A multiscale model of complex endothelial cell dynamics in early angiogenesis

Abstract

We introduce a hybrid two-dimensional multiscale model of angiogenesis, the process by which endothelial cells (ECs) migrate from a pre-existing vascular bed in response to local environmental cues and cell-cell interactions, to create a new vascular network. Recent experimental studies have highlighted a central role of cell rearrangements in the formation of angiogenic networks. Our model accounts for this phenomenon via the heterogeneous response of ECs to their microenvironment. These cell rearrangements, in turn, dynamically remodel the local environment. The model reproduces characteristic features of angiogenic sprouting that include branching, chemotactic sensitivity, the brush border effect, and cell mixing. These properties, rather than being hardwired into the model, emerge naturally from the gene expression patterns of individual cells. After calibrating and validating our model against experimental data, we use it to predict how the structure of the vascular network changes as the baseline gene expression levels of the VEGF-Delta-Notch pathway, and the composition of the extracellular environment, vary. In order to investigate the impact of cell rearrangements on the vascular network structure, we introduce the mixing measure, a scalar metric that quantifies cell mixing as the vascular network grows. We calculate the mixing measure for the simulated vascular networks generated by ECs of different lineages (wild type cells and mutant cells with impaired expression of a specific receptor). Our results show that the time evolution of the mixing measure is directly correlated to the generic features of the vascular branching pattern, thus, supporting the hypothesis that cell rearrangements play an essential role in sprouting angiogenesis. Furthermore, we predict that lower cell rearrangement leads to an imbalance between branching and sprout elongation. Since the computation of this statistic requires only individual cell trajectories, it can be computed for networks generated in biological experiments, making it a potential biomarker for pathological angiogenesis.

Topological data analysis distinguishes parameter regimes in the Anderson-Chaplain model of angiogenesis

“…The tumor is not explicitly modeled in the Anderson-Chaplain model, but many studies couple angiogenesis and tumor growth [ 25 , 27 , 29 , 72 , 73 ]. More complex models have been developed that account for mechanical factors such as mechanotaxis, pressure-driven convective transport of extracellular factors, mechanical stimulation of endothelial cell proliferation, and subcellular signalling pathways that guide cell fate specification of tip and stalk cells [ 26 , 27 , 29 , 74 ]. For example, Vavourakis et al developed a 3D model of angiogenic tumor growth that incorporates the effects of mechanotaxis on vessel sprouting and mechano-sensitive vascular remodelling [ 29 ].…”

“…While more detailed theoretical models have been developed (see reviews [21][22][23][24]), we focus on the Anderson-Chaplain model due to its simplicity and wide adoption in the mathematical biology literature. The methods presented in this work can also be used to study alternative models of angiogenesis, such as the phase-field model presented in [25], the 2D model of early angiogenesis and cell fate specification in [26], the 3D hybrid model presented in [27], and multiscale models of vascular tumor growth, such as those presented in [28][29][30][31].…”

The role of calcium oscillations in the phenotype selection in endothelial cells

“…Stable configurations in EC phenotypes are usually distinguished by a specific gene expression of DLL4 25 , 37 . Here, we follow the same logic and consider DLL4 concentration as the sole determiner of expression of the tip cell phenotype.…”

Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data

“…In Stepanova et al [ 77 ], a multiscale cellular automaton model for angiogenesis was developed and compared to experimental data using the displacement, orientation, and directionality of endothelial cells across multiple concentrations of VEGF. The displacement, orientation, and directionality of endothelial cells was calculated in the model and compared with experimental values from longitudinal confocal microscopy images collected every 15 min for 36 h, under concentrations of 0 ng/mL, 5 ng/mL, and 50 ng/mL of VEGF.…”