Investigating key cell types and molecules dynamics in PyMT mice model of breast cancer through a mathematical model

Abstract

The most common kind of cancer among women is breast cancer. Understanding the tumor microenvironment and the interactions between individual cells and cytokines assists us in arriving at more effective treatments. Here, we develop a data-driven mathematical model to investigate the dynamics of key cell types and cytokines involved in breast cancer development. We use time-course gene expression profiles of a mouse model to estimate the relative abundance of cells and cytokines. We then employ a least-squares optimization method to evaluate the model's parameters based on the mice data. The resulting dynamics of the cells and cytokines obtained from the optimal set of parameters exhibit a decent agreement between the data and predictions. We perform a sensitivity analysis to identify the crucial parameters of the model and then perform a local bifurcation on them. The results reveal a strong connection between adipocytes, IL6, and the cancer population, suggesting them as potential targets for therapies.

Fig 1. Interaction network.

Diagram of interactions between different cell types and molecules in breast tumors for the mouse model, as it has been modeled in this paper. Variables of the model with their descriptions are given in Table 1.

Fig 2. Immune cell frequencies for each mouse at different time points.

Results acquired from deconvolution of gene expression data at each time point using CIBERSORTx B-mode.

Fig 3. Comparison of the dynamics and mouse data.

By solving the system of ODEs, the mouse data are compared to the values estimated using the optimal parameters obtained from the least-squares optimization. Time zero corresponds to 6 weeks which is the beginning of the mice data sampling.

Fig 4. Sensitivity results.

Sensitivity levels of the top 6 most sensitive parameters for cancer and total number of cells.

Fig 5. Sensitivity results.

Other sensitive parameters for cancer and total number of cells.

Fig 6. Varying dynamics.

The transparent regions are acquired by 20% perturbation of all the sensitive parameters in Figs 4 and 5.

Fig 7. Bifurcation plots.

Bifurcation of cancer values after 12 weeks with respect to the most sensitive parameters in Fig 4, namely (a)δ_C (b) λ_C (c) λ_CA (d) ${\lambda }_{CI{L}_6}$ (e) δ_A and (f) λ_A.