Mechanistic characterization of endothelial sprouting mediated by pro-angiogenic signaling

Abstract

Objective: We aim to quantitatively characterize the crosstalk between VEGF- and FGF-mediated angiogenic signaling and endothelial sprouting, to gain mechanistic insights and identify novel therapeutic strategies.

Methods: We constructed an experimentally validated hybrid agent-based mathematical model that characterizes endothelial sprouting driven by FGF- and VEGF-mediated signaling. We predicted the total sprout length, number of sprouts, and average length by the mono- and co-stimulation of FGF and VEGF.

Results: The experimentally fitted and validated model predicts that FGF induces stronger angiogenic responses in the long-term compared with VEGF stimulation. Also, FGF plays a dominant role in the combination effects in endothelial sprouting. Moreover, the model suggests that ERK and Akt pathways and cellular responses contribute differently to the sprouting process. Last, the model predicts that the strategies to modulate endothelial sprouting are context-dependent, and our model can identify potential effective pro- and anti-angiogenic targets under different conditions and study their efficacy.

Conclusions: The model provides detailed mechanistic insight into VEGF and FGF interactions in sprouting angiogenesis. More broadly, this model can be utilized to identify targets that influence angiogenic signaling leading to endothelial sprouting and to study the effects of pro- and anti-angiogenic therapies.

Keywords: agent-based model; angiogenesis; cell signaling; endothelial cell; sprouting.

FIGURE 1

Endothelial spheroid sprouting process. (A) Activated endothelial cells become tip cells and start to migrate and the stalk cells behind tip cells are proliferative. Finally, the endothelial cells sprout into linear cord‐like structures. (B) The sprouting process involves tip cell migration, stalk cell proliferation, and elongation. (C) Growth factors, FGF and VEGF, binding to their receptors initiate intracellular signaling and regulate cellular responses in all endothelial cells

FIGURE 2

Flowchart of the endothelial sprouting agent‐based model. The model simulates each endothelial cell as one agent that has its own properties and makes its own cellular decisions in every time step

FIGURE 3

Model comparison to training and validation data for FGF or VEGF stimulation. (A) Relative change of endothelial cell proliferation for 10⁴ cells cultured for 48 h in response to 0.01–30 ng/ml FGF stimulation compared with the reference FGF concentration of 1 ng/ml. (B) Relative change of endothelial cell proliferation for 5000 cells cultured for 48 h by the stimulation of 0.1–10 ng/ml VEGF, compared with the reference VEGF concentration of 1 ng/ml. (C) Total sprout length induced by 0–64 ng/ml VEGF for 24 h cultured with 500‐cell spheroid initially. (D) The fold change of the average length and number of sprouts induced by 25 ng/ml FGF and 25 ng/ml VEGF for 24 h cultured with 400‐cell spheroid initially compared to the control. Circles, squares, and diamonds in Panels A–C are experimental data., , , Circles in Panel A, squares in Panels A and B, and diamonds in Panel C are experimental data from West et al., Jih et al., and Heiss et al., respectively. The light yellow circles and light blue squares in Panels A, B are experimental data used for model fitting. The orange circles and squares and dark blue squares are experimental data used for model validation. Curves in Panels A, B and C are the mean model predictions of the 21 and 18 best fits, respectively. Shaded regions show standard deviation of the fits. Solid and dashed bars in Panel D are mean ± standard deviation of Liebler et al. data and model predictions, respectively

FIGURE 4

Predicted sprouting responses stimulated by single agents. Response to FGF stimulation, left panels: Predicted TL (μm) (A), NS (C), and AL (μm) (E) stimulated by low, intermediate, and high levels of FGF. Response to VEGF stimulation, right panels: Predicted TL (μm) (B), NS (D), and AL (μm) (F) stimulated by low, intermediate, and high levels of VEGF. 250‐, 500‐, and 750‐cell spheroid sprouting responses when simulated for 1, 2, and 3 days. Bars are mean model prediction + standard deviation of 18 best fits

FIGURE 5

Predicted sprouting responses in response to FGF and VEGF co‐stimulation. Co‐stimulation of FGF‐ and VEGF‐induced TL (μm) on Day 1 (A), Day 2 (D), and Day 3 (G); NS on Day 1 (B), Day 2 (E), and Day 3 (H); and AL (μm) on Day 1 (C), Day 2 (F), and Day 3 (I)

FIGURE 6

Predicted r_cp , r_sg , and p in response to mono‐ and co‐stimulation of FGF and VEGF. Effects of mono‐stimulation of FGF (yellow) or VEGF (blue) on r_cp (A), r_sg (B), and p (C). Effects of co‐stimulation of FGF and VEGF on r_cp (D), r_sg (E), and p (F). Curves in Panels A–C are the mean model predictions of 18 best fits. Shaded regions show standard deviation of the fits

FIGURE 7

The contributions of MAPK and PI3K/Akt pathways to r_cp and r_sg in response to FGF and VEGF mono‐stimulation. Contributions of pERK (purple), pAkt (green), and basal (gray) for FGF‐induced rates of cell proliferation, r_cp (A) and sprout growth, r_sg (C). Contributions of pERK (purple), pAkt (green), and basal (gray) for VEGF‐induced cell proliferation, r_cp (B) and sprout growth, r_sg (D)

FIGURE 8

Predicted representative targets for modulating r_cp and r_sg . Predicted r_cp (A) and r_sg (D) from baseline model. Predicted r_cp (B) and r_sg (E) when ERK is varied by 0.1‐ (left) and 10‐fold (right). Predicted r_cp (C) and r_sg (F) when Akt is varied by 0.1‐ (left) and 10‐fold (right)

FIGURE 9

Predicted effects of varying ERK. Predicted TL (A), NS (B), and AL (C) when ERK is varied by 0.1‐ (left) and 10‐fold (right), compared with baseline model predictions (middle) on days 1–3 (i–iii)

FIGURE 10

Predicted effects of varying Akt. Predicted TL (μm) (A), NS (B), and AL (μm) (C) when Akt is varied by 0.1‐ (left) and 10‐fold (right), compared with baseline model predictions (middle) on days 1–3 (i–iii)