Multiscale model of the different modes of cancer cell invasion

Abstract

Motivation: Mathematical models of biological processes altered in cancer are built using the knowledge of complex networks of signaling pathways, detailing the molecular regulations inside different cell types, such as tumor cells, immune and other stromal cells. If these models mainly focus on intracellular information, they often omit a description of the spatial organization among cells and their interactions, and with the tumoral microenvironment.

Results: We present here a model of tumor cell invasion simulated with PhysiBoSS, a multiscale framework, which combines agent-based modeling and continuous time Markov processes applied on Boolean network models. With this model, we aim to study the different modes of cell migration and to predict means to block it by considering not only spatial information obtained from the agent-based simulation but also intracellular regulation obtained from the Boolean model.

Our multiscale model integrates the impact of gene mutations with the perturbation of the environmental conditions and allows the visualization of the results with 2D and 3D representations. The model successfully reproduces single and collective migration processes and is validated on published experiments on cell invasion. In silico experiments are suggested to search for possible targets that can block the more invasive tumoral phenotypes.

Availability and implementation: https://github.com/sysbio-curie/Invasion_model_PhysiBoSS.

Figure 1.

Influence network of the intracellular model, illustrating the intricate interplay between genes, proteins, inputs, and outputs. Rectangular nodes at the top represent inputs, while rectangular nodes at the bottom depict outputs (or phenotypic read-outs). Notably, the figure reveals the presence of highly connected nodes, characterized by a high number of incoming and outgoing arrows, highlighting the complexity and interconnectedness of the pathways involved.

Figure 2.

The 3D representation of the simulation. For (A) and (B), different values of the parameters have been used to reproduce single (black arrows) and collective cell migration (white arrows). More details about the quantification of single and collective migration are given in Supplementary Section S13. The color bar represents the amount of cell junction used to establish cellular adhesion. (A) cell_ecm_repulsion =10, epith_cell_junction_attach =0.5, mes_cell_junction_detach =0.03, migration_bias =0.9, migration_speed =0.8. (B) cell_ecm_repulsion =15, cell_junction_attach =0.005, cell_junction_detach =0.001, migration_bias =0.8, migration_speed =0.7.

Figure 3.

Reproduction of the p63 knockin/knockout experiment from Lodillinsky et al. (2021). The color of the ECM (blue gradient) shows its local density. The initial conditions are the same for both simulations (left panel): Oxygen =1, Growth_factor =1, Neighbor =1, ECM =1, TGFbeta =1, and DNAdamage =0. In p63 overexpression condition (upper middle panel), the ECM can be degraded with the MMPs ON and shows tumor expansion at the cell population level. The intracellular model (right upper panel) shows the two phenotypes: ECM_degrad and EMT ON. In p63 knockout condition (lower middle panel), the MMPs cannot be released leading to the inhibition of the ECM degradation phenotype. The intracellular model (right lower panel) shows that the cell has undergone EMT but is unable to degrade the ECM, which is interpreted at the population level as tumor confinement. Cell density analysis confirms that in a condition of p63 overexpression, the area occupied by the tumor increases, decreasing the cell density. On the other hand, inhibition of p63 decreases the area occupied by the tumor, increasing cell density (Supplementary Section S9 and Supplementary Fig. S7).

Figure 4.

Reproduction of the SRC experiments. (A) Experimental results of SRC activation at different time points from Moitrier et al. (2019). The blue circle indicates the area of the blue light activation. After 33 h, the light source is removed, reversing the collective extrusion phenotype. (B) Model simulation in 2D of the SRC experiments. We introduced a substrate that simulates the light in the middle of the epithelial monolayer (blue cells) trapped in the ECM (grey voxels). The white voxels correspond to space where the ECM has been degraded. The substrate virtually interacts with cells with a SRC activating mutation. The cells undergo EMT and become mesenchymal (green cells), trying to migrate and forming aggregates. When the substrate is removed, the mesenchymal cells return epithelials. SRC is found active at the borders of the monolayer in contact with ECM.