DOI: 10.5061/dryad.k6djh9whr
title: Rigidity of epithelial tissues as a double optimization problem

description: 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.
description: 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.
description: # 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 to
 `p0_T0Swap0` for a vertex model minimized with respect to only cell vertex
 positions. * `p0_T0Swap1e4`: The preferred cell shape index values, same
 as `p0_T0Swap0`. * `mean_shear_modulus_T0Swap1e4`: The mean shear modulus
 corresponding to `p0_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`, and `a0`. *
 **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`, and `a0`.
 * **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.