Multiscale coupled modeling of Plexin-D1 and notch signaling in retinal sprouting angiogenesis
We present a hybrid (continuous and discrete) mathematical model to simulate the morphological and signaling features observed in the postnatal development of the mouse retinal vascular network. We solve numerically a multiscale differential system consisting of two parts: macro and micro; and analyze its solutions for different values of the sensitivity coefficients. These results provide information regarding the mechanism of how VEGF-Notch signaling system directs the formation of morphological features in the retina, including the development of retinal vascularization, plexus density, and plexus irregularity. Additionally, we use this model to predict how crosstalk molecules signal to the VEGF-Notch axis to modulate various vascular phenotypes. We obtain analytical expressions of the differences in the steady-state solutions of a simplified two-cell signaling system. We investigate in particular the stabilizing effect of Plexin-D1 on the VEGF-Notch micro-system. This work provides an insight into the molecular mechanism of retinal sprouting angiogenesis and can help identify potentially synergistic therapeutic approaches.
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