Model Predicts Distinct Mechanisms of Endothelial Cell Growth Upon the Stimulation of FGF and VEGF

Angiogenesis is the formation of new blood capillaries from pre-existing ones. The essential role of blood vessels in delivering nutrients makes angiogenesis important in the survival of tissues, such as wound healing process and tumor growth. Thus, targeting angiogenesis is a prominent strategy in both tissue engineering and cancer treatment. However, not all approaches to target angiogenesis lead to successful outcomes. Current therapies primarily target pro-angiogenic factors such as vascular endothelial growth factor (VEGF) and fibroblast growth factor (FGF) in isolation. However, there is a limited understanding of how these promoters combine together to stimulate angiogenesis. We aim to quantitatively characterize the crosstalk between VEGF- and FGF-mediated angiogenic signaling in endothelial cells and the effects of the interactions on a cellular level, specifically endothelial cell growth, in order to identify novel therapeutic strategies. We constructed a hybrid agent-based mathematical model that characterizes endothelial cell growth driven by FGF and VEGF-mediated signaling. The molecular interactions were implemented with our published ordinary differential equation model that focuses on FGF- and VEGF-induced mitogen-activated protein kinase (MAPK) signaling and the phosphatidylinositol 3-kinase/protein kinase B (PI3K/Akt) pathway which promote cell survival and proliferation. To link the molecular signals with the cellular responses, we assumed that the endothelial cell growth is dependent on the maximum pAkt and pERK levels upon the stimulation of FGF and VEGF within two hours, following Hill functions. We used the total number of endothelial cells as an indicator of cell growth. Cell heterogeneity within a cell population is also considered in the model. The parameters that significantly influence cell growth rate were identified using a global sensitivity analysis and estimated by fitting the model to experimental data using particle swarm optimization. The model was validated against independent experimental data. The trained and validated model predicts the optimal concentrations for mono- and co-stimulation of FGF and VEGF needed to maximize endothelial cell growth. Also, FGF and VEGF show different mechanisms in promoting the overall cell growth rate. Additionally, combinations of FGF and VEGF do not exhibit an obvious greater effect in promoting cell growth compared to FGF stimulation alone. Moreover, our model identifies the influential species and kinetic parameters that specifically modulate the cell growth, which represent potential targets for modulating angiogenesis signaling. The model provides mechanistic insight into VEGF and FGF interactions in angiogenesis and predicts the combination effects of FGF and VEGF co-stimulation. More broadly, this model can be utilized to identify targets that influence angiogenic signaling leading to cell growth and to study the effects of pro- and anti-angiogenic therapies.