Modeling cellular self-organization in strain-stiffening hydrogels

This Python software repository contains the code to reproduce data and images from

Modeling cellular self-organization in strain-stiffening hydrogels

by A. H. Erhardt, D. Peschka, C. Dazzi, L. Schmeller, A. Petersen, S. Checa, A. Münch, B. Wagner

published in Computational Mechanics (Springer, online 2024). 10.1007/s00466-024-02536-7.

The preprint is available here in bioRxiv here 10.1101/2023.12.21.572812.

Abstract: We derive a three-dimensional hydrogel model as a two-phase system of a fibre network and liquid solvent, where the nonlinear elastic network accounts for the strain-stiffening properties typically encountered in biological gels. We use this model to formulate free boundary value problems for a hydrogel layer that allows for swelling or contraction. We derive two-dimensional plain-strain and plain-stress approximations for thick and thin layers respectively, that are subject to external loads and serve as a minimal model for scaffolds for cell attachment and growth. For the collective evolution of the cells as they mechanically interact with the hydrogel layer, we couple it to an agent-based model that also accounts for the traction force exerted by each cell on the hydrogel sheet and other cells during migration. We develop a numerical algorithm for the coupled system and present results on the influence of strain-stiffening, layer geometry, external load and solvent in/outflux on the shape of the layers and on the cell patterns. In particular, we discuss alignment of cells and chain formation under varying conditions.

Dependencies: Requires Python with legacy FEniCS 2019.1.0 and some standard libraries for plotting and data processing.

Figure: Single horizontal cell pulling on an elastic Gent-type material. The shading shows the corresponding solvent concentration.

Hydrogel and cell coupling

Folder: ./abm_hydrogel

Data: Generates data for Fig. 12,13,14,15,16 in the manuscript.

Usage: With each of the json files in the folder run the command

python3 main_ABM_Allen_Cahn_Hilliard.py JSONFILENAME.json

to generate the corresponding data in an output folder. Then use the ... to generate the output.

ABM single and double cell interaction

Folder: ./abm_interaction

Data: Generates data for Fig. 17,18,19 in the manuscript.

Usage: With each of the json files in the folder run the command

python3 main_interaction.py JSONFILENAME.json

to generate the corresponding data or directly run the Linux run0.sh and run1.sh shell script. Similarly use

python3 main_plotter.py JSONFILENAME.json and python3 main_plotter_stretch.py JSONFILENAME.json to generate the corresponding output files in the undeformed and deformed configuration, respectively.

Pure elastic material and hydrogel (no cells)

Folder: ./elastic_hydrogel

Data: Generates data for Fig. 6,7,8,9 in the manuscript.

Usage: With each of the json files in the folder run the command

python3 main_stretching_Allen_Cahn_Hilliard.py JSONFILENAME.json

to generate the corresponding output data. Some intermediate ouput data is creater by running python3 main_stretching_postprocessing.py. Finally, call python3 plot_fig_{6,7,8,9}.py to generate the corresponding plot in the manuscript.

Highly resolved single cells

Folder: ./highres_singlecell

Data: Generates data for Fig. 20 in the manuscript.

Usage: With each of the json files in the folder run the command

python3 main_singlecell.py JSONFILENAME.json

or the corresponding Linux shell script run.sh. Then run python3 main_plothighlight.py JSONFILENAME.json or the corresponding shell script gen_plots.sh to generate the figure.