Rigidity of epithelial tissues as a double optimization problem
Data files
Feb 05, 2025 version files 20.56 KB
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data_fig1_inset.csv
2.84 KB
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data_fig1_main.csv
6.60 KB
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figure_2_inset.csv
892 B
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figure_2_main.csv
927 B
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figure_3a.csv
1.68 KB
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figure_3b.csv
1.77 KB
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README.md
5.85 KB
Abstract
This dataset contains numerical values extracted from simulations of vertex models, supporting the analysis of epithelial tissue mechanics presented in the associated manuscript (Physical Review Research, in preparation). The data provides key mechanical properties such as the shear modulus, computed for different simulation conditions. It is organized to enable straightforward reproduction of the figures in the main text while facilitating further analysis and reuse in studies of rigidity transitions and tissue mechanics. The dataset structure includes tabulated values for each figure in the manuscript. Full methodological details, including simulation protocols, parameter choices, and analysis techniques, can be found in the manuscript.
README: Rigidity of epithelial tissues as a double optimization problem
Authors: S. Arzash, I. Tah, A. J. Liu, M. L. Manning
This dataset can be used to reproduce the figures in the corresponding manuscript, in preparation for publication in the Physical Review Research. It contains quantities derived from ensembles of simulated vertex models, which were used to analyze the mechanical properties of epithelial tissues. The simulations involve minimizing the system's elastic energy with respect to either cell vertex positions (physical degrees of freedom) or both vertex positions and additional tunable parameters, such as target cell shapes. For each sample, the shear modulus was computed using linear response theory. Detailed methods and analyses are provided in the associated manuscript.
Description of Dataset and Files
Each CSV file contains specific datasets that support figures and analyses presented in the manuscript. Below, you will find a detailed description of each file, including its structure and how it relates to the findings in the manuscript.
1. data_fig1_main.csv
- Purpose: This file contains the main data used to generate the primary plot of Figure 1.
- Columns:
p0_T0Swap0
: The preferred cell shape index values.mean_shear_modulus_T0Swap0
: The mean shear modulus corresponding top0_T0Swap0
for a vertex model minimized with respect to only cell vertex positions.p0_T0Swap1e4
: The preferred cell shape index values, same asp0_T0Swap0
.mean_shear_modulus_T0Swap1e4
: The mean shear modulus corresponding top0_T0Swap1e4
for a vertex model after 1e4 zero-temperature swap Monte Carlo moves over p0 degrees of freedom.
- Context: This data demonstrates the variation of the shear modulus (G) as a function of the preferred cell shape index (p0) for different conditions.
2. data_fig1_inset.csv
- Purpose: This file contains data used for the inset plot of Figure 1.
- Columns:
p0_diff_T0Swap0
: Difference between critical p0 and current p0 values for a vertex model minimized with respect to only cell vertex positions.mean_shear_modulus_diff_T0Swap0
: Mean shear modulus for a vertex model minimized with respect to only cell vertex positions.p0_diff_T0Swap1e4
: Difference between critical p0 and current p0 values for a vertex model after 1e4 zero-temperature swap Monte Carlo moves over p0 degrees of freedom.mean_shear_modulus_diff_T0Swap1e4
: Mean shear modulus for a vertex model after 1e4 zero-temperature swap Monte Carlo moves over p0 degrees of freedom.
- Context: This dataset explores the scaling behavior of the shear modulus near the critical point.
3. figure_2_main.csv
- Purpose: Contains the primary data used to plot Figure 2.
- Columns:
ConstList
: List of constraint numbers applied to the tunable degrees of freedom.N400_delta_p0_critical_mean_p0
: Mean shift in the critical p0 value for a system with 400 cells.N400_delta_p0_critical_std_p0
: Standard deviation of the shift in critical p0 for a system with 400 cells.- Additional columns follow the same pattern for
ka
,kp
, anda0
.
- Context: This data illustrates the effect of varying constraints on the rigidity transition.
4. figure_2_inset.csv
- Purpose: Data used for the inset plot of Figure 2.
- Columns:
NList
: List of system sizes (number of cells).delta_p0_critical_mean_p0
: Mean shift in the critical p0 value as a function of system size.delta_p0_critical_std_p0
: Standard deviation of the shift in critical p0.- Additional columns follow the same pattern for
ka
,kp
, anda0
.
- Context: Highlights finite-size effects on the shift in the rigidity transition point.
5. figure_3a.csv
- Purpose: Data used for part (a) of Figure 3.
- Columns:
std_list
: Standard deviations of the p0 distribution.p0_critical_only_physical_mean
: Mean critical p0 values for the vertex model minimized with respect to only cell vertex positions.p0_critical_only_physical_error
: Standard error of the critical p0 values for the vertex model minimized with respect to only cell vertex positions.- Additional columns provide similar data for the vertex model after 1e4 zero-temperature swap Monte Carlo moves over p0 degrees of freedom and delta values.
- Context: Demonstrates the relationship between distribution width (std) and the critical rigidity transition point.
6. figure_3b.csv
- Purpose: Data used for part (b) of Figure 3.
- Columns:
std_list_a0
: Standard deviations of target cell areas.p0_critical_only_physical_mean_a0
: Mean critical p0 values for the vertex model minimized with respect to only cell vertex positions.p0_critical_only_physical_error_a0
: Standard error of the critical p0 values for the vertex model minimized with respect to only cell vertex positions.- Additional columns provide similar data for the vertex model after 1e4 zero-temperature swap Monte Carlo moves over a0 degrees of freedom and delta values.
- Context: Explores how heterogeneity in target areas impacts the rigidity transition.
References
- Corresponding publication: Arzash, S., Tah, I., Liu, A. J., Manning, M. L., PRR, (2024);
- Dataset citation: Arzash, S., Tah, I., Liu, A. J., Manning, M. L., PRR, (2024). Rigidity of Epithelial Tissues as a Double Optimization Problem: https://doi.org/10.5061/dryad.k6djh9whr
Plotting Software
The attached Python Notebook can be used to load and plot the data from the CSVs. For ease of use and readability, some functionality is achieved by commenting or un-commenting small blocks of code. The script is commented to describe how the data is loaded, organized, and plotted.
Methods
The data were generated from large ensembles of tissue simulations using the vertex model framework. The open-source code cellGPU was employed for running the simulations in C++. Statistical quantities were subsequently computed in Python, utilizing scientific computing libraries such as NumPy and SciPy. These quantities were processed and exported to CSV files to facilitate ease of access and analysis.