csv
Purpose: Time evolution of moduli at fixed small frequency in the active tension network.
Columns:
Tw_list: Waiting times.G_prime_omega_num_0_mean: Mean storage modulus at low frequency.G_double_prime_omega_num_0_mean: Mean loss modulus at low frequency.
Plotting Software
The Python notebook plot_data.ipynb can be used to load the CSV files and reproduce all figures listed above.
Key libraries: pandas, numpy, matplotlib.
Reference
Corresponding publication:
Damavandi*, O. K., Arzash*, S., Lawson-Keister, E., Manning, M.L.
Universality in the Mechanical Behavior of Vertex Models for Biological Tissues, PRX Life (2025).
DOI: https://doi.org/10.1103/9ktk-6rqc
Dataset citation:
Damavandi*, O. K., Arzash*, S., Lawson-Keister, E., Manning, M.L. (2025).
Universality in the Mechanical Behavior of Vertex Models for Biological Tissues. Dryad Digital Repository.
https://doi.org/10.5061/dryad.qbzkh18w9