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Nonlinear time-delay dynamical model of oscillatory gene expression in BMP-4/9 vascular endothelial cell network


Bone morphogenic proteins (BMPs) and their inhibitors are increasingly being appreciated for their role in vascular development. Matrix Gla protein (MGP) and crosssveinless 2 (CV2) antagonize BMP-4 and BMP-9, respectively, and the expression of both are stimulated by time-delayed BMP-9/ALK1 signaling, while ALK1 is stimulated by delayed BMP-4 signaling. This double negative feedback system is an important regulator of endothelial cell differentiation, angiogenesis, and maturation. Our collaborators recently discovered oscillatory gene expression of these proteins in human pulmonary artery endothelial cells (HPAECs) undergoing maturation in cell culture. We set out to explore the biological mechanisms guiding this periodic gene expression and to propose a functional role for these oscillations.

We used delay differential equations to mathematically model this network and applied dimensionless analysis to study the impact of relative protein degradation rates on oscillations. Monte Carlo parameter sampling and Hopf bifurcation analysis, while adjusting 1 and 2 parameters, helped identify conditions yielding periodic dynamics. We discovered that the presence of the activator, BMP-4, is critical for oscillations and that its inhibitor, MGP, opposes them, making their mutual regulation important for oscillatory gene expression. We also identified other mechanisms for oscillations including the necessary existence of three time-delays, the presence of BMP-9 as a feedback regulator, and the function of CV2 as an indirect inhibitor of MGP. Findings from the cell culture experiments and the mathematical model led us to postulate that oscillations in this network are important for the maintenance of progenitor HPAECs and the lack of oscillations is associated with HPAEC maturation.

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